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Determinants Class 11 Commerce Maths 1 Chapter 6 Exercise 6.2 Answers Maharashtra Board

Balbharati Maharashtra State Board 11th Commerce Maths Solution Book Pdf Chapter 6 Determinants Ex 6.2 Questions and Answers.

Std 11 Maths 1 Exercise 6.2 Solutions Commerce Maths

Question 1.
Without expanding, evaluate the following determinants.
(i) \(\left|\begin{array}{lll}
1 & a & b+c \\
1 & b & c+a \\
1 & c & a+b
\end{array}\right|\)
Solution:

(ii) \(\left|\begin{array}{ccc}
2 & 3 & 4 \\
5 & 6 & 8 \\
6 x & 9 x & 12 x
\end{array}\right|\)
Solution:

(iii) \(\left|\begin{array}{lll}
2 & 7 & 65 \\
3 & 8 & 75 \\
5 & 9 & 86
\end{array}\right|\)
Solution:

Question 2.
Using properties of determinants, show that \(\left|\begin{array}{ccc}
a+b & a & b \\
a & a+c & c \\
b & c & b+c
\end{array}\right|\) = 4abc
Solution:

Question 3.
Solve the following equation.
\(\left|\begin{array}{ccc}
x+2 & x+6 & x-1 \\
x+6 & x-1 & x+2 \\
x-1 & x+2 & x+6
\end{array}\right|=0\)
Solution:
\(\left|\begin{array}{ccc}
x+2 & x+6 & x-1 \\
x+6 & x-1 & x+2 \\
x-1 & x+2 & x+6
\end{array}\right|=0\)
Applying R₂ → R₂ – R₁ and R₃ → R₃ – R₁, we get
\(\left|\begin{array}{ccc}
x+2 & x+6 & x-1 \\
4 & -7 & 3 \\
-3 & -4 & 7
\end{array}\right|=0\)
∴ (x + 2)(-49 + 12) – (x + 6)(28 + 9) + (x – 1)(-16 – 21) = 0
∴ (x + 2) (-37) – (x + 6) (37) + (x – 1) (-37) = 0
∴ -37(x + 2 + x + 6 + x – 1) = 0
∴ 3x + 7 = 0
∴ x = \(\frac{-7}{3}\)

Question 4.
If \(\left|\begin{array}{lll}
4+x & 4-x & 4-x \\
4-x & 4+x & 4-x \\
4-x & 4-x & 4+x
\end{array}\right|=0\), then find the values of x.
Solution:

∴ (12 – x)[1(4x² – 0) – (4 – x)(0 – 0) + (4 – x)(0 – 0)] = 0
∴ (12 – x)(4x²) = 0
∴ x²(12 – x) = 0
∴ x = 0 or 12 – x = 0
∴ x = 0 or x = 12

Question 5.
Without expanding determinants, show that
\(\left|\begin{array}{ccc}
1 & 3 & 6 \\
6 & 1 & 4 \\
3 & 7 & 12
\end{array}\right|+4\left|\begin{array}{lll}
2 & 3 & 3 \\
2 & 1 & 2 \\
1 & 7 & 6
\end{array}\right|=10\left|\begin{array}{lll}
1 & 2 & 1 \\
3 & 1 & 7 \\
3 & 2 & 6
\end{array}\right|\)
Solution:

Question 6.
Without expanding determinants, find the value of
(i) \(\left|\begin{array}{lll}
10 & 57 & 107 \\
12 & 64 & 124 \\
15 & 78 & 153
\end{array}\right|\)
Solution:

(ii) \(\left|\begin{array}{lll}
2014 & 2017 & 1 \\
2020 & 2023 & 1 \\
2023 & 2026 & 1
\end{array}\right|\)
Solution:

Question 7.
Without expanding determinants, prove that
(i) \(\left|\begin{array}{lll}
a_{1} & b_{1} & c_{1} \\
a_{2} & b_{2} & c_{2} \\
a_{3} & b_{3} & c_{3}
\end{array}\right|=\left|\begin{array}{lll}
b_{1} & c_{1} & a_{1} \\
b_{2} & c_{2} & a_{2} \\
b_{3} & c_{3} & a_{3}
\end{array}\right|=\left|\begin{array}{lll}
c_{1} & a_{1} & b_{1} \\
c_{2} & a_{2} & b_{2} \\
c_{3} & a_{3} & b_{3}
\end{array}\right|\)
Solution:

(ii) \(\left|\begin{array}{lll}
1 & y z & y+z \\
1 & z x & z+x \\
1 & x y & x+y
\end{array}\right|=\left|\begin{array}{lll}
1 & x & x^{2} \\
1 & y & y^{2} \\
1 & z & z^{2}
\end{array}\right|\)
Solution:

In 1st determinant, taking (x + y + z) common from C₃ and in 2nd determinant, taking \(\frac{1}{x}, \frac{1}{y}, \frac{1}{z}\) common from R₁, R₂, R₃ respectively, we get

11th Commerce Maths Digest Pdf

• 11th Commerce Maths Exercise 6.1 Solutions
• 11th Commerce Maths Exercise 6.2 Solutions
• 11th Commerce Maths Exercise 6.3 Solutions
• 11th Commerce Maths Miscellaneous Exercise 6 Solutions

Functions Class 11 Commerce Maths 1 Chapter 2 Exercise 2.1 Answers Maharashtra Board

Balbharati Maharashtra State Board 11th Commerce Maths Solution Book Pdf Chapter 2 Functions Ex 2.1 Questions and Answers.

Std 11 Maths 1 Exercise 2.1 Solutions Commerce Maths

Question 1.
Check if the following relations are functions.


Solution:
(a) Yes
Reason: Every element of set A has been assigned a unique element in set B.

(b) No
Reason: An element of set A has been assigned more than one element from set B.

(c) No
Reason: Not every element of set A has been assigned an image from set B.

Question 2.
Which sets of ordered pairs represent functions from A = {1, 2, 3, 4} to B = {-1, 0, 1, 2, 3}? Justify.
(i) {(1, 0), (3, 3), (2, -1), (4, 1), (2, 2)}
(ii) {(1, 2), (2, -1), (3, 1), (4, 3)}
(iii) {(1, 3), (4, 1), (2, 2)}
(iv) {(1, 1), (2, 1), (3, 1), (4, 1)}
Solution:
(i) {(1, 0), (3, 3), (2, -1), (4, 1), (2, 2)} does not represent a function.
Reason: (2, -1) and (2, 2) show that element 2 ∈ A has been assigned two images -1 and 2 from set B.

(ii) {(1, 2), (2, -1), (3, 1), (4, 3)} represents a function.
Reason: Every element of set A has a unique image in set B.

(iii) {(1, 3), (4, 1), (2, 2)} does not represent a function.
Reason: 3 ∈ A does not have an image in set B.

(iv) {(1, 1), (2, 1), (3, 1), (4, 1)} represents a function
Reason: Every element of set A has been assigned a unique image in set B.

Question 3.
If f(m) = m² – 3m + 1, find
(i) f(0)
(ii) f(-3)
(iii) f(\(\frac{1}{2}\))
(iv) f(x + 1)
(v) f(-x)
Solution:
f(m) = m² – 3m + 1
(i) f(0) = 0² – 3(0) + 1 = 1

(ii) f(-3) = (-3)² – 3(-3) + 1
= 9 + 9 + 1
= 19

(iii) \(f\left(\frac{1}{2}\right)=\left(\frac{1}{2}\right)^{2}-3\left(\frac{1}{2}\right)+1\)
= \(\frac{1}{4}-\frac{3}{2}+1\)
= \(\frac{1-6+4}{4}\)
= \(-\frac{1}{4}\)

(iv) f(x + 1) = (x + 1)² – 3(x + 1) + 1
= x² + 2x + 1 – 3x – 3 + 1
= x² – x – 1

(v) f(-x) = (-x)² – 3(-x) + 1 = x² + 3x + 1

Question 4.
Find x, if g(x) = 0 where
(i) g(x) = \(\frac{5 x-6}{7}\)
(ii) g(x) = \(\frac{18-2 x^{2}}{7}\)
(iii) g(x) = 6x² + x – 2
Solution:
(i) g(x) = \(\frac{5 x-6}{7}\)
g(x) = 0
∴ \(\frac{5 x-6}{7}\) = 0
∴ 5x – 6 = 0
∴ x = \(\frac{6}{5}\)

(ii) g(x) = \(\frac{18-2 x^{2}}{7}\)
g(x) = 0
∴ \(\frac{18-2 x^{2}}{7}\) = 0
∴ 18 – 2x² = 0
∴ x² = 9
∴ x = ±3

(iii) g(x) = 6x² + x – 2
g(x) = 0
∴ 6x² + x – 2 = 0
∴ 6x² + 4x – 3x – 2 = 0
∴ 2x(3x + 2) – 1(3x + 2) = 0
∴ (2x – 1)(3x + 2) = 0
∴ 2x – 1 = 0 or 3x + 2 = 0
∴ x = \(\frac{1}{2}\) or x = \(\frac{-2}{3}\)

Question 5.
Find x, if f(x) = g(x) where f(x) = x⁴ + 2x², g(x) = 11x².
Solution:
f(x) = x⁴ + 2x², g(x) = 11x²
f(x) = g(x)
∴ x⁴ + 2x² = 11x²
∴ x⁴ – 9x² = 0
∴ x²(x² – 9) = 0
∴ x² = 0 or x² – 9 = 0
∴ x = 0 or x² = 9
∴ x = 0 or x = ±3

Question 6.
If f(x) = \(\begin{cases}x^{2}+3, & x \leq 2 \\ 5 x+7, & x>2\end{cases}\), then find
(i) f(3)
(ii) f(2)
(iii) f(0)
Solution:
f(x) = x² + 3, x ≤ 2
= 5x + 7, x > 2
(i) f(3) = 5(3) + 7 = 15 + 7 = 22
(ii) f(2) = 2² + 3 = 4 + 3 = 7
(iii) f(0) = 0² + 3 = 3

Question 7.
If f(x) = \(\left\{\begin{array}{cl}
4 x-2, & x \leq-3 \\
5, & -3<x<3 \\
x^{2}, & x \geq 3
\end{array}\right.\), then fmd
(i) f(-4)
(ii) f(-3)
(iii) f(1)
(iv) f(5)
Solution:
f(x) = 4x – 2, x ≤ -3
= 5, -3 < x < 3
= x², x ≥ 3
(i) f(-4) = 4(-4) – 2 = -16 – 2 = -18
(ii) f(-3) = 4(-3) – 2 = -12 – 2 = -14
(iii) f(1) = 5
(iv) f(5) = 5² = 25

Question 8.
If f(x) = 3x + 5, g(x) = 6x – 1, then find
(i) (f + g)(x)
(ii) (f – g)(2)
(iii) (fg)(3)
(iv) \(\left(\frac{\mathbf{f}}{\mathbf{g}}\right)(x)\) and its domain
Solution:
f(x) = 3x + 5, g(x) = 6x – 1
(i) (f + g)(x) = f(x) + g(x)
= 3x + 5 + 6x – 1
= 9x + 4

(ii) (f – g) (2) = f(2) – g(2)
= [3(2) + 5] – [6(2) – 1]
= 6 + 5 – 12 + 1
= 0

(iii) (fg)(3) = f(3) g(3)
= [3(3) + 5] [6(3) – 1]
= (14) (17)
= 238

(iv) \(\left(\frac{\mathrm{f}}{\mathrm{g}}\right) x=\frac{\mathrm{f}(x)}{\mathrm{g}(x)}=\frac{3 x+5}{6 x-1}, x \neq \frac{1}{6}\)
Domain = R – {\(\frac{1}{6}\)}

Question 9.
If f(x) = 2x² + 3, g(x) = 5x – 2, then find
(i) fog
(ii) gof
(iii) fof
(iv) gog
Solution:
f(x) = 2x² + 3, g(x) = 5x – 2
(i) (fog)(x) = f(g(x))
= f(5x – 2)
= 2(5x – 2)² + 3
= 2(25x² – 20x + 4) + 3
= 50x² – 40x + 8 + 3
= 50x² – 40x + 11

(ii) (gof)(x) = g(f(x))
= g(2x² + 3)
= 5(2x² + 3) – 2
= 10x² + 15 – 2
= 10x² + 13

(iii) (fof)(x) = f(f(x))
= f(2x² + 3)
= 2(2x² + 3)² + 3
= 2(4x⁴ + 12x² + 9) + 3
= 8x⁴ + 24x² + 18 + 3
= 8x⁴ + 24x² + 21

(iv) (gog)(x) = g(g(x))
= g(5x – 2)
= 5(5x – 2) – 2
= 25x – 10 – 2
= 25x – 12

11th Commerce Maths Digest Pdf

• 11th Commerce Maths Exercise 2.1 Solutions
• 11th Commerce Maths Miscellaneous Exercise 2 Solutions

Limits Class 11 Commerce Maths 1 Chapter 7 Exercise 7.4 Answers Maharashtra Board

Balbharati Maharashtra State Board 11th Commerce Maths Solution Book Pdf Chapter 7 Limits Ex 7.4 Questions and Answers.

Std 11 Maths 1 Exercise 7.4 Solutions Commerce Maths

I. Evaluate the following:

Question 1.
\(\lim _{x \rightarrow 0}\left[\frac{9^{x}-5^{x}}{4^{x}-1}\right]\)
Solution:

Question 2.
\(\lim _{x \rightarrow 0}\left[\frac{5^{x}+3^{x}-2^{x}-1}{x}\right]\)
Solution:

Question 3.
\(\lim _{x \rightarrow 0}\left[\frac{\log (2+x)-\log (2-x)}{x}\right]\)
Solution:

II. Evaluate the following:

Question 1.
\(\lim _{x \rightarrow 0}\left[\frac{3^{x}+3^{-x}-2}{x^{2}}\right]\)
Solution:

Question 2.
\(\lim _{x \rightarrow 0}\left[\frac{3+x}{3-x}\right]^{\frac{1}{x}}\)
Solution:

Question 3.
\(\lim _{x \rightarrow 0}\left[\frac{\log (3-x)-\log (3+x)}{x}\right]\)
Solution:

III. Evaluate the following:

Question 1.
\(\lim _{x \rightarrow 0}\left[\frac{a^{3 x}-b^{2 x}}{\log (1+4 x)}\right]\)
Solution:

Question 2.
\(\lim _{x \rightarrow 0}\left[\frac{\left(2^{x}-1\right)^{2}}{\left(3^{x}-1\right) \cdot \log (1+x)}\right]\)
Solution:

Question 3.
\(\lim _{x \rightarrow 0}\left[\frac{15^{x}-5^{x}-3^{x}+1}{x^{2}}\right]\)
Solution:

Question 4.
\(\lim _{x \rightarrow 2}\left[\frac{3^{\frac{x}{2}}-3}{3^{x}-9}\right]\)
Solution:

IV. Evaluate the following:

Question 1.
\(\lim _{x \rightarrow 0}\left[\frac{(25)^{x}-2(5)^{x}+1}{x^{2}}\right]\)
Solution:

Question 2.
\(\lim _{x \rightarrow 0}\left[\frac{(49)^{x}-2(35)^{x}+(25)^{x}}{x^{2}}\right]\)
Solution:

11th Commerce Maths Digest Pdf

• 11th Commerce Maths Exercise 7.1 Solutions
• 11th Commerce Maths Exercise 7.2 Solutions
• 11th Commerce Maths Exercise 7.3 Solutions
• 11th Commerce Maths Exercise 7.4 Solutions
• 11th Commerce Maths Miscellaneous Exercise 7 Solutions

Sets and Relations Class 11 Commerce Maths 1 Chapter 1 Miscellaneous Exercise 1 Answers Maharashtra Board

Balbharati Maharashtra State Board 11th Commerce Maths Solution Book Pdf Chapter 1 Sets and Relations Miscellaneous Exercise 1 Questions and Answers.

