Balbharti Maharashtra State Board 11th Maths Book Solutions Pdf Chapter 4 Methods of Induction and Binomial Theorem Ex 4.4 Questions and Answers.

## Maharashtra State Board 11th Maths Solutions Chapter 4 Methods of Induction and Binomial Theorem Ex 4.4

Question 1.

State, by writing the first four terms, the expansion of the following, where |x| < 1.

(i) (1 + x)^{-4}

Solution:

(ii) (1 – x)^{1/3}

Solution:

(iii) (1 – x^{2})^{-3}

Solution:

(iv) (1 + x)^{-1/5}

Solution:

(v) (1 + x^{2})^{-1}

Solution:

Question 2.

State by writing first four terms, the expansion of the following, where |b| < |a|.

(i) (a – b)^{-3}

Solution:

(a – b)^{-3} = \(\left[a\left(1-\frac{b}{a}\right)\right]^{-3}\)

(ii) (a + b)^{-4}

Solution:

(iii) (a + b)^{1/4}

Solution:

(iv) (a – b)^{-1/4}

Solution:

(a – b)^{-1/4} = \(\left[a\left(1-\frac{b}{a}\right)\right]^{\frac{-1}{4}}\)

(v) (a + b)^{-1/3}

Solution:

Question 3.

Simplify the first three terms in the expansion of the following:

(i) (1 + 2x)^{-4}

Solution:

(ii) (1 + 3x)^{-1/2}

Solution:

(iii) (2 – 3x)^{1/3}

Solution:

(iv) (5 + 4x)^{-1/2}

Solution:

(v) (5 – 3x)^{-1/3}

Solution:

Question 4.

Use the binomial theorem to evaluate the following upto four places of decimals.

(i) √99

Solution:

= 10 [1 – 0.005 – 0.0000125 – ……]

= 10(0.9949875)

= 9.94987 5

= 9.9499

(ii) \(\sqrt[3]{126}\)

Solution:

(iii) \(\sqrt[4]{16.08}\)

Solution:

(iv) (1.02)^{-5}

Solution:

(v) (0.98)^{-3}

Solution: