## Rajasthan Board RBSE Class 11 Maths Chapter 7 Binomial Theorem Ex 7.5

Question 1.

If y is two small as compared to x, then prove

Solution:

Question 2.

If x is too small such that x^{2} and higher powers are negligible then find the value of following expressions :

Solution:

Ignoring x^{2} and terms of higher order

Question 3.

Find the value of:

(i) √3o upto 4 places of decimal

(ii) (1.03)^{1/3} upto 4 places of decimal

(iii) [latex]\frac { 1 }{ { (8.16) }^{ 1/3 } } [/latex] 4 places of decimal

(iv) Cube root of 126 upto 5 places of decimal

Solution :

(i) Value of √30 upto 4 places of decimal

= 6 (1 – 0 08333 – 0 – 00347 – 0 – 00029 + …]

= 6 (1 – 0 – 08709] = 6(0 – 91291]

= 5.47746 = 5- 4775 (upto four places).

(ii) Value of (1.03)^{1/3} upto 4 places of decimal (1.03)^{1/3}= (1 + 0-03)^{1/3
}

(iv) Value of cube root of 126 upto 5 places of decimal Cube root of 126

Question 4.

If x is approximately equal to 1, then prove that :

Solution:

Question 5.

If p and q are approximately equal, then Prove that

Solution:

∵ p and q are approximately equal

∴ p = q + h

where h is too small whose higher order terms can be neglected.