Std 11 Maths 1 Miscellaneous Exercise 1 Solutions Commerce Maths

Question 1.
Write the following sets in set builder form:
(i) {10, 20, 30, 40, 50}
(ii) {a, e, i, o, u}
(iii) {Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday}
Solution:
(i) Let A = {10, 20, 30, 40, 50}
∴ A = {x / x = 10n, n ∈ N and n ≤ 5}

(ii) Let B = {a, e, i, o, u}
∴ B = {x / x is a vowel of English alphabets}

(iii) Let C = {Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday}
∴ C = {x / x represents days of a week}

Question 2.
If U = {x / x ∈ N, 1 ≤ x ≤ 12}, A = {1, 4, 7, 10}, B = {2, 4, 6, 7, 11}, C = {3, 5, 8, 9, 12}.
Write the sets
(i) A ∪ B
(ii) B ∩ C
(iii) A – B
(iv) B – C
(v) A ∪ B ∪ C
(vi) A ∩ (B ∪ C)
Solution:
U = {x / x ∈ N, 1 ≤ x ≤ 12} = {1, 2, 3, …., 12}
A = {1, 4, 7, 10}, B = {2, 4, 6, 7, 11}, C = {3, 5, 8, 9, 12}
(i) A ∪ B = {1, 2, 4, 6, 7, 10, 11}

(ii) B ∩ C = { }

(iii) A – B = {1, 10}

(iv) B – C = {2, 4, 6, 7, 11}

(v) A ∪ B ∪ C = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}

(vi) B ∪ C = {2, 3, 4, 5, 6, 7, 8, 9, 11, 12}
∴ A ∩ (B ∪ C) = {4, 7}

Question 3.
In a survey of 425 students in a school, it was found that 115 drink apple juice, 160 drink orange juice, and 80 drink both apple as well as orange juice. How many drinks neither apple juice nor orange juice?
Solution:
Let A = set of students who drink apple juice
B = set of students who drink orange juice
X = set of all students
∴ n(X) = 425, n(A) = 115, n(B) = 160, n(A ∩ B) = 80

No. of students who neither drink apple juice nor orange juice
n(A’ ∩ B’) = n(A ∪ B)’
= n(X) – n(A ∪ B)
= 425 – [n(A) + n(B) – n(A ∩ B)]
= 425 – (115 + 160 – 80)
= 230

Question 4.
In a school, there are 20 teachers who teach Mathematics or Physics. of these, 12 teach Mathematics and 4 teach both Physics and Mathematics. How many teachers teach Physics?
Solution:
Let A = set of teachers who teach Mathematics
B = set of teachers who teach Physics
n(A ∪ B) = 20, n(A) = 12, n(A ∩ B) = 4

Since, n(A ∪ B) = n(A) + n(B) – n(A ∩ B)
∴ 20 = 12 + n(B) – 4
∴ n(B) = 12
∴ Number of teachers who teach physics = 12

Question 5.
(i) If A = {1, 2, 3} and B = {2, 4}, state the elements of A × A, A × B, B × A, B × B, (A × B) ∩ (B × A).
(ii) If A = {-1, 1}, find A × A × A.
Solution:
(i) A = {1, 2, 3} and B = {2, 4}
A × A = {(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (3, 3)}
A × B = {(1, 2), (1, 4), (2, 2), (2, 4), (3, 2), (3, 4)}
B × A = {(2, 1), (2, 2), (2, 3), (4, 1), (4, 2), (4, 3)}
B × B = {(2, 2), (2, 4), (4, 2), (4, 4)}
(A × B) ∩ (B × A) = {(2, 2)}

(ii) A = {-1, 1}
∴ A × A × A = {(-1, -1, -1), (-1, -1, 1), (-1, 1, -1), (-1, 1, 1), (1, -1, -1), (1, -1, 1), (1, 1, -1),(1, 1, 1)}

Question 6.
If A = {1, 2, 3}, B = {4, 5, 6}, which of the following are relations from A to B.
(i) R₁ = {(1, 4), (1, 5), (1, 6)}
(ii) R₂ = {(1, 5), (2, 4), (3, 6)}
(iii) R₃ = {(1, 4), (1, 5), (3, 6), (2, 6), (3, 4)}
(iv) R₄ = {(4, 2), (2, 6), (5, 1), (2, 4)}
Solution:
A = {1, 2, 3}, B = {4, 5, 6}
∴ A × B = {(1, 4), (1, 5), (1, 6), (2, 4), (2, 5), (2, 6), (3, 4), (3, 5), (3, 6)}
(i) R₁ = {(1, 4), (1, 5), (1, 6)}
Since, R₁ ⊆ A × B
∴ R₁ is a relation from A to B.

(ii) R₂ = {(1, 5), (2, 4), (3, 6)}
Since, R₂ ⊆ A × B
∴ R₂ is a relation from A to B.

(iii) R₃ = {(1, 4), (1, 5), (3, 6), (2, 6), (3, 4)}
Since, R₃ ⊆ A × B
∴ R₃ is a relation from A to B.

(iv) R₄ = {(4,2), (2, 6), (5,1), (2, 4)}
Since, (4, 2) ∈ R₄, but (4, 2) ∉ A × B
∴ R₄ ⊄ A × B
∴ R₄ is not a relation from A to B.

Question 7.
Determine the domain and range of the following relation.
R = {(a, b) / a ∈ N, a < 5, b = 4}
Solution:
R = {(a, b) / a ∈ N, a < 5, b = 4}
∴ Domain (R) = {a / a ∈ N, a < 5} = {1, 2, 3, 4}
Range (R) = {b / b = 4} = {4}

11th Commerce Maths Digest Pdf

• 11th Commerce Maths Exercise 1.1 Solutions
• 11th Commerce Maths Exercise 1.2 Solutions
• 11th Commerce Maths Miscellaneous Exercise 1 Solutions

Limits Class 11 Commerce Maths 1 Chapter 7 Exercise 7.3 Answers Maharashtra Board

Balbharati Maharashtra State Board 11th Commerce Maths Solution Book Pdf Chapter 7 Limits Ex 7.3 Questions and Answers.

Std 11 Maths 1 Exercise 7.3 Solutions Commerce Maths

I. Evaluate the following limits:

Question 1.
\(\lim _{x \rightarrow 0}\left[\frac{\sqrt{6+x+x^{2}}-\sqrt{6}}{x}\right]\)
Solution:

Question 2.
\(\lim _{y \rightarrow 0}\left[\frac{\sqrt{1-y^{2}}-\sqrt{1+y^{2}}}{y^{2}}\right]\)
Solution:

Question 3.
\(\lim _{x \rightarrow 2}\left[\frac{\sqrt{2+x}-\sqrt{6-x}}{\sqrt{x}-\sqrt{2}}\right]\)
Solution:

II. Evaluate the following limits:

Question 1.
\(\lim _{x \rightarrow a}\left[\frac{\sqrt{a+2 x}-\sqrt{3 x}}{\sqrt{3 a+x}-2 \sqrt{x}}\right]\)
Solution:

Question 2.
\(\lim _{x \rightarrow 2}\left[\frac{x^{2}-4}{\sqrt{x+2}-\sqrt{3 x-2}}\right]\)
Solution:

III. Evaluate the following limits:

Question 1.
\(\lim _{x \rightarrow 1}\left[\frac{x^{2}+x \sqrt{x}-2}{x-1}\right]\)
Solution:

Question 2.
\(\lim _{x \rightarrow 0}\left[\frac{\sqrt{1+x^{2}}-\sqrt{1+x}}{\sqrt{1+x^{3}}-\sqrt{1+x}}\right]\)
Solution:

Question 3.
\(\lim _{x \rightarrow 4}\left[\frac{x^{2}+x-20}{\sqrt{3 x+4}-4}\right]\)
Solution:

Question 4.
\(\lim _{x \rightarrow 2}\left[\frac{x^{3}-8}{\sqrt{x+2}-\sqrt{3 x-2}}\right]\)
Solution:

IV. Evaluate the following limits:

Question 1.
\(\lim _{y \rightarrow 2}\left[\frac{2-y}{\sqrt{3-y}-1}\right]\)
Solution:

Question 2.
\(\lim _{z \rightarrow 4}\left[\frac{3-\sqrt{5+z}}{1-\sqrt{5-z}}\right]\)
Solution:

11th Commerce Maths Digest Pdf

• 11th Commerce Maths Exercise 7.1 Solutions
• 11th Commerce Maths Exercise 7.2 Solutions
• 11th Commerce Maths Exercise 7.3 Solutions
• 11th Commerce Maths Exercise 7.4 Solutions
• 11th Commerce Maths Miscellaneous Exercise 7 Solutions

Sets and Relations Class 11 Commerce Maths 1 Chapter 1 Exercise 1.2 Answers Maharashtra Board

Balbharati Maharashtra State Board 11th Commerce Maths Solution Book Pdf Chapter 1 Sets and Relations Ex 1.2 Questions and Answers.

Std 11 Maths 1 Exercise 1.2 Solutions Commerce Maths

Question 1.
If (x – 1, y + 4) = (1, 2), find the values of x and y.
Solution:
(x – 1, y + 4) = (1, 2)
By the definition of equality of ordered pairs, we have
x – 1 = 1 and y + 4 = 2
∴ x = 2 and y = -2

Question 2.
If \(\left(x+\frac{1}{3}, \frac{y}{3}-1\right)=\left(\frac{1}{3}, \frac{3}{2}\right)\), find x and y.
Solution:
\(\left(x+\frac{1}{3}, \frac{y}{3}-1\right)=\left(\frac{1}{3}, \frac{3}{2}\right)\)
By the definition of equality of ordered pairs, we have
\(x+\frac{1}{3}=\frac{1}{3}\) and \(\frac{y}{3}-1=\frac{3}{2}\)
\(x=\frac{1}{3}-\frac{1}{3}\) and \(\frac{y}{3}=\frac{3}{2}+1=\frac{5}{2}\)
x = 0 and y = \(\frac{15}{2}\)

Question 3.
If A = {a, b, c}, B = {x, y}, find A × B, B × A, A × A, B × B.
Solution:
A = {a, b, c}, B = {x, y}
A × B = {(a, x), (a, y), (b, x), (b, y), (c, x), (c, y)}
B × A = {(x, a), (x, b), (x, c), (y, a), (y, b), (y, c)}
A × A = {(a, a), (a, b), (a, c), (b, a), (b, b), (b, c), (c, a), (c, b), (c, c)}
B × B = {(x, x), (x, y), (y, x), (y, y)}

Question 4.
If P = {1, 2, 3} and Q = {6, 4}, find the sets P × Q and Q × P.
Solution:
P = {1, 2, 3}, Q = {6, 4}
P × Q = {(1, 6), (1, 4), (2, 6), (2, 4), (3, 6), (3, 4)}
Q × P = {(6, 1), (6, 2), (6, 3), (4, 1), (4, 2), (4, 3)}

Question 5.
Let A = {1, 2, 3, 4}, B = {4, 5, 6}, C = {5, 6}. Find
(i) A × (B ∩ C)
(ii) (A × B) ∩ (A × C)
(iii) A × (B ∪ C)
(iv) (A × B) ∪ (A × C)
Solution:
A= {1, 2, 3, 4}, B = {4, 5, 6}, C = {5, 6}
(i) B ∩ C = {5, 6}
∴ A × (B ∩ C) = {(1, 5), (1, 6), (2, 5), (2, 6), (3, 5), (3, 6), (4, 5), (4, 6)}

(ii) A × B = {(1, 4), (1, 5), (1, 6), (2, 4), (2, 5), (2, 6), (3, 4), (3, 5), (3, 6), (4, 4), (4, 5), (4, 6)}
A × C = {(1, 5), (1, 6), (2, 5), (2, 6), (3, 5), (3, 6), (4, 5), (4, 6)}
∴ (A × B) ∩ (A × C) = {(1, 5), (1, 6), (2, 5), (2, 6), (3, 5), (3, 6), (4, 5), (4, 6)}

(iii) B ∪ C = {4, 5, 6}
∴ A × (B ∪ C) = {(1, 4), (1, 5), (1, 6), (2, 4), (2, 5), (2, 6), (3, 4), (3, 5), (3, 6), (4, 4), (4, 5), (4, 6)}

(iv) A × B = {(1, 4), (1, 5), (1, 6), (2, 4), (2, 5), (2, 6), (3, 4), (3, 5), (3, 6), (4, 4), (4, 5), (4, 6)}
A × C = {(1, 5), (1, 6), (2, 5), (2, 6), (3, 5), (3, 6), (4, 5), (4, 6)}
∴ (A × B) ∪ (A × C) = {(1, 4), (1, 5), (1, 6), (2, 4), (2, 5), (2, 6), (3, 4), (3, 5), (3, 6), (4, 4), (4, 5), (4, 6)}

Question 6.
Express {(x, y) / x² + y² = 100, where x, y ∈ W} as a set of ordered pairs.
Solution:
{(x, y) / x² + y² = 100, where x, y ∈ W}
We have, x² + y² = 100
When x = 0 and y = 10,
x² + y² = 0² + 10² = 100
When x = 6 andy = 8,
x² + y² = 6² + 8² = 100
When x = 8 and y = 6,
x² + y² = 8² + 6² = 100
When x = 10 and y = 0,
x² + y² = 10² + 0² = 100
∴ Set of ordered pairs = {(0, 10), (6, 8), (8, 6), (10, 0)}

Question 7.
Write the domain and range of the following relations.
(i) {(a, b) / a ∈ N, a < 6 and b = 4}
(ii) {(a, b) / a, b ∈ N, a + b = 12}
(iii) {(2, 4), (2, 5), (2, 6), (2, 7)}
Solution:
(i) Let R₁ = {(a, b)/ a ∈ N, a < 6 and b = 4}
Set of values of ‘a’ are domain and set of values of ‘b’ are range.
a ∈ N and a < 6
∴ a = 1, 2, 3, 4, 5 and b = 4
Domain (R₁) = {1, 2, 3, 4, 5}
Range (R₁) = {4}

(ii) Let R₂ = {(a, b)/a, b ∈ N and a + b = 12}
Now, a, b ∈ N and a + b = 12
When a = 1, b = 11
When a = 2, b = 10
When a = 3, b = 9
When a = 4, b = 8
When a = 5, b = 7
When a = 6, b = 6
When a = 7, b = 5
When a = 8, b = 4
When a = 9, b = 3
When a = 10, b = 2
When a = 11, b = 1
∴ Domain (R₂) = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}
Range (R₂) = {11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1}

(iii) Let R₃ = {(2, 4), (2, 5), (2, 6), (2, 7)}
Domain (R₃) = {2}
Range (R₃) = {4, 5, 6, 7}

Question 8.
Let A = {6, 8} and B = {1, 3, 5}.
Let R = {(a, b) / a ∈ A, b ∈ B, a – b is an even number}.
Show that R is an empty relation from A to B.
Solution:
A= {6, 8}, B = {1, 3, 5}
R = {(a, b)/ a ∈ A, b ∈ B, a – b is an even number}
a ∈ A
∴ a = 6, 8
b ∈ B
∴ b = 1, 3, 5
When a = 6 and b = 1, a – b = 5 which is odd
When a = 6 and b = 3, a – b = 3 which is odd
When a = 6 and b = 5, a – b = 1 which is odd
When a = 8 and b = 1, a – b = 7 which is odd
When a = 8 and b = 3, a – b = 5 which is odd
When a = 8 and b = 5, a – b = 3 which is odd
Thus, no set of values of a and b gives a – b even.
∴ R is an empty relation from A to B.

Question 9.
Write the relation in the Roster form and hence find its domain and range.
(i) R₁ = {(a, a²) / a is a prime number less than 15}
(ii) R₂ = {(a, \(\frac{1}{a}\)) / 0 < a ≤ 5, a ∈ N}
Solution:
(i) R₁ = {(a, a²) / a is a prime number less than 15}
∴ a = 2, 3, 5, 7, 11, 13
∴ a2 = 4, 9, 25, 49, 121, 169
∴ R₁ = {(2, 4), (3, 9), (5, 25), (7, 49), (11, 121), (13, 169)}
∴ Domain (R₁) = {a/a is a prime number less than 15} = {2, 3, 5, 7, 11, 13}
Range (R₁) = {a²/a is a prime number less than 15} = {4, 9, 25, 49, 121, 169}

Question 10.
R = {(a, b) / b = a + 1, a ∈ Z, 0 < a < 5}. Find the range of R.
Solution:
R = {(a, b) / b = a + 1, a ∈ Z, 0 < a < 5}
∴ a = 1, 2, 3, 4
∴ b = 2, 3, 4, 5
∴ Range (R) = {2, 3, 4, 5}

Question 11.
Find the following relations as sets of ordered pairs.
(i) {(x, y) / y = 3x, x ∈ {1, 2, 3}, y ∈ {3, 6, 9, 12}}
(ii) {(x,y) / y > x + 1, x ∈ {1, 2} and y ∈ {2, 4, 6}}
(iii) {(x, y) / x + y = 3, x, y ∈ {0, 1, 2, 3}}
Solution:
(i) {(x, y) / y = 3x, x ∈ {1, 2, 3}, y ∈ {3, 6, 9, 12}}
Here y = 3x
When x = 1, y = 3(1) = 3
When x = 2, y = 3(2) = 6
When x = 3, y = 3(3) = 9
∴ Ordered pairs are {(1, 3), (2, 6), (3, 9)}

(ii) {(x, y) / y > x + 1, x ∈ {1, 2} and y ∈ {2, 4, 6}}
Here, y > x + 1
When x = 1 and y = 2, 2 ≯ 1 + 1
When x = 1 and y = 4, 4 > 1 + 1
When x = 1 and y = 6, 6 > 1 + 1
When x = 2 and y = 2, 2 ≯ 2 + 1
When x = 2 and y = 4, 4 > 2 + 1
When x = 2 and y = 6, 6 > 2 + 1
∴ Ordered pairs are {(1, 4), (1, 6), (2, 4), (2, 6)}

(iii) {(x, y) / x + y = 3, x, y ∈ {0, 1, 2, 3}}
Here, x + y = 3
When x = 0, y = 3
When x = 1, y = 2
When x = 2, y = 1
When x = 3, y = 0
∴ Ordered pairs are {(0, 3), (1, 2), (2, 1), (3, 0)}

11th Commerce Maths Digest Pdf

• 11th Commerce Maths Exercise 1.1 Solutions
• 11th Commerce Maths Exercise 1.2 Solutions
• 11th Commerce Maths Miscellaneous Exercise 1 Solutions

Differentiation Class 11 Commerce Maths 1 Chapter 9 Exercise 9.2 Answers Maharashtra Board

Balbharati Maharashtra State Board 11th Commerce Maths Solution Book Pdf Chapter 9 Differentiation Ex 9.2 Questions and Answers.

Std 11 Maths 1 Exercise 9.2 Solutions Commerce Maths

I. Differentiate the following functions w.r.t. x.

Question 1.
\(\frac{x}{x+1}\)
Solution:

Question 2.
\(\frac{x^{2}+1}{x}\)
Solution:

Question 3.
\(\frac{1}{e^{x}+1}\)
Solution:

Question 4.
\(\frac{e^{x}}{e^{x}+1}\)
Solution:

Question 5.
\(\frac{x}{\log x}\)
Solution:

Question 6.
\(\frac{2^{x}}{\log x}\)
Solution:

Question 7.
\(\frac{\left(2 e^{x}-1\right)}{\left(2 e^{x}+1\right)}\)
Solution:

Question 8.
\(\frac{(x+1)(x-1)}{\left(e^{x}+1\right)}\)
Solution:

II. Solve the following examples:

Question 1.
The demand D for a price P is given as D = \(\frac{27}{P}\), find the rate of change of demand when the price is 3.
Solution:
Demand, D = \(\frac{27}{P}\)
Rate of change of demand = \(\frac{dD}{dP}\)

When price P = 3,
Rate of change of demand,
\(\left(\frac{\mathrm{dD}}{\mathrm{dP}}\right)_{\mathrm{P}=3}=\frac{-27}{(3)^{2}}=-3\)
∴ When price is 3, Rate of change of demand is -3.

Question 2.
If for a commodity; the price-demand relation is given as D = \(\frac{P+5}{P-1}\). Find the marginal demand when the price is 2.
Solution:

Question 3.
The demand function of a commodity is given as P = 20 + D – D². Find the rate at which price is changing when demand is 3.
Solution:
Given, P = 20 + D – D²
Rate of change of price = \(\frac{dP}{dD}\)
= \(\frac{d}{dD}\)(20 + D – D²)
= 0 + 1 – 2D
= 1 – 2D
Rate of change of price at D = 3 is
\(\left(\frac{\mathrm{dP}}{\mathrm{dD}}\right)_{\mathrm{D}=3}\) = 1 – 2(3) = -5
∴ Price is changing at a rate of -5, when demand is 3.

Question 4.
If the total cost function is given by; C = 5x³ + 7x² + 7; find the average cost and the marginal cost when x = 4.
Solution:
Total cost function, C = 5x³ + 7x² + 7
Average cost = \(\frac{C}{x}\)

When x = 4, Marginal cost = \(\left(\frac{\mathrm{dC}}{\mathrm{d} x}\right)_{x=4}\)
= 15(4)² + 4(4)
= 240 + 16
= 256
∴ the average cost and marginal cost at x = 4 are \(\frac{359}{4}\) and 256 respectively.

Question 5.
The total cost function of producing n notebooks is given by
C = 1500 – 75n + 2n² + \(\frac{n^{3}}{5}\)
Find the marginal cost at n = 10.
Solution:
The total cost function,


∴ Marginal cost at n = 10 is 25.

Question 6.
The total cost of ‘t’ toy cars is given by C = 5(2t) + 17. Find the marginal cost and average cost at t = 3.
Solution:
Total cost of ‘t’ toy cars, C = 5(2t) + 17

∴ at t = 3, the Marginal cost is 40 log 2 and the Average cost is 19.

Question 7.
If for a commodity; the demand function is given by, D = \(\sqrt{75-3 P}\). Find the marginal demand function when P = 5.
Solution:
Demand function, D = \(\sqrt{75-3 P}\)
Now, Marginal demand = \(\frac{dD}{dP}\)

Question 8.
The total cost of producing x units is given by C = 10e^2x, find its marginal cost and average cost when x = 2.
Solution:

Question 9.
The demand function is given as P = 175 + 9D + 25D². Find the revenue, average revenue, and marginal revenue when demand is 10.
Solution:
Given, P = 175 + 9D + 25D²
Total revenue, R = P.D
= (175 + 9D + 25D²)D
= 175D + 9D² + 25D³
Average revenue = P = 175 + 9D + 25D²
Marginal revenue = \(\frac{dR}{dD}\)
= \(\frac{d}{dD}\) (175D + 9D² + 25D³)
= 175 \(\frac{d}{dD}\) (D) + 9 \(\frac{d}{dD}\) (D²) + 25 \(\frac{d}{dD}\) (D³)
= 175(1) + 9(2D) + 25(3D²)
= 175 + 18D + 75D²
When D = 10,
Total revenue = 175(10) + 9(10)² + 25(10)³
= 1750 + 900 + 25000
= 27650
Average revenue = 175 + 9(10) + 25(10)²
= 175 + 90 + 2500
= 2765
Marginal revenue = 175 + 18(10) + 75(10)²
= 175 + 180 + 7500
= 7855
∴ When Demand = 10,
Total revenue = 27650, Average revenue = 2765, Marginal revenue = 7855.

Question 10.
The supply S for a commodity at price P is given by S = P² + 9P – 2. Find the marginal supply when the price is 7.
Solution:
Given, S = P² + 9P – 2

∴ The marginal supply is 23, at P = 7.

Question 11.
The cost of producing x articles is given by C = x² + 15x + 81. Find the average cost and marginal cost functions. Find marginal cost when x = 10. Find x for which the marginal cost equals the average cost.
Solution:
Given, cost C = x² + 15x + 81

If marginal cost = average cost, then
2x + 15 = x + 15 + \(\frac{81}{x}\)
∴ x = \(\frac{81}{x}\)
∴ x² = 81
∴ x = 9 …..[∵ x > 0]

11th Commerce Maths Digest Pdf

• 11th Commerce Maths Exercise 9.1 Solutions
• 11th Commerce Maths Exercise 9.2 Solutions
• 11th Commerce Maths Miscellaneous Exercise 9 Solutions

Company Meetings – II 11th Secretarial Practice Chapter 8 Solutions Maharashtra Board

Balbharti Maharashtra State Board Class 11 Secretarial Practice Solutions Chapter 8 Company Meetings – II Textbook Exercise Questions and Answers.

Class 11 Secretarial Practice Chapter 8 Exercise Solutions

1A. Select the correct answer from the options given below and rewrite the statements.

Question 1.
The secretary has to prepare ____________ before the meeting.
(a) resolution
(b) notice
(c) minutes
Answer:
(b) notice

Question 2.
General Meeting must have a notice of at least ____________ clear days.
(a) 7
(b) 21
(c) 14
Answer:
(b) 21

Question 3.
The gap between two annual general meetings should not be more than months.
(a) 15
(b) 18
(c) 24
Answer:
(a) 15

Question 4.
Auditor is appointed in ____________
(a) Annual General Meeting
(b) Creditors Meeting
(c) Extra ordinary General Meeting
Answer:
(a) Annual General Meeting

Question 5.
The business transacted in extra ordinary general meeting is ____________ business.
(a) Ordinary
(b) Routine
(c) Special
Answer:
(c) Special

Question 6.
An extraordinary general meeting is held ____________
(a) once in a year
(b) once in the life time
(c) under special circumstances
Answer:
(c) under special circumstances

Question 7.
Writing the minutes of meeting is the duty of the ____________
(a) Chairman
(b) Director
(c) Secretary
Answer:
(c) Secretary

Question 8.
New Directors in place of retiring Directors are appointed in the ____________
(a) Class Meeting
(b) Annual General Meeting
(c) Creditors Meeting
Answer:
(b) Annual General Meeting

Question 9.
Before the Annual General Meeting is held the Secretary has to compile ____________
(a) Auditor’s Report
(b) Committee Report
(c) Annual Report
Answer:
(c) Annual Report

Question 10.
The Secretary has to draft the minutes of the meeting within ____________ days of the meeting.
(a) Fifteen
(b) Sixty
(c) Forty
Answer:
(a) Fifteen

1B. Match the pairs.

Question 1.

Group ‘A’	Group ‘B’
(a) Board Meeting	(1) Once in the year
(b) Auditor	(2) Minimum 4 meetings in a year
(c) Annual General Meeting	(3) Prepare at any time
(d) Extraordinary General Meeting	(4) Auditor’s Report
(e) Minutes of Meeting	(5) Prepared before the meeting
	(6) Prepared after the meeting
	(7) Under special circumstance
	(8) Prepared during the meeting
	(9) Once in Six months
	(10) Meeting of creditors

Answer:

Group ‘A’	Group ‘B’
(a) Board Meeting	(2) Minimum 4 meetings in a year
(b) Auditor	(4) Auditor’s Report
(c) Annual General Meeting	(1) Once in the year
(d) Extraordinary General Meeting	(7) Under special circumstance
(e) Minutes of Meeting	(6) Prepared after the meeting

1C. Write a word or a term or a phrase that can substitute each of the following statements.

Question 1.
A meeting of shareholders which is held once a year.
Answer:
Annual General Meeting

Question 2.
A meeting of shareholders is held between two annual general meetings.
Answer:
Extra Ordinary General Meeting

Question 3.
A Report which is prepared before Annual General Meeting.
Answer:
Annual Report

Question 4.
A meeting of the shareholders is held under special circumstances.
Answer:
Extra Ordinary General Meeting

Question 5.
A meeting of the preference shareholders of a company.
Answer:
Class Meeting

1D. State whether the following statements are True or False.

Question 1.
Only special business is transacted at Annual General Meeting.
Answer:
False

Question 2.
Annual Report is prepared by members.
Answer:
False

Question 3.
Extraordinary General Meeting is called for a special and urgent purpose.
Answer:
True

Question 4.
A member has a right to attend a Board meeting.
Answer:
False

Question 5.
A class meeting is the meeting of a particular class of shareholders.
Answer:
True

Question 6.
Director cannot appoint a proxy to attend and vote at the board meetings.
Answer:
True

Question 7.
21 clear days notice should be given in case of Board Meeting.
Answer:
False

Question 8.
Secretary has to arrange to take down the notes of the proceedings of the meeting.
Answer:
True

1E. Find the odd one.

Question 1.
Annual General Meeting, Extra Ordinary General Meeting, Board Meeting.
Answer:
Board Meeting

Question 2.
Annual General Meeting, Committee Meeting, Class Meeting.
Answer:
Committee Meeting

1F. Complete the sentences.

Question 1.
The meeting which is held once in every financial year is called as ____________
Answer:
Annual General Meeting

Question 2.
The meeting held to discuss and decide any special or urgent matters is called as ____________
Answer:
Extra-ordinary General Meeting

Question 3.
Meeting of all Directors is called as ____________
Answer:
Board Meeting

Question 4.
The Authority to convene the Annual General Meeting is with the ____________
Answer:
Board of Directors

1G. Select the correct option from the bracket.

Question 1.

Group ‘A’	Group ‘B’
(1) Interval between two Annual General Meetings	…………………….
(2) First Board Meeting	…………………….
(3) ……………………….	21 clear days
(4) ……………………….	Alteration in Memorandum of Association

(Notice of General Meeting, Extraordinary General Meeting, Not more than 15 months, within 30 days of company’s Incorporation)
Answer:

Group ‘A’	Group ‘B’
(1) Interval between two Annual General Meeting	Not more than 15 months
(2) First Board Meeting	within 30 days of companies Incorporations
(3) Notice of General Meeting	21 clear days
(4) Extraordinary General meeting	Alteration in Memorandum of Association

1H. Answer in one sentence.

Question 1.
Who can attend Board Meetings?
Answer:
Board of Directors attends Board Meetings.

Question 2.
When can an Adjourned Annual General meeting be held?
Answer:
Adjourned Annual General Meeting will be held on the same day, same place and same time in the next week.

Question 3.
Why is Extra-Ordinary General Meeting held?
Answer:
Extra Ordinary General Meeting is held under special circumstances to discuss urgent and important matters.

Question 4.
When should the first Annual General Meeting be held?
Answer:
The first Annual General Meeting must be held within nine (9) months of the closing of the first financial year of the company.

Question 5.
What should be the interval between two Annual General Meetings?
Answer:
The time interval between two Annual General Meetings should not be more than 15 months.

Question 6.
What should be the gap between two Board Meetings?
Answer:
The gap between the two Board Meetings should not be more than 120 days.

1I. Correct the underlined word and rewrite the following sentences.

Question 1.
Minimum four Committee Meetings must be held in a year.
Answer:
Minimum four Directors Meetings must be held in a year.

Question 2.
Creditors Meeting must be held once a year.
Answer:
Annual General Meeting must be held once a year.

Question 3.
Extra Ordinary Meeting must be held every year.
Answer:
Annual General Meeting must be held every year.

Question 4.
The Meeting of all Directors is called Annual General Meeting.
Answer:
The Meeting of all Directors is Called Director’s Meeting.

2. Explain the following terms/concepts.

Question 1.
Committee Meeting
Answer:
The Board of Directors may from the committee and delegate some of its powers to them. This committee should consist of only directors. The delegation of such powers to committees is to be authorized by Articles of Association and should be subject to the provisions of the Companies Act. A meeting of Allotment Committee, Transfer Committee, etc are examples of Committee Meeting.

Question 2.
Virtual Meeting
Answer:
If there is any urgency to call Board Meeting and practically not possible for Directors to attend the meeting in a short notice, so with the help of technology, a virtual meeting can be held. The meetings are recorded and active participation of Directors is also possible through video conferencing. Certain special and confidential matters cannot be dealt with through video conferencing as per the directions of the Central Government.

Question 3.
Creditor’s Meeting
Answer:
Creditors of the company include Debenture holders, Depositors, Banks, and others. The meeting of creditors is called when the company proposes to make a scheme for an arrangement with its creditors.
E.g. In the case of winding up of the company, a meeting of creditors and of contributors is held to ascertain the total amount due by the company and also to appoint a liquidator to wind up the affairs of the company.

3. Study the following case/situation and express your opinion.

1. Platinum Limited Company was incorporated on 1st January 2018. Advice the Board of Directors on the following matters.

Question (a).
Within what period should the company hold its 1st Annual General Meeting?
Answer:
First Annual General Meeting must be held within Nine (9) months of the closing of its financial year.

Question (b).
At which place should the Annual General Meeting be held?
Answer:
Annual General Meeting should be held at the registered office or at some other place within the city or village which the registered office of the company is situated.

Question (c).
How many days in advance should the notice and agenda be sent to members?
Answer:
Notice and Agenda should be sent 21 clear days before the Annual General Meeting.

2. XYZ Ltd held its Annual General Meeting on 11th May 2018. On 1st June Mr. X, a Director of the company was arrested for a financial scam. Hence the shareholders of the company want to remove him.

Question (a).
Can the company call for the next Annual General Meeting to be held immediately to remove the Director?
Answer:
No, the company cannot call the next Annual General Meeting immediately to remove the director.

Question (b).
Which meeting of members should the company hold to discuss the removal of the Director?
Answer:
Extra Ordinary General Meeting should be called to discuss removal of the director.

Question (c).
What type of resolution will be passed in this meeting for the removal of the Director?
Answer:
A resolution requiring special notice (section 115) will be passed in the meeting for the removal of the director.

4. Distinguish between the following.

Question 1.
Shareholders’ Meeting and Board Meeting.
Answer:

Basis	Shareholder’s Meeting (Annual General Meeting)	Board Meeting (Director’s Meeting)
1. Meaning	It is the meeting of all the members or shareholders of the company.	It is the meeting of all the Directors of the company.
2. Number of times	Annual General Meeting is held once every year. Extra Ordinary General Meeting is held to discuss urgent and important matters. It is called in between two Annual General Meetings.	Minimum 4 meetings to be held in a year and the gap between two meetings should not be more than 120 days.
3. Quorum	Quorum in case of Public Company is as follows: No. of Shareholders Quorum Up to 1000 5 members 1000-5000 15 members More than 5000 30 members In the case of the private company, 2 members present in person shall be the quorum.	The quorum for the Board Meeting is a minimum of 2 Directors or 1/3rd of its total Directors whichever is higher.
4. Proxy	Members can appoint a proxy to attend and vote at the meeting on their behalf.	Directors cannot appoint a proxy to attend and vote at the meeting.
5. Notice	Notice of shareholder’s meeting must be sent to all the members at least 21 clear days before the meeting.	Notice of Board Meeting must be sent to every Director at least 7 days before the meeting.
6. Purpose	The purpose of this meeting is to take approvals from shareholders on the Annual Report, Appointment of Auditor, etc.	The purpose of this meeting is to discuss policy matters, future planning, etc.

Question 2.
Annual General Meeting and Extra-ordinary General Meeting
Answer:

Points	Annual General Meeting	Extraordinary General Meeting
1. Meaning	It is a meeting of shareholders held once in a year as per the provisions of Section 96 of the Companies Act, 2013.	It is a meeting of shareholders held under special conditions to discuss urgent and important matters as per the provisions of Section 100 of the Companies Act, 2013.
2. Purpose	The purpose is to give information about the progress made by the company during the year.	The purpose is to discuss urgent and important matters that cannot be postponed till next Annual General Meeting.
3. Number of times	The first Annual General Meeting is held within 9 months of the completion of the financial year and the subsequent Annual General Meeting is held within 6 months of the completion of the financial year.	Extraordinary General Meeting is held anytime between two Annual General Meetings.
4. Authority	Annual General Meeting is normally called by the Board of Directors and can be called by the Central Government under special circumstances.	Extra-ordinary General Meeting can be called by: Board of Directors Board of Directors on the requisition of members The National Company Law Tribunal
5. Business transacted	To approve annual accounts To approve Auditors and Director’s Report To appoint Auditors, Directors, etc. To declare a dividend.	To alter Articles of Association. To alter Memorandum of Association. Removal of Director. Voluntary winding up of a company.
6. Penalty	In case of default in holding Annual General Meeting, every officer concerned is punishable with a fine upto ₹ 1,00,000 and fine of ₹ 5,000 per day till default continues.	If the directors fail to hold this meeting on requisition, the requisionist themselves can hold it and recover the expenses from defaulting directors.

5. Answer in brief.

Question 1.
List the duties of a Secretary after the Annual General Meeting.
Answer:
Duties of a Secretary after Annual General Meeting:

• Drafting Minutes: The secretary drafts the minutes of the meeting on the basis of the notes taken down during the proceedings of the meeting.
• Implementation of decisions: The secretary instructs the concerned department for implementing the decisions taken at the meeting.
• Dispatch Dividend Warrants: The secretary has to make an arrangement to dispatch dividend warrants to the shareholders.
• Filing Resolutions: The secretary has to file an Annual Report with the Registrar. In case of a special resolution, the secretary has to file the special resolution with the Registrar within 30 days of passing that resolution.
• Information to Absent Members: The secretary sends the information of the proceedings of the meeting to the absent members.

Question 2.
State the objectives of the Annual General Meeting.
Answer:
Purpose or objectives of Annual General Meeting: The main objective of holding an Annual General Meeting is to provide an opportunity to members to discuss the functioning of the company.

• To review the progress and performance of the company.
• To approve annual accounts, director’s report, and auditor’s report.
• To appoint auditors and fix their remuneration.
• To declare a dividend.
• To elect new directors in place of retiring Directors To transact special business, if any like-
  • business of the company taken over by the Government.
  • the company did not function well through the year, etc.

Question 3.
State any four legal provisions regarding Board Meeting.
Answer:
Legal Provisions relating to Board Meeting:
(i) Authority to Convene:
The chairman of the Board is the proper authority to call the Board Meeting.

(ii) Number of Board Meetings:

• First Board Meeting shall be held within 30 days of the date of its incorporation.
• Subsequently, there should be four meetings in a year.
• The gap between the two meetings should not be more than 120 days.
• At least one Board meeting should be held in 6 months in case of one person company, small company and dormant company.
• The gap between two meetings should not be more than 90 days in the case of one person company, a small company, and a dormant company.

(iii) Notice [Section 173(3)]:

• The notice of every Board Meeting must be given to every director at least 7 days before the meeting at his registered address along with an agenda of the meeting.
• It can also be sent by post or by hand delivery or by E-mail.
• If a company fails to send notice within a given time, then every officer in default shall be liable to a penalty of Rs. 25,000.

(iv) Quorum (Section – 174):

• The quorum for the Board Meeting is 1/3rd of the total number of directors or two directors whichever is higher.
• Any fraction should be rounded to one.
• Interested directors (personal interest in any matter) are not included in the quorum.

Question 4.
What are Class Meetings?
Answer:
Class Meetings (Section 48):

• When the meeting of a particular class of shareholders takes place such as a preference shareholders meeting, it is known as a class meeting.
• Such a meeting may be called for an alteration in the right and privileges of that particular class of shareholders.
• It can also be called for the purpose of conversion of one class of shares into another.
• The class meeting is not held regularly.

Question 5.
What is the purpose of conducting an Extra-ordinary General Meeting?
Answer:
Purpose or Objectives of Extra-Ordinary General Meeting:
The main purpose behind calling this meeting is to make shareholders aware of the happenings in the company or to seek their approval on some urgent and important matters of the company.

• Alteration in the Memorandum of Association.
• Alteration in Articles of Association.
• Reduction of Share Capital.
• Removal of a Director before the expiry of his term.
• Removal of an Auditor before the expiry of his term.
• Voluntary winding up of the company.

6. Justify the following statements.

Question 1.
Annual General Meeting is adjourned in absence of a quorum.
Answer:

• Quorum is a minimum number of members to be present for a valid Meeting.
• As per the Companies Act, 2013, the quorum for the Annual General Meeting of a public company is as follows:

No. of Shareholders	Quorum
Up to 1000	5 Members
1000 – 5000	15 Members
More than 5000	30 Members

• For a private company minimum of 2 members should be present
• If the meeting is conducted without a quorum, it is considered invalid.
• In the absence of a quorum, Annual General Meeting is adjourned.
• Adjourned Meeting will be convened on the same day, same time, and the same place in the next week.

Question 2.
A notice of the meeting must be sent to all members in case of the General Meeting.
Answer:

• The Board of Directors is the authority to convene general meetings.
• The notice must be given 21 clear days before the meeting to all those who are entitled to receive it.
• The notice must be sent to all the members at their registered address in India.
• Notice can be sent by registered post, if requested by the member, charges for the same is to be paid in advance.
• Notice is also given in all leading newspapers.
• Notice is accompanied by agenda and also Annual report, Auditor report, Annual accounts, etc. in case of Annual General Meeting.

Question 3.
Extra Ordinary General Meeting is called under special circumstances.
Answer:

1. Extraordinary General Meeting is held in between two Annual General Meetings.
2. It is held when the matter is of utmost importance and it cannot be postponed till the next Annual General Meeting.
3. It can be called to make shareholders aware of the happenings in the company.
4. It can also be called to seek their approval on important and urgent matters.
5. Important and urgent matters can be:
   • Alteration in Memorandum of Association
   • Alteration in Articles of Association
   • Reduction in share capital
   • Removal of a director or auditor
   • Voluntary winding up of a company, etc.

Question 4.
Board of Directors can exercise their powers collectively through the Board Meeting.
Answer:

1. Directors collectively are called as Board of Directors.
2. The Board of Directors has to meet frequently with reference to the day-to-day working of the company.
3. All important decisions can be taken by the Board of Directors in the Board Meeting collectively.
4. Powers which can be exercised at Board Meeting are:
   • The power to fill casual vacancies in the Board.
   • To recommend the rate of dividend.
   • The power to appoint managing Director, Manager, etc.
   • To sanction a contract.
   • To give loans or invest in shares of other companies.

Question 5.
The Quorum for the Annual General Meeting of a public company depends upon the number of shareholders.
Answer:

• Quorum is a minimum number of members to be present for a valid meeting.
• As per the Companies Act, 2013, the quorum for the Annual General Meeting of a public company are as follows:

No. of Shareholders	Quorum
Up to 1000	5 Members
1000 – 5000	15 Members
More than 5000	30 Members

• • If the number of shareholders is up to 1000, then the required quorum is 5 members.
  • If the number of shareholders is more than 1000 and up to 5000, then the required quorum is 15 members.
  • If the number of shareholders exceeds 5000 then the quorum is 30 members for a public company.
• In the absence of a quorum, if the meeting is conducted or a resolution is passed, it is considered illegal and invalid.
• In the absence of a quorum, the meeting is adjourned to the same day, same place, and same time in the next week.

Question 6.
When a company is in financial difficulty it may call a meeting of creditors.
Answer:

• Creditors of the company include Debenture holders, Depositors, Banks, financial institutions, etc.
• When a company is in a financial crisis, it seeks the help of creditors.
• The company can request creditors to alter the rate of interest, to alter the terms of security, etc.
• Meeting of creditors can be called to compromise in a dispute with them.
• Creditors and contributors can provide financial help to the company to safeguard them and also to protect them to avoid winding up of a company.

Question 7.
As per the Companies Act, every company has to hold the Annual General Meeting.
Answer:

• Every company other than one person company must hold an Annual General Meeting once a year.
• Annual General Meeting is held to review the working of the company during the previous financial year and take an effective decision for the next year.
• It is mainly called to approve Annual Report, Auditor Report, Annual Accounts, to declare a dividend, to elect Directors, Auditors and to transact special business, if any.
• First AGM shall be held within 9 months of the closing of the first financial year of the company.
• The time interval between two Annual General Meetings should not be more than 15 months.
• If the default is made in holding AGM then the company and every officer of the company in default are punishable with a fine which may extend up to ₹ 1,00,000 and up to ₹ 5,000 per day till default continues.

7. Answer the following questions.

Question 1.
Explain the functions of a secretary related to the Annual General Meeting.
Answer:
Functions (duties) of secretary related with Annual General Meeting:
Secretary has to perform many functions related to all types of meetings like Board Meeting, Annual General Meeting, etc. He has to perform all duties in compliance with the provisions of the Act. Secretary has to perform functions before, during, and after the meeting.

Functions of a secretary related to Annual General Meeting are as follows:
Functions Before the Annual General Meeting:
(i) Preparation of Accounts and Reports:
The secretary has to ensure that the Annual Accounts, Annual Report, and Auditor Report are prepared for consideration and approval.

(ii) Board Meeting:
Board Meeting is called to transact the following business:

• To adopt Annual Accounts duly audited.
• To adopt Director’s Report
• To consider the rate of dividend
• To fix the day, date, time, and place of the Annual General Meeting.

(iii) Notice:
The secretary has to send 21 clear days’ notice of a meeting to members and auditors before the meeting along with the auditor report, annual report, annual accounts, agenda, etc. The secretary has to arrange for publishing the notice of the meeting in leading newspapers.

(iv) Chairman Speech:
The secretary has to assist the chairman in drafting his speech to be delivered at the meeting.

(v) Preliminary Arrangement:
The secretary has to make arrangements such as booking of hall, refreshments, Register of Members, Members Attendance Book, etc.

Functions During the Annual General Meeting:
(i) Attendance:
The secretary has to get signatures of members present at the meeting in ‘Members Attendance Book.’

(ii) Quorum:
The secretary should see that the required quorum is present at the meeting and informs the chairman of the meeting.

(iii) Reading of Reports:
The secretary has to read the notice, Director’s Report, and Auditor’s Report as directed by the Chairman.

(iv) Notice of Proceedings:
The secretary should take down the notes of the proceedings of the meeting. He has to draft the minutes on the basis of these notes.

(v) Assist Chairman:
The secretary has to assist the chairman during the meeting. He should provide information, documents, etc as and when needed.

(vi) Conduct of Poll:
Secretary makes arrangements for conducting the poll if it is demanded by the members.

Functions After the Annual General Meeting:
(i) Drafting Minutes:
The secretary drafts the minutes of the meeting on the basis of the notes taken down during the proceedings of the meeting.

(ii) Implementation of decisions:
The secretary instructs the concerned department for implementing the decisions taken at the meeting.

(iii) Dispatch Dividend Warrants:
The secretary has to make an arrangement to dispatch dividend warrants to the shareholders.

(iv) Filing Resolutions:
The secretary has to file the Annual Report with the Registrar. In case of a special resolution, the secretary has to file the special resolution with the Registrar within 30 days of passing that resolution.

(v) Information to Absent Members :
The secretary sends the information of the proceedings of the meeting to the absent members.

Question 2.
Explain the different types of General Meetings of a company.
Answer:
General Meetings are meetings of Equity shareholders of the company. There are two types of General Meetings:

• Annual General Meeting
• Extraordinary General Meeting.

1. Annual General Meeting (Section 96):
Every Company other than One Person Company must hold Annual General Meeting once in a year.
Purpose or Objective of Annual General Meeting:

• To review the progress and performance of the company.
• To approve annual accounts, director’s report, and auditor’s report.
• To appoint auditors and fix their remuneration.
• To declare a dividend.
• To elect new directors in place of retiring directors.
• To transact special business, if any.

Legal Provisions relating to Annual General Meeting:
(i) Time Limit:

• The time interval between two Annual General Meetings should not be more than 15 months.
• Extension of time for holding the Annual General Meeting may be given by the Registrar to the company for a period not more than three months, except for the first Annual General Meeting.
• One person company is exempted from the provision of Annual General Meeting.

(ii) Authority to Convene Annual General Meeting:
The Board of Directors is the proper authority to convene the Annual General Meeting.

(iii) Notice:
The notice must be given to all those who are entitled to receive it, at least 21 clear days in advance of the meeting. It is sent to the members at their registered address by post or through electronic mode like Email, etc.

(iv) Time, Day, and Place of Annual General Meeting:
Annual General Meeting shall be called during business hours between 9 am to 6 pm on any day other than National holidays. It can be held at the registered office or at some other place within the city or village in which the registered office of the company is situated.

(v) Quorum:
According to the Companies Act, 2013, the quorum for the Annual General Meeting of a public company is as follows:

No. of Shareholders	Quorum
Upto 1000	5 Members
1000 – 5000	15 Members
More than 5000	30 Members

For a private company minimum of two members should be present in person.

(vi) Adjournment:
In the absence of a quorum, Annual General Meeting stands adjourned. It will be convened on the same day, same time and the same place in the next week.

(vii) Default:
If the default is made in holding the Annual General Meeting as per the provisions of the Act or as per the instructions of the Central Government, the company and every officer of the company who is in default are punishable with a fine which may extend up to ₹ 1,00,000/-. If the default continues fine may extend up to ₹ 5,000 per day till the default continues.

2. Extra-Ordinary General Meeting (Section – 100):
Meaning:
It is a meeting which is called in between two Annual General Meetings under special circumstances, which cannot be postponed till the next Annual General Meeting. The matters discussed under this meeting is of utmost importance and urgent by nature.

Purpose or Objectives of Extra-Ordinary General Meeting:
The main purpose behind calling this meeting is to make shareholders aware of the happenings in the company or to seek their approval on some urgent and important matters of the company.

• Alteration in the Memorandum of Association.
• Alteration in Articles of Association.
• Reduction of Share Capital of the company.
• Removal of a Director before the expiry of his term.
• Removal of an Auditor before the expiry of his term.
• Voluntary winding up of the company.

Legal Provisions relating to Extra Ordinary General Meeting:
(i) Time for holding a meeting:
Extra Ordinary General Meeting is held between two Annual General Meetings under special circumstances. It can be held at any time as per the requirements of the company.

(ii) Authority to Convene:

• The Board of Directors has the right to call an Extra-Ordinary General Meeting by sending a proper notice to the shareholders.
• Extra-Ordinary General Meeting can be called by the members holding at least 1/10th of the paid-up capital or 1/10th of voting power in the company. Board must call Extra-Ordinary General Meeting within 45 days of receiving the requisition from the members.
• If the Board fails to call such a meeting then the requisitionists themselves call this meeting within 3 months from the date of deposit of the requisition. The company shall pay all the expenses incurred for holding such meetings by the requisitionist.
• National Company Law Tribunal (NCLT) can order such meetings on its own or at the request of a director or any members having voting rights.

(iii) Notice:
The notice must be given to all those who are entitled to receive it, at least 21 clear days in advance of the meeting. It is sent to the members at their registered address by post or through electronic mode like Email, etc.

(iv) Quorum:
According to the Companies Act, 2013, the quorum for the Annual General Meeting of a public company is as follows:

No. of Shareholders	Quorum
Up to 1000	5 Members
1000 – 5000	15 Members
More than 5000	30 Members

For a private company minimum of two members should be present in person.

Question 3.
Explain the different types of Director’s Meetings.
Answer:
Director’s meeting:
Directors collectively are called as Board of Directors. They meet regularly to discuss and decide upon company matters, implementation of plans and review the progress made by the company.

(i) Board Meeting (Section 173):
It is a meeting of the Board of Directors. The Board of Directors has to meet frequently with reference to day to day working of the company. The Board of Directors can exercise their powers collectively through the Board Meeting.

Legal Provisions relating to Board Meeting:
(a) Authority to Convene:
The chairman of the Board is the proper authority to call the Board Meeting.

(b) Number of Board Meetings:

• First Board Meeting shall be held within 30 days of the date of its incorporation.
• Subsequently, there should be four meetings in a year.
• The gap between the two meetings should not be more than 120 days.
• At least one Board meeting should be held in 6 months in case of one person company, small company, and dormant company.
• The gap between two meetings should not be more than 90 days in the case of one person company.

(c) Virtual Meeting/Video Conferencing:
If there is any urgency to call Board Meeting and practically not possible for Directors to attend the meeting in a short notice, so with the help of technology, a virtual meeting can be held. The meetings are recorded and active participation of Directors is also possible through video conferencing. Certain special and confidential matters cannot be dealt with through video conferencing as per the directions of the Central Government.

(d) Notice [Section 173(3)]:
The notice of every Board Meeting must be given to every director at least 7 days before the meeting at his registered address along with an agenda of the meeting.
It can also be sent by post or by hand delivery or by E-mail.
If a company fails to send notice within a given time, then every officer in default shall be liable to a penalty of Rs. 25,000.

(e) Quorum (Section – 174)

• The quorum for the Board Meeting is 1/3rd of the total number of directors or two directors whichever is higher.
  Any fraction should be rounded to one.
• Interested directors (personal interest in any matter) are not included in the quorum.

(f) Adjournment:
The meeting of the Board of directors can be adjourned in the absence of a quorum.
The adjourned meeting can be held on the same day, same time and the same place in the next week.

(ii) Committee Meeting:

• The Board of Directors may from the committee and delegate some of its powers to them.
• This committee should consist of only directors. The delegation of such powers to committees is to be authorized by Articles of Association and should be subject to the provisions of the Companies Act.
• A meeting of Allotment Committee, Transfer Committee, etc are examples of Committee Meeting.

Activity 1 (Textbook Page No. 123)

Visit the website of any public company and study its Annual Report/Director’s Report.
Answer:
[Note: Students should do this activity by themselves with the help of the internet.]

Activity 2 (Textbook Page No. 127)

Enlist the functions of a Secretary related to an Extra-Ordinary Meeting.
Answer:
Functions of Secretary Relating to Extra Ordinary General Meeting:
(i) Before the Meeting:

• Time of Holding: To decide the date, time, place, and agenda for holding the meeting in consultation with the chairman of the company and to convene the Board Meeting for finalization of these things by passing a resolution to that effect.
• Drafting of Resolution: To draft the proposed resolution and explanatory statements and to get them approved by the board.
• Notice: To draft the notice of the meeting and arrange to get the same printed together with the explanatory statements, proxy forms, and admission cards. To send the notice with agenda to all the members, at least 21 days before the meeting.
• Public Notice: The notice is also published in the leading newspapers for the information of the general public.
• Notice to Stock Authorities: If the shares are listed on the stock exchange, a notice of the meeting is sent to stock exchange authorities too.
• Proxy: To verify proxy forms received and enter them in the proxy register.
• Preparing Documents: The important documents, records, Books, etc. are kept ready for reference during the meeting.

(ii) During the Meeting:

• Checking: To check the admission card of the members.
• Attendance: To take attendance of members.
• Ascertaining Quorum: To ascertain the quorum.
• Reading Notice: To read the notice convening meeting.
• Assist Chairman: To assist the chairman, by providing necessary information, records documents.
• Notes of Proceedings: To make notes of the proceedings of the meeting.

(iii) After the Meeting:

• Drafting Minutes: To draft the minutes of the meeting and enter the same in the Minute Book.
• Signed by the Chairman: To get Minutes signed by the chairman of the meeting.
• Filing of Resolution: To file the certified copy of the resolution passed at the meeting, to the Registrar of Companies.
• Sending Intimation: To send intimation to the concerned persons.
• Implementations: To carry out decisions taken at the meeting.

Maharashtra State Board 11th Std Secretarial Practice Textbook Solutions Digest

• 11th Secretarial Practice Chapter 1 Practical Problems
• 11th Secretarial Practice Chapter 2 Practical Problems
• 11th Secretarial Practice Chapter 3 Practical Problems
• 11th Secretarial Practice Chapter 4 Practical Problems
• 11th Secretarial Practice Chapter 5 Practical Problems
• 11th Secretarial Practice Chapter 6 Practical Problems
• 11th Secretarial Practice Chapter 7 Practical Problems
• 11th Secretarial Practice Chapter 8 Practical Problems
• 11th Secretarial Practice Chapter 9 Practical Problems
• 11th Secretarial Practice Chapter 10 Practical Problems
• 11th Secretarial Practice Chapter 11 Practical Problems
• 11th Secretarial Practice Chapter 12 Practical Problems

Correspondence with Statutory Authorities 11th Secretarial Practice Chapter 12 Solutions Maharashtra Board

Balbharti Maharashtra State Board Class 11 Secretarial Practice Solutions Chapter 12 Correspondence with Statutory Authorities Textbook Exercise Questions and Answers.

Class 11 Secretarial Practice Chapter 12 Exercise Solutions

1A. Select the correct answer from the options given below and rewrite the statements.

Question 1.
_____________ is the main authority to regulate the administration of Companies Act, 2013 in India.
(a) MCA
(b) Company Secretary
(c) Board of Directors
Answer:
(a) MCA

Question 2.
The headquarters of MCA is at _____________
(a) Mumbai
(b) New Delhi
(c) Pune
Answer:
(b) New Delhi

Question 3.
To administer the provisions of the Companies Act, 2013 is the objective of _____________
(a) MCA
(b) ROC
(c) Directors
Answer:
(a) MCA

Question 4.
_____________ is responsible for registering companies.
(a) ROC
(b) SEBI
(c) Auditors
Answer:
(a) ROC

Question 5.
The Certificate of Incorporation is issued by _____________
(a) ROC
(b) MCA
(c) NCLT
Answer:
(a) ROC

Question 6.
_____________ can strike off or remove the name of a company from the Register of Companies.
(a) MCA
(b) ROC
(c) SEBI
Answer:
(b) ROC

Question 7.
Central Government exercises administrative control over ROCs through the _____________
(a) MCA
(b) SEBI
(c) Regional Directors
Answer:
(c) Regional Directors

Question 8.
_____________ is the quasi-judicial body set up by the Central Government to grant certain approvals and decide disputes under the provisions of the Companies Act.
(a) MCA
(b) ROC
(c) NCLT
Answer:
(c) NCLT

Question 9.
_____________ can hear appeals against the orders issued by NCLT.
(a) NCLAT
(b) SEBI
(c) MCA
Answer:
(a) NCLAT

Question 10.
An appeal against the order of NCLAT can be filed in the _____________
(a) MCA
(b) SEBI
(c) Supreme Court
Answer:
(c) Supreme Court

Question 11.
_____________ was established as a statutory body to regulate the securities market in India.
(a) NCLT
(b) MCA
(c) SEBI
Answer:
(c) SEBI

Question 12.
_____________ regulates the functioning of Stock Exchange in India.
(a) SEBI
(b) MCA
(c) ROC
Answer:
(a) SEBI

1B. Match the pairs.

Question 1.

Group ‘A’	Group ‘B’
(a) Administration of Companies Act, 2013	(1) SEBI
(b) ROC	(2) Hears appeals against orders of NCLT
(c) NCLAT	(3) NCLT
(d) Regulator of Securities Market	(4) Incorporation of companies
(e) Quasi-judicial body	(5) MCA
	(6) Board of directors
	(7) Companies Act 2013
	(8) Regional Director
	(9) Chennai
	(10) Liquidator

Answer:

Group ‘A’	Group ‘B’
(a) Administration of Companies Act, 2013	(5) MCA
(b) ROC	(4) Incorporation of companies
(c) NCLAT	(2) Hears appeals against orders of NCLT
(d) Regulator of Securities Market	(1) SEBI
(e) Quasi-judicial body	(3) NCLT

1C. Write a word or a term or a phrase that can substitute each of the following statements.

Question 1.
The main authority is concerned with the administration of the Companies Act.
Answer:
MCA

Question 2.
The organization is responsible for administering the Companies Act and regulating professional bodies like ICAI, ICSI, etc.
Answer:
MCA

Question 3.
The authority which issues Certificate of Incorporation to company.
Answer:
ROC

Question 4.
Every company has to apply for incorporation to this authority situated in the state where its head office is to be located.
Answer:
ROC

Question 5.
The authority that handles corporate civil disputes in India.
Answer:
NCLT

Question 6.
An appeal against the orders of NCLT is heard by this authority.
Answer:
NCLAT

Question 7.
Regulator of the securities market in India.
Answer:
SEBI

Question 8.
An institution that regulates the functioning of stock exchanges and intermediaries in the securities market.
Answer:
SEBI

1D. State whether the following statements are True or False.

Question 1.
MCA regulates the functioning of the corporate sector as well as administers the Companies Act.
Answer:
True

Question 2.
MCA has no supervisory authority over professional bodies like ICSI, ICAI, etc.
Answer:
False

Question 3.
ROC is concerned with the registration of companies.
Answer:
True

Question 4.
On payment of fees, ROC allows the public to inspect certain documents filed with it.
Answer:
True

Question 5.
NCLT has jurisdiction over proceedings on matters of disputes arising under the Companies Act.
Answer:
True

Question 6.
NCLAT can hear appeals against the order of NCLT.
Answer:
True

Question 7.
NCLAT may confirm, modify or reject the orders passed by the NCLT.
Answer:
True

Question 8.
SEBI protects the interest of investors in the securities market.
Answer:
True

Question 9.
ROC is the regulator of the securities market.
Answer:
False

1E. Complete the sentences.

Question 1.
Administration of Companies Act and other laws related to corporate world is the responsibility of _____________
Answer:
MCA (Ministry of Corporate Affairs)

Question 2.
Registration of companies is done by _____________
Answer:
ROC (Registrar of Companies)

Question 3.
The authority which handles corporate civil disputes is called as _____________
Answer:
NCLT (National Company Law Tribunal)

Question 4.
The authority which hears appeals against the orders of NCLT is called as _____________
Answer:
NCLAT (National Company Law Appellate Tribunal)

1F. Select the correct option from the bracket.

Question 1.

Group ‘A’	Group ‘B’
(1) Regulator of Securities Market	……………………….
(2) MCA	……………………….
(3) ……………………	Hears appeals against orders of NCLT

(NCLAT, Administers Companies Act, SEBI)
Answer:

Group ‘A’	Group ‘B’
(1) Regulator of Securities Market	SEBI
(2) MCA	Administers Companies Act
(3) NCLAT	Hears appeals against orders of NCLT

1G. Answer in one sentence.

Question 1.
Name the authority which administers the Companies Act and Partnership Act.
Answer:
MCA (Ministry of Corporate Affairs).

Question 2.
Name the authority attached to the High Court which helps in the winding up of companies.
Answer:
The authority attached to the High Court which helps in the winding up of Companies is the Official Liquidator.

1H. Correct the underlined word and rewrite the following sentences.

Question 1.
ROC supervises and controls the operations of stock exchanges in India.
Answer:
SEBI supervises and controls the operation of stock exchanges in India.

Question 2.
An appeal can be made against the order issued by NCLT to NCLAT within 90 days.
Answer:
An appeal can be made against the order issued by NCLT to NCLAT within 45 days.

2. Explain the following terms/concepts.

Question 1.
Ministry of Corporate Affairs (MCA)
Answer:

• The MCA is primarily concerned with the administration of the Companies Act, 2013.
• The MCA is responsible to prevent practices from having an adverse effect on competition, to promote and sustain competition in markets.
• MCA supervises certain professional bodies like the Institute of Chartered Accountants of India. (ICAI), Institute of Company Secretaries of India (ICSI), Institute of Cost Accountants of India.
• It works with the help of Regional Directors, ROC, and Official Liquidator.

Question 2.
Registrar of Companies (ROC)
Answer:
The Registrar of Companies (ROC) is an office under the Ministry of Corporate Affairs (MCA) which deals with the administration of Companies and Limited Liability Partnerships in India.

• At present 22 Registrar of Companies is operating in all major states.
• States like Tamilnadu and Maharashtra have more than one ROC.
• ROC is a full-time field officer who has wide powers and responsibilities in administering the Companies Act.
• ROC has to examine various documents filed with it by the companies in compliance with the Companies Act, 2013.
• The ROC has to take decisions on documents filed with it and reply within 30 days from the date of filing the documents.

Question 3.
National Company Law Tribunal (NCLT)
Answer:

• The Central Government has constituted National Company Law Tribunal in June 2016.
• It is a quasi-judicial body, which grants approvals and handles Corporate Civil Disputes.
• The Tribunal operates through 15 ‘Benches’ consisting of 2 members i.e. a judicial member and a technical member.
• The Tribunal has to dispose of every application or petition within 3 months of receiving it.
• An appeal against the order of NCLT can be made to National Company Law Appellate Tribunal (NCLAT).

Question 4.
National Company Law Appellate Tribunal (NCLAT)
Answer:
National Company Law Appellate Tribunal was constituted for hearing appeals against the orders of the National Company Law Tribunal.

• NCLAT is also the Appellate Tribunal for hearing appeals against the order passed by the Insolvency and Bankruptcy Board of India.
• It is headed by a chairperson and has a maximum of 11 members comprising of judicial and technical members.
• An appeal can be made against the order issued by NCLT to NCLAT within 45 days.
• An appeal can be made against the orders of NCLAT to Supreme Court within 60 days.

Question 5.
Securities and Exchange Board of India (SEBI)
Answer:

• SEBI was established in 1992 as a statutory body to regulate the Securities Market in India.
• Its head office is in Mumbai.
• It supervises and controls the operations of Stock Exchanges, Companies issuing securities, and other intermediaries like Underwriters, Merchant Bankers, Brokers, etc.
• It protects and safeguards the interest of the investors in the security market.
• The main objective is to regulate the functioning of securities markets and stock exchanges.
• It develops a code of conduct for fair practices by intermediaries.

3. Answer in brief.

Question 1.
State the powers of ROC.
Answer:
The Registrar of Companies (ROC) is an office under the Ministry of Corporate Affairs (MCA) which deals with the administration of Companies and Limited Liability Partnerships in India. At present 22 Registrar of Companies is operating in all the major states. States like Tamilnadu and Maharashtra have more than one ROC. ROC is a full-time field officer who has wide powers and responsibility in administering the Companies Act.

Following are the powers of ROC:

• To extend the time of the Annual General Meeting other than the first AGM by a period not more than 3 months.
• To inspect or call for books of account, other books, and papers.
• To seek in writing any information or explanation with regard to any document furnished to ROC.
• Seek the Special Court to issue an order for seizure of books and papers of the company, if the ROC feels that such records may be destroyed, altered, or falsified.
• To strike off the name of a company from the Registrar of Companies.

Question 2.
State the powers of NCLT.
Answer:
Meaning of NCLT:
The Central Government has constituted National Company Law Tribunal in June 2016. The NCLT is a quasi-judicial body, which grants approvals and handles Corporate Civil disputes.

Powers of NCLT:

• To hear and decide all proceedings related to compromise, arrangement, and reconstruction of a company.
• To hear and decide all winding up petitions on the ground of inability to pay its debts and on other grounds.
• To hear and decide petition for an extension of time for repayment of deposits.
• To hear and decide cases pertaining to oppression and mismanagement of a company.
• To call for holding AGM or EOGM of a company.
• To direct a company not to dispose of funds of a company and to freeze the assets of a company for being used against the interest of the company.
• To hear and decide grievances of rejection in transferring shares and securities.

Question 3.
What are the objectives of MCA?
Answer:
The MCA is primarily concerned with the administration of the Companies Act, 2013.
It frames the rules and regulations for regulating the functioning of the corporate sector in accordance with the law.

Objectives of MCA:

• To administer the provisions of the Companies Act, 2013, and other allied laws.
• To quickly identify non-compliance with the Companies Act.
• To encourage companies to improve Corporate Governance and adopt responsible business practices.
• To promote fair competition.
• To make available to the public, corporate data.
• To offer various services to the stakeholders.

4. Justify the following statements.

Question 1.
The MCA was set up by Central Government to fulfill certain objectives.
Answer:
The MCA is primarily concerned with the administration of the Companies Act, 2013.
It frames the rules and regulations for regulating the functioning of the corporate sector in accordance with the law.

Objectives of MCA:

• To administer the provisions of the Companies Act, 2013, and other allied laws.
• To quickly identify non-compliance with the Companies Act.
• To encourage companies to improve Corporate Governance and adopt responsible business practices.
• To promote fair competition.
• To make available to the public, corporate data.
• To offer various services to the stakeholders.

Question 2.
The Companies Act, 2013 has given certain Powers to ROC.
Answer:
The Registrar of Companies (ROC) is an office under the Ministry of Corporate Affairs (MCA) which deals with the administration of Companies and Limited Liability Partnerships in India. At present 22 Registrar of Companies is operating in all the major states. States like Tamilnadu and Maharashtra have more than one ROC. ROC is a full-time field officer who has wide powers and responsibility in administering the Companies Act.

Following are the powers of ROC:

• To extend the time of the Annual General Meeting other than the first AGM by a period not more than 3 months.
• To inspect or call for books of account, other books, and papers.
• To seek in writing any information or explanation with regard to any document furnished to ROC.
• Seek the Special Court to issue an order for seizure of books and papers of the company, if the ROC feels that such records may be destroyed, altered or falsified.
• To strike off the name of a company from the Registrar of Companies.

Question 3.
The Central Government has empowered NCLT with certain powers.
Answer:
Meaning of NCLT:
The Central Government has constituted National Company Law Tribunal in June 2016. The NCLT is a quasi-judicial body, which grants approvals and handles Corporate Civil disputes.

Powers of NCLT:

• To hear and decide all proceedings related to compromise, arrangement, and reconstruction of a company.
• To hear and decide all winding up petitions on the ground of inability to pay its debts and on other grounds.
• To hear and decide petition for an extension of time for repayment of deposits.
• To hear and decide cases pertaining to oppression and mismanagement of a company.
• To call for holding AGM or EOGM of a company.
• To direct a company not to dispose of funds of a company and to freeze the assets of a company for being used against the interest of the company.
• To hear and decide grievances of rejection in transferring shares and securities.

5. Attempt the following.

Question 1.
Write a letter to ROC seeking an extension of time to hold the AGM.
Answer:

STARTRACK LIMITED Registered Office: Galaxy House Rainbow Township, Mira Road, Mumbai – 400609 CIN: L13471 MH 2012 PLC 000222 Phone: 022-22135649, 91-9910190332 Website: www.startracklimited.com Email: startrack@limited.com Date: 30th July 2019. Ref No: ROC/AGM – 99. The Registrar of Companies Churchgate, Mumbai – 400019. Sub: Extension of time for holding 6th Annual General Meeting. Dear Sir, As per the Companies Act, 2013, our Company must hold its 6th Annual General Meeting on or before 30th September 2019, for the financial year ending on 31st March 2019 We are extremely sorry to inform, that due to most of our directors are on travel abroad during that period, we will not be able to hold the Annual General Meeting before 30th September 2019. We, therefore, request you to grant us an extension period of two months for holding the said AGM i.e. up to 30th November 2019. We will be highly obliged if you grant us the permission to extend the said meeting. Thanking you, Yours faithfully, for STAR TRACK LIMITED. Sign Company Secretary Encl: Copy of Annual Report 2017-18.

Question 2.
Write a letter to MCA with regard to ‘Ticket Raising’.
Answer:

STARTRACK LIMITED Registered Office: Galaxy House Rainbow Township, Mira Road, Mumbai – 400609 CIN: L13471 MH 2012 PLC 000222 Phone: 022-22135649, 91-9910190332 Website: www.startracklimited.com Email: startrack@limited.com Date: 1st April 2019. Ref No: MCA/ST – 19 The Manager (Web-service Dept) Vaibhav Apartment, Vaibhav Nagar, New Delhi – 110003 Sub: Difficulty in downloading e-form. Dear Sir, This is to inform you that company is intending to download e-form (Form SH-7) to intimate the ROC about the alteration made in the share capital of our company. However, we are not able to download the form due to some technical error, and the message that pops up on pressing the ‘ENTER’ button is “The file is damaged and cannot be repaired”. In spite of our repeated effort, we are not able to download the form. So we earnestly request you to look into the matter at your earliest. Also, let us know the next step to resolve the above matter. Thanking you, Yours faithfully, for STAR TRACK LIMITED. Sign Company Secretary Encl: Copy of message as appearing on the website.

Question 3.
Write a reply to a complaint by the Investor.
Answer:

STARTRACK LIMITED Registered Office: Galaxy House Rainbow Township, Mira Road, Mumbai – 400609 CIN: L13471 MH 2012 PLC 000222 Phone: 022-22124745, 91-9920380555 Website: www.startracklimited.com Email: startrack@limited.com Date: 2nd June 2019. Ref No: IC/ 219. Ms.Vaishali Rane, Birla House, Bhagwati Road, Kandivli (W). Mumbai – 400018. Sub: Non-Receipt of Annual Report. Dear Sir, We are in receipt of your letter dated 20th May 2019 regarding the non-receipt of the Annual Report. As per the Companies Act, 2019, we have sent by post to all the members, the notice of 8th AGM along with the Annual Report well in advance, as per the address provided by you in our Register of Members. It is however unfortunate to know that you have not received the Notice and the Annual report. We are once again sending you the same to the address mentioned in your letter. Yours faithfully, for STAR TRACK LIMITED Sign Company Secretary Encl: Annual Report 2018-19 CC to: SEBI

Question 4.
Write a letter to NCLT seeking an extension of time to repay Public Deposits.
Answer:

STARTRACK LIMITED Registered Office: Galaxy House Rainbow Township, Mira Road, Mumbai – 400609 CIN: L13471 MH 2012 PLC 000222 Phone: 022-22135649, 91-9910190332 Website: www.startracklimited.com Email: startrack@limited.com Date: 30th July 2019. Ref No: NCLT/99 The National Company Law Tribunal Board. ‘C’ wing, 25th Floor, Priyadarshini Bhavan, M.G. Road, New Delhi – 110004. Sub: Extension of time to repay Pubic Deposit. Sir, The company had accepted Public Deposits worth 20 lacs on 1st April 2016 for a period of two years. The Deposits are to be repaid on or before 31st March 2018. However, as the company is passing through financial problems, we are is unable to repay deposits on the above-mentioned date. The board held a meeting on 29th December 2017 and passed a resolution for seeking an extension from NCLT for a period of three months, to repay deposits. Therefore, we request you to grant us an extension for three months to repay it. Copy of the petition is attached in two sets. We assure you that the company will pay the deposits on or before 30th June 2019. Yours faithfully, for STAR TRACK LIMITED Sign Company Secretary Encl: Certified copy of Board Resolution. Petition for Extension of time. Challan for fees paid.

Maharashtra State Board 11th Std Secretarial Practice Textbook Solutions Digest

• 11th Secretarial Practice Chapter 1 Practical Problems
• 11th Secretarial Practice Chapter 2 Practical Problems
• 11th Secretarial Practice Chapter 3 Practical Problems
• 11th Secretarial Practice Chapter 4 Practical Problems
• 11th Secretarial Practice Chapter 5 Practical Problems
• 11th Secretarial Practice Chapter 6 Practical Problems
• 11th Secretarial Practice Chapter 7 Practical Problems
• 11th Secretarial Practice Chapter 8 Practical Problems
• 11th Secretarial Practice Chapter 9 Practical Problems
• 11th Secretarial Practice Chapter 10 Practical Problems
• 11th Secretarial Practice Chapter 11 Practical Problems
• 11th Secretarial Practice Chapter 12 Practical Problems

Directors and Key Managerial Personnel of a Company 11th Secretarial Practice Chapter 6 Solutions Maharashtra Board

Balbharti Maharashtra State Board Class 11 Secretarial Practice Solutions Chapter 6 Directors and Key Managerial Personnel of a Company Textbook Exercise Questions and Answers.

Class 11 Secretarial Practice Chapter 6 Exercise Solutions

1A. Select the correct answer from the options given below and rewrite the statements.

Question 1.
_____________ comprises of a team of Directors.
(a) Board of Directors
(b) Board of Trustees
(c) Board of Managers
Answer:
(a) Board of Directors

Question 2.
_____________ can be a director.
(a) An Individual
(b) A Firm
(c) A Body corporate
Answer:
(a) An individual

Question 3.
Upto _____________ as maximum directors are allowed to a company.
(a) five
(b) fifteen
(c) fifty
Answer:
(b) fifteen

Question 4.
A maximum of _____________ Directorships is allowed to a person.
(a) two
(b) ten
(c) twenty
Answer:
(c) twenty

Question 5.
A maximum of _____________ Directorships of a public company is allowed to a person.
(a) one
(b) ten
(c) twenty
Answer:
(b) ten

Question 6.
_____________ is a unique identification number required to be a Director.
(a) PIN
(b) DIN
(c) TIN
Answer:
(b) DIN

Question 7.
_____________ powers are the powers given to Board under the Act.
(a) Statutory
(b) Managerial
(c) Administrative
Answer:
(a) Statutory

Question 8.
Director represents company in his role as _____________
(a) Agent
(b) Managing Partner
(c) employee
Answer:
(a) Agent

Question 9.
Managing Director is appointed for a period of _____________ years
(a) 5
(b) 10
(c) 15
Answer:
(a) 5

Question 10.
_____________ is required to work under superintendence, control, guidance of the Board.
(a) Government
(b) ROC
(c) Managing Director
Answer:
(c) Managing Director

Question 11.
_____________ is an employee of the company.
(a) Alternate director
(b) Non-executive Director
(c) Whole-time director
Answer:
(c) Whole time Director

Question 12.
_____________ need not be a director of the company.
(a) Manager
(b) Managing Director
(c) Whole-time director
Answer:
(a) Manager

Question 13.
_____________ needs a whole time director.
(a) Listed company
(b) Partnership
(c) OPC
Answer:
(a) Listed company

Question 14.
To provide guidance to Board is _____________ duty of Company Secretary.
(a) Personal
(b) General
(c) Statutory
Answer:
(c) Statutory

Question 15.
Only a member of _____________ can be a practicing Company Secretary.
(a) ICAI
(b) ACCA
(c) ICSI
Answer:
(c) ICSI

Question 16.
_____________ is to be prepared in prescribed form MR-3.
(a) Annual Report
(b) Auditors Report
(c) Secretarial Audit Report
Answer:
(c) Secretarial Audit Report

1B. Match the pairs.

Question 1.

Group ‘A’	Group ‘B’
(a) Board of Directors	(1) Nominated by the Board
(b) Managing Director	(2) Assists and advises the Board
(c) Company Secretary	(3) Automatic Appointment
(d) First Directors	(4) Appointed by ROC
(e) Alternate Director	(5) Extensive Powers of management
	(6) Substantial Powers of management
	(7) Appointed by Promoter
	(8) Assist and Advises the Government
	(9) Negligible Powers of management
	(10) Nominated by Council

Answer:

Group ‘A’	Group ‘B’
(a) Board of Directors	(5) Extensive Powers of management
(b) Managing Director	(6) Substantial Powers of management
(c) Company Secretary	(2) Assists and advises the Board
(d) First Directors	(7) Appointed by Promoter
(e) Alternate Director	(1) Nominated by the Board

Question 2.

Group ‘A’	Group ‘B’
(a) Public company	(1) Arises due to death of Director
(b) Private company	(2) Collective Powers
(c) Secretarial Auditor	(3) Individual Powers to Directors
(d) Casual Vacancy of a Director	(4) Arises due to additional work
(e) Powers of the Board	(5) Appointed by Managing Director
	(6) At least 2 (two) Directors
	(7) At least 3 (three) Directors
	(8) At least 15 (fifteen) Directors
	(9) At least 1 (one) Director
	(10) Appointed by the Board

Answer:

Group ‘A’	Group ‘B’
(a) Public company	(7) At least 3 (three) Directors
(b) Private company	(6) At least 2 (two) Directors
(c) Secretarial Auditor	(10) Appointed by the Board
(d) Casual Vacancy of a Director	(1) Arises due to death of Director
(e) Powers of the Board	(2) Collective Powers

1C. Write a word or a term or a phrase that can substitute each of the following statements.

Question 1.
The organization with distinct features of separate ownership and management.
Answer:
Joint-stock company

Question 2.
The officer is responsible for the company’s finances.
Answer:
Chief Financial Officer

Question 3.
The body of elected representatives of the company.
Answer:
The Board of Directors

Question 4.
The officer is a statutory and administrative officer and also acts as co-ordinator of the company.
Answer:
Company Secretary

Question 5.
Qualification required to be a Company Secretary.
Answer:
Member of ICSI

Question 6.
Agents, Trustees, and Managing Partners of the company.
Answer:
The Board of Directors

Question 7.
The audit which checks compliances of different legislations.
Answer:
Secretarial audit

Question 8.
This KMP signs documents of the company requiring authentication by the company.
Answer:
Company Secretary

Question 9.
The nature of the relationship of Directors with the company.
Answer:
Fiduciary

Question 10.
Name the Secretarial Standard – 1.
Answer:
Secretarial Standards on meetings of the BOD

Question 11.
Name the Secretarial Standard – 2.
Answer:
Secretarial Standards on General Meeting

Question 12.
Name the Secretarial Standard – 3.
Answer:
Secretarial Standards on Dividend

1D. State whether the following statements are True or False.

Question 1.
A large number of shareholders necessitates the company to have a separate managerial body.
Answer:
True

Question 2.
The maximum number of Directors allowed to a company is 15 (fifteen).
Answer:
True

Question 3.
A public company should have a minimum of 10 (ten) directors.
Answer:
False

Question 4.
DIN is required for Secretaryship.
Answer:
False

Question 5.
Executive Director is called an outside Director.
Answer:
False

Question 6.
The promoter of a company cannot be the Independent Director.
Answer:
True

Question 7.
Only individuals can be directors.
Answer:
True

Question 8.
The casual vacancy of the Board is filled by the members.
Answer:
False

Question 9.
To function as per Articles of Association of the company is the statutory duty of the Board.
Answer:
True

Question 10.
A Director is an employee of the company.
Answer:
False

Question 11.
The Managing Director is appointed by a resolution.
Answer:
True

Question 12.
The minimum and maximum age to be a Managing Director is 21 and 70 respectively.
Answer:
True

Question 13.
A company may appoint more than one M.D.
Answer:
True

Question 14.
Indian companies prefer a Managing Director over a Manager.
Answer:
True

1E. Find the odd one.

Question 1.
Woman Director, Promoter, Executive Director.
Answer:
Promoter

Question 2.
Absent at Board Meeting, failure to disclose an interest, DIN.
Answer:
DIN

1F. Complete the sentences.

Question 1.
Separate ownership and management is a unique feature of _____________
Answer:
Company

Question 2.
Minimum number of Directors for a private company should be _____________
Answer:
Two

Question 3.
Minimum number of Directors for a public company should be _____________
Answer:
Three

Question 4.
Minimum number of Directors for an OPC should be _____________
Answer:
One

Question 5.
First Directors of a company are appointed by _____________
Answer:
Promoter

Question 6.
At least one Woman Director is required by _____________ company.
Answer:
Listed Company

Question 7.
Casual vacancy on Board is filled by _____________
Answer:
Board

Question 8.
Director is the guardian of interest of company as _____________
Answer:
Trustees

Question 9.
First Secretary is appointed by _____________
Answer:
Promoters

Question 10.
The audit which checks the compliance of Companies Act is called as _____________
Answer:
Secretarial Audit

1G. Select the correct option from the bracket.

Question 1.

Group ‘A’	Group ‘B’
(1) Rotational Director	…………………..
(2) ……………………….	Alternate Director
(3) Woman Director	…………………..
(4) ……………………….	First Director

(Every Listed Company, Appointee by Promoters, Appointed in Place of a director who is absent, Retire by Rotation)
rotation)
Answer:

Group ‘A’	Group ‘B’
(1) Rotational Director	Retire by Rotation
(2) Appointed in Place of a director who is absent	Alternate Director
(3) Woman Director	Every Listed Company
(4) Appointee by Promoters	First Director

1H. Answer in one sentence.

Question 1.
Who is the officer responsible for the company’s financial plan?
Answer:
Chief Financial Officer is responsible for the company’s financial plan.

Question 2.
What is the importance of Secretarial Standards?
Answer:
The main aim of Secretarial Standards is to standardize all diverse secretarial practices prevailing in the corporate world.

Question 3.
Who provides guidance to the Board of Directors?
Answer:
Company Secretary provides guidance to the Board of Directors.

Question 4.
What is the tenure of ‘Managing Director?
Answer:
The tenure of the Managing director is Five Years.

1I. Correct the underlined word and rewrite the following sentences.

Question 1.
A public company must have a minimum of 15 directors.
Answer:
A public company must have a minimum of 03 directors.

Question 2.
First Directors are appointed by ROC.
Answer:
First Directors are appointed by Promoters.

Question 3.
Secretarial Standards are given by the Companies Act, 2013.
Answer:
Secretarial Standards are given by the Institute of Company Secretaries of India.

2. Explain the following terms/concepts.

Question 1.
Director
Answer:
Director is a person appointed to manage, direct and supervise the company. According to Sec-2(34) of the act, “Director means a director appointed to the Board of the company”.

Question 2.
Managing Director
Answer:
Managing Director is a director appointed by virtue of an agreement with the company; or by passing a resolution in the general meeting or by its Board of Directors or by virtue of Memorandum of Associations or Articles of Association. He is entrusted with substantial powers of management of the affairs of the company. He is appointed for a period of 5 years.

Question 3.
Independent Director
Answer:
As per section 149 of the Companies Act, 2013, any director other than a managing director, whole-time director, or a nominee director is termed as an independent director.

Question 4.
Executive Director
Answer:
Executive Director is also called as ‘Whole Time Director’, He is in full-time employment with the company. He plays an important role in the day-to-day management of the company.

Question 5.
Non-Executive Director
Answer:
Non-Executive Director is known as ‘Outside Director’. Non-Executive Director is not involved in the day-to-day management of the company. He is appointed to get second opinions from the board.

Question 6.
Alternate Director
Answer:
Alternate Director is a director who is nominated by the board in the place of absence director. He is appointed for a minimum of 3 months.

Question 7.
Casual vacancy of Director
Answer:
The casual vacancy is created due to the death of a director, which is filled by the board at the board meeting. It is valid till the vacating director’s incomplete term.

Question 8.
Chief Financial officer
Answer:
An officer responsible for the company’s finances is called Chief Financial Officer. He need not be a director of the company. He has to compulsory sign the audited financial statements of the company.

Question 9.
Company Secretary
Answer:
The company secretary is appointed to perform functions of the company and he is appointed by a resolution of the Board. He has to follow the terms and conditions decided by the board. He should be a member of ICSI.

Question 10.
Secretarial Standard
Answer:
It is formulated by ICSI and approved by Central Government through the Ministry of Corporate Affairs (MCA). The main purpose of setting Secretarial Standards is to standardized fine corporate government practices prevailing in companies.

Question 11.
Secretarial Audit
Answer:
It is an audit that monitors the compliance requirements of the company. The main aim of such an audit is to detect errors and mistakes in compliance with the rules and regulations of the Companies Act. It builds confidence among regulators, management, and shareholders of the company.

Question 12.
The Board of Directors
Answer:
Representatives elected by the Equity Shareholder in their Annual General Meeting are called as Board of Directors. They are allotted certain powers to control and manage the business of the firms.

3. Study the following case/situation and express your opinion.

1. Mr. A is a commerce graduate. He has vast experience in the field of finance and the financial market. He wishes to become a director of PQR Co. Ltd.

Question (a).
Is he required to obtain DIN?
Answer:
He was required to obtain DIN. It is compulsory to acquire DIN for every Director.

Question (b).
Can PQR Co. Ltd. object to his directorship on lack of specialized qualification?
Answer:
The company act has not prescribed any academic or professional qualification for directors, so he can obtain directorship.

Question (c).
If he is appointed as director of PQR Co. Ltd, is he entitled to remuneration?
Answer:
The managerial position entitles him to get managerial remuneration so if Mr. A is appointed as director of PQR Co. Ltd then he is entitled to remuneration.

2. Mr. Z is a member of the Institute of Company Secretaries of India.

Question (a).
Can Mr. Z be appointed as pro-tem Secretary of LMN Ltd. which is under formation?
Answer:
Yes, Mr. Z can be appointed as pro-tem secretary of LMN Ltd. which is under formation. The First Secretary is appointed by the promoters of the company.

Question (b).
Can Mr. Z work as Secretarial Auditor?
Answer:
Yes, Mr. Z can work as Secretarial Auditor because he is a member of ICSI.

Question (c).
Mr. Z wishes to be employed as whole time Secretary in companies ABC Ltd. and OPC Ltd. Is he allowed?
Answer:
Mr. Z, as a whole-time secretary, cannot hold office in more than one company. So, Mr. Z can be employed either in ABC Ltd or One Person Company and not in both.

3. Mr. M wishes to be the Managing director of QRS Ltd.

Question (a).
The age of Mr. M is 30 years. Can he be appointed as MD of a company?
Answer:
Yes, Mr. M is 30 years old and the age required to be completed for MD’s post is 21 years. So he can be appointed as MD of a Company.

Question (b).
Is it necessary that Mr. M should be one of the directors on the Board of QRS Ltd?
Answer:
Yes, It is necessary that Mr. M should be one of the directors on the board of QRS Ltd. He should be appointed by the board.

Question (c).
For how long a period QRS Ltd. can appoint Mr. M. as a Managing Director?
Answer:
QRS Ltd can appoint Mr. M. as a managing director for a period of 5 years.

4. Distinguish between the following.

Question 1.
Director and Managing Director
Answer:

Basis	Director	Managing Director
1. Meaning	Director is the elected representative of the shareholders of the company.	The managing director represents the board in the day-to-day activities of the business.
2. Appointment	He is elected at the Annual General Meeting by the members of the company.	He is appointed by the board of directors.
3. Tenure	Directors of public companies retire by rotation. Maximum tenure is of 3 years, 1/3 of Independent Director is not liable to retire by rotation.	The tenure of managing director is for a term of five years.
4. Remuneration	Remuneration for services is given as per specific provisions. The director is given sitting fees to attend the board meeting which may extend up to ₹ 1 lakh plus remuneration.	M.D is entitled to either a monthly salary or 5 % of the net profit. If more than one M.D. is appointed then maximum remuneration cannot be more than 10% of the net profit.
5. Status	Directors are elected representatives of the shareholders managing company in absence of shareholders. They can be agents of the company but not employees of the company.	Managing Director has dual status i.e. a director and a manager (employee).
6. Positions held	Director is the only member or person on the board.	The managing director is the director on the Board. M.D. is the whole time manager in the company.
7. Number of companies	Director can work in 20 companies at a time wherein a maximum of 10 public companies at a time.	A person can be an M.D. of a maximum of 2 companies at a time.

Question 2.
Managing Director and Manager
Answer:

Basis	Managing Director	Manager
1. Meaning	The Managing Director is appointed by the Board to look after the day-to-day administration of the company.	The manager is in charge of the whole management affairs of the company.
2. Appointment	The managing director is appointed by an agreement with the company or by resolution passed by the company in a Board meeting or by virtue of its Articles of Associations of the company.	The manager is appointed under a contract of service.
3. Remuneration	MD is entitled to either a monthly salary or 5% of net profit. If there is more than one managing director, the maximum remuneration payable is 10% of the net profit.	Maximum remuneration to a manager cannot be more than 5% of the net profit.
4. Number of posts	A company may have more than one Managing Director. He can be M.D. in maximum of 2 companies.	The company can have only one post of manager.
5. Power	He is given substantial powers of management.	He is entrusted with whole powers of management.
6. Position held	The managing director must be the director of the company.	The manager need not be a director of the company.

Question 3.
Managing Director and Whole Time Director
Answer:

Basis	Managing Director	Whole Time Director
1. Meaning	The managing director represents the board in the day-to-day management of the company.	The whole time director devotes whole time to the working of the company.
2. Powers	The Managing Director is given substantial powers of management.	A whole-time director does not have the power to take decisions on policy matters.
3. Number of posts	A person can be an M.D. of a maximum of 2 companies at a time.	More than one whole-time directorship is not possible at a time.
4. Performance	He manages the affairs and business of the company.	He performs important administrative functions of the company.

5. Answer in brief.

Question 1.
What is DIN?
Answer:

• It means Director Identification Number.
• DIN is a Unique Identification Number for an existing director or person intending to be the director of a company.
• It is compulsory to acquire DIN by Director.
• It helps in the detection and handling of offenses committed by a director.
• It is obtained through an online process by filing an application.

Question 2.
State any four powers of the Board of Directors.
Answer:

• Director is a person appointed to manage, direct and supervise the affairs of the company.
• The power of the Board of Directors are as follows:
• To appoint or remove key managerial personnel: The Board of Directors has the power to appoint and remove key managerial personnel.
• To recommend dividend: The board of directors recommends the dividend to the shareholders.
• To fill a casual vacancy in the Board: Casual vacancy in the board arises due to different reasons such as the death of a director who is filled by the Board at the Board meeting.
• To issue securities whether in India or abroad: Board of Director’s issue securities means shares, debentures, bonds) in India and abroad also.

Question 3.
Mention any four ways in which the office of a director becomes vacant.
Answer:
The office of a Director shall automatically become vacant in the following ways:

• Any disqualification: A person cannot be appointed as a director if he is of unsound mind or insolvent or convicted by the court.
• Absentee at Board meeting: Director who has been absent in the meeting of the board of directors held during the period of 12 months with or without taking leave of absence of the Board.
• Disqualification by Court or Tribunal: Director has to vacate office if he has been disqualified by an order of a court or the Tribunal.
• Provision of the Act: Director has to vacate office if he is removed under the provisions of the Companies Act.

Question 4.
State the powers of a Managing Director.
Answer:
As it is stated in the definition itself the Managing Director is entrusted with the substantial powers of management, which clearly indicates that he has been given certain important powers of routine business matters of a company.
The powers exercised by him are fellows:

• To act as a link between the Board of Directors and the managerial staff.
• To look after the management and administration of a company.
• To appoint the company employees.
• To participate in policymaking as well as policy execution.
• To sign contracts on behalf of a company.
• To decide about the investment of funds of a company.
• To receive remuneration from a company.

Question 5.
State the statutory duties of a company secretary.
Answer:
Secretary is an employee of the company. He enjoys the power and advises the management.
Statutory duties of a company secretary are as follows:

• To organize meetings and be present at all the meetings of the company.
• To maintain the minutes of all meetings.
• To issue notices and circulars to the members of the company.
• To maintain and update the Register of members and debenture holders and other books of the company.
• To file all necessary returns with the Registrar of Companies.
• To communicate with the shareholders on various matters.

6. Justify the following statements.

Question 1.
Directors are managing partners.
Answer:

• Directors have to work as a team as Board of Directors, not as an individual.
• The powers by Board are subject to provisions of the Companies Act and Memorandum and Articles of Associations.
• Director is required to perform his functions.
• He represents shareholders to conduct and manage the business of the company on their behalf.
• They are entrusted with vast powers of management and perform several functions which are proprietary in nature like allotment of shares, raising of loans, investing funds of the company.
• This is because they themselves are significant shareholders of the company.
• In fact, they are the most active shareholders of the company.
• Thus, Directors are the managing partners of the company.

Question 2.
A Director is an agent of the company.
Answer:

• Since the company is an artificial person, it needs to be represented by the Director.
• They deal on behalf of the company.
• Directors should deal skillfully, carefully, and diligently.
• Directors are held liable as an, while company is held liable as the principal.
• A Director is an agent as he acts between the company and shareholders.
• Thus, a director is an agent of the company.

Question 3.
The company has a distinct feature of separate ownership and management.
Answer:

• The company has a unique feature of separate ownership and management.
• Shareholders are its owner and Directors are its managers.
• Being an artificial person, it needs a human agent to manage and control the working of the company.
• Shareholders are scattered all over therefore management of the company by them is not possible.
• Also, the shareholders are not interested in the management of such a big organization.
• The company as an artificial person having no physical existence needs humans to control its affair.
• Thus, the company has a distinct feature of separate ownership and management.

Question 4.
DIN helps investors of the company.
Answer:

• DIN is a unique identification number for an existing director or person intending to be the director of the company.
• It is compulsory to acquire DIN by every Director.
• Din is Pre-require for e-filling of company’s documents.
• It helps the investors of the company to make a more accurate and informed decisions because they get to known the composition of the top management of the company.
• It also helps to handle the problems created due to a company after collecting or raising money from the public.
• Thus, I agree with the given statement.

Question 5.
Directors have to work as a team.
Answer:

• Directors have to work as a team of “Board of Directors” and not individually.
• He exercises the power as a Board which is subject to provision of the Act.
• Director is a representative of shareholders so he has to work collectively in the best interest of the company and its shareholders.
• He cannot take decisions alone on behalf of the company.
• Thus, directors have to work as a team.

Question 6.
Directors play a triple role.
Answer:

• Directors play a triple role i.e. in the form of an agent, as a managing partner, and as a trustee.
• As an agent, the director deals skillfully, carefully, and elegantly while representing the company with outsiders.
• As a managing partner, the director acts as a representative of the shareholder and manages the company on their behalf.
• As a trustee, the director acts as a guardian of the interest of shareholders and a company.
• They use the company’s funds in the most appropriate manner and cautiously.
• They are also the trustee of all the assets of the company.
• Thus, directors play a triple role.

Question 7.
Company Secretary plays a triple role.
Answer:

• Company Secretary plays a three-fold role in the form of – as a statutory officer, as a coordinator, and as an administration officer.
• As a statutory officer, the secretary signs the document for authentication, files annual returns to ROC, maintains various statutory registers and ensures compliance with the law.
• As a coordinator, the secretary acts as a network between the Board of Directors and other executive officers at different levels. He acts as an internal as well as external coordinator for the company.
• As an administrative officer, the secretary ensures the implementation of various policies of the company and also supervises and controls the functioning of various departments of the company.
• Thus, Company Secretary plays a triple role.

Question 8.
A director cannot be called an employee of the company.
Answer:

• Directors are elected representatives of the company’s shareholders.
• The status of an employee is within the limits of his contract and service.
• His employer holds the ultimate control to guide his activities and functions.
• These limits of an employee cannot be applied to a director.
• So a director cannot be called an employee of the company.
• Thus, a director cannot be called an employee of the company.

Question 9.
The managing Director has substantial powers of management.
Answer:
As it is stated in the definition itself the Managing Director is entrusted with the substantial powers of management, which clearly indicates that he has been given certain important powers of routine business matters of a company.
The powers exercised by him are as follows:

• To act as a link between the Board of Directors and the managerial staff.
• To look after the management and administration of a company.
• To appoint the company employees.
• To participate in policymaking as well as policy execution.
• To sign contracts on behalf of a company.
• To decide about the investment of funds of a company.
• To receive remuneration from a company.

Question 10.
Indian companies prefer to appoint a Managing Director than a Manager.
Answer:

• Indian company prefers to appoint managing director rather than manager because Managing Directors holds dual authorities and he is able to influence the board of director in a better way.
• Manager need not be a director of a company while the managing director has to be director of a company,
• The company cannot have more than one manager, while it can have more than one managing director.
• Thus, Indian companies prefer to appoint a managing director than a manager.

Question 11.
Pro-tem secretary is helpful to the company.
Answer:

• The first secretary of the company is appointed by the promoters of the company.
• The first secretary is called as ‘pro-tem’ secretary.
• Pro-tem secretary appointed by promoters may or may not be appointed as full-time or regular Secretary.
• Pro-tem secretary helps in fulfilling different formalities during the formation of the company.
• Thus, the Pro-tem secretary is helpful to the company.

Question 12.
Secretarial Standards should be in conformity with the Act.
Answer:

• The Secretarial Standards are formulated by the Institute of Company Secretaries of India and approved by the Central Government through the Ministry of Corporate Affairs.
• The Companies Act, 2013, makes compliance with the Secretarial Standard mandatory.
• It leads to provide better monitoring of compliances of law, strengthening the process of the Board, and create confidence in investors.
• The Secretarial Standards aim at achieving integrating, harmonizing, and standardizing fine corporate governance practices across all companies.
• Thus, Secretarial Standards should be in conformity with the Act.

Question 13.
Secretarial Standards lead to better legal compliance.
Answer:

• Companies follow diverse practices based on differing business cultures and varied usages over a period of time.
• The Secretarial Standards aim at achieving integrating, harmonizing, and standardizing fine, corporate governance across all companies
• It leads to provide better monitoring of compliance of the law, strengthening the process of the Board, and create confidence in investors.
• Secretarial Standards are reviewed by Secretarial Standard Board (SSB) once a year or whenever changes are made in the law.
• Thus, Secretarial Standards lead to better legal compliance

Question 14.
A secretarial Audit is required under the laws.
Answer:

• It is an audit that checks the compliance of various legislation including the Companies Act, other Corporate Acts, and economic laws.
• It aims at detecting errors and mistakes in the compliance mechanisms.
• It gives confidence to regulators, management authorities, and shareholders that the company is following a disciplined approach of evaluation and improve effectiveness and risk management.
• Thus, Secretarial Audit is required under the laws.

7. Answer the following questions.

Question 1.
Explain the Role of Directors.
Answer:
Director is a person appointed to manage, direct and supervise the affairs of the company.
The elected representatives of the shareholders are called Directors.

Role of the Directors:

• He helps the investors to take accurate decision.
• He has to fill casual vacancies on the board.
• He has to recommend dividends.
• He has to issue securities in India or abroad.
• He manages a company on behalf of the shareholder.
• He appoints the first auditor of the company.
• He can appoint or remove Key Managerial Personnel.
• He can borrow the money on behalf of the company.
• His role is full of trust, loyalty, care, and good faith.
• Directors act as a trustee, agent and managing partner for the company.

Question 2.
Explain the duties of a Director.
Answer:
A director’s relationship with a company is regarded as fiduciary in nature. It means his duty is full of trust, care, and good faith.
The duties of directors can be categorized into two heads:

1. Statutory Duties:
   • To file a return of Allotment.
   • To act in accordance with the Articles of the company.
   • To disclose an interest in a transaction.
   • To attend Board meetings.
   • To appoint first Auditors of the company.
2. General Duties:
   • Duty of good faith i.e. he must act in the best interest of the company.
   • Duty of care i.e. he must take utmost care in the performance of work assigned.
   • Duty not to delegate i.e. he is required to perform his function personally. He may delegate in case of emergency.

Question 3.
Explain the Managing Director.
Answer:
Definition: The Companies Act, has defined a Managing Director as “A Director who by virtue of an agreement with the company or of a resolution passed by a company in the general meeting or by its Board of Directors or by virtue of its Memorandum or Articles of Association, is entrusted with substantial powers of management of the company”.

Disqualification:

• Any person less than 21 years of age and more than 70 years of age.
• A person who is an undischarged insolvent person or has at any time been adjudged as an insolvent.
• A person who has suspended payment to his creditors or made a composition with them.
• A person who is, or has been convicted by a court of an offense with a sentence of more than 6 months period.

Appointment:
A Managing Director may be appointed by any one of the following ways:

• by an agreement with a company.
• by the resolution passed at the general meeting.
• by the Board of Directors.

Term of office:
The term of office of the Managing Director cannot exceed 5 years at a time, but he can be reappointed as such for a further period of five years.

The number of Managing Directorship:
A Managing Director can not act as such for more than two companies at the same time.

Remuneration:
The remuneration paid to the Managing Director is subject to the maximum limit of 5% of the net profit of a company or a monthly salary. If a company has more than one Managing Director then total remuneration paid to them (all) shall not exceed 10% of the net profit.

Powers of a Managing Director:

• To act as a link between the Board of Directors and the managerial staff.
• To look after the management and administration of a company.
• To appoint the company employees.
• To participate in policymaking as well as policy execution.
• To sign contracts on behalf of a company.
• To decide about the investment of funds of a company.
• To receive remuneration from a company.

Duties of a Managing Director:

• To act on behalf (agent) of the Board of Directors.
• To implement the decision of the Board.
• To supervise, direct, control, and guide the day-to-day affairs of the business.
• To guide the senior executives in their administrative work.
• To report to the Board about programmes made or any problem faced by a company.
• To chair the Board meetings and general meetings, if necessary.
• To manage routine work of a company.
• To sign all the contracts and documents on behalf of the company.

Question 4.
Explain the Company Secretary.
Answer:
Meaning:

• Secretary is an employee of the company and he is appointed to perform functions of a company secretary,
• He should be a member of the Institute of Company Secretaries of India (ICSI).
• The first secretary is appointed by the promoter of the company and he is called a ‘pro-tem’ secretary.
• He holds liable for non-compliance with the provisions of the Act.

Duties of a Company Secretary:
It is categorized as (A) Statutory Duties and (B) General Duties.

(A) Statutory Duties:

• To organize and attend meetings of the company.
• To prepare minutes of meetings.
• To communicate with shareholders on various matters.
• To issue notices and circulars to the members of the company.
• To maintain various Registers and books of the company
• To file returns with the ROC.

(B) General Duties:

• To provide guidance to the Board of Directors as needed.
• To discharge duties towards regulators and authorities of the company.
• To assist the Board of Directors in conducting the business of the company.
• To perform duties allotted by the Board.

Rights of a Secretary:

• To control and supervise the working of departments of the company.
• To get indemnified by the company, if any loss is suffered by the secretary.
• To sign documents requiring authentication.
• To get remuneration from the company.

Question 5.
Explain the role of the Company Secretary.
Answer:
The company secretary plays a crucial and important role in the administration of the company.
The emphasis on good governance has increased the role of the secretary in protecting the interest of investors.

Role of Company Secretary:

• Secretary as a Statutory officer:
• To sign documents for authentication.
• To sign and deliver Annual Returns and other documents and to the Registrar of Companies.
• To maintain different statutory registers like
  • Minutes of General and Board meetings of the company.
  • Registers of Members and Debenture holders Register of Directors and KMP and their shareholdings.
• To ensure compliance with the law

(ii) Secretary as a Co- ordinator:

• To implement policies framed by the Board.
• To act as a link between the Board and other executives at different levels.
• To act as a mouthpiece or spokesperson of the Board.
• To act as an internal and external coordinator.

(iii) Secretary as an Administration officer:

• To ensure implementation of the policies of the company.
• To supervise and control the functioning of different departments of the company.
• To take an overall view of different aspects of the company’s administration and develop a strong and efficient organizational setup.
• To contribute to the administration of the company.

Maharashtra State Board 11th Std Secretarial Practice Textbook Solutions Digest

• 11th Secretarial Practice Chapter 1 Practical Problems
• 11th Secretarial Practice Chapter 2 Practical Problems
• 11th Secretarial Practice Chapter 3 Practical Problems
• 11th Secretarial Practice Chapter 4 Practical Problems
• 11th Secretarial Practice Chapter 5 Practical Problems
• 11th Secretarial Practice Chapter 6 Practical Problems
• 11th Secretarial Practice Chapter 7 Practical Problems
• 11th Secretarial Practice Chapter 8 Practical Problems
• 11th Secretarial Practice Chapter 9 Practical Problems
• 11th Secretarial Practice Chapter 10 Practical Problems
• 11th Secretarial Practice Chapter 11 Practical Problems
• 11th Secretarial Practice Chapter 12 Practical Problems