CBSE Class 11 Mathematics Binomial Theorem Worksheet Set 01

Q.1 Find the middle term in the expansion of (x - 1/6y)¹⁰.

Q.2 If a and b are distinct integers, prove that a – b is a factor of aⁿ – bⁿ, whenever n is a positive integer.

Q.3 Write the general term in the expansion of (x² – y)⁶.

Q.4 The sum of first two terms of a G.P. is -1/64 and the sum of first three terms is 6/34. What is the seventh term?

Q.5 In the expansion of (1 + x)³⁴, the coefficients of (2r+1)th and (r +2)th terms are equal, find r.

Q.6 Find the coefficient of a4 in the product (1+2a)⁴.(2-a)⁵, using binomial theorem.

Q.7 Find the value of (a² + √a² - 2)⁴ + (a² - √a² - 1)⁴

Q.8 Find an approximation of (0.99)5 using the first three terms of its expansion.

Q.9 Find the expansion of (3x² – 2ax + 3a²)³ using binomial theorem.

Q.10 In the expansion of (1+a)^m+n, prove that coefficients of am and an are equal.

Q.11 Find the coefficient of x⁵y⁷ in the expansion of (x + 2y)¹².

Q.12 Find the general term in the expansion of (5x² - 1/6x)¹¹

Q.13 Find the number of terms in the expansion of [(x + y)³(x - y)³]².

Q.14 Find the rth term from the end in the expansion of (x+a)ⁿ.

Q.15 If the coefficients of T_r, T_r+1, T_r+2 terms of (1 + x)¹⁴ are in arithmetic progression, then find the value of r.

Q.16 If the coefficients of 7^th and 13^th terms in the expansion of (1 + x)n are equal then find the value of n.

Q.17 If the ratio of the coefficients of 3rd and 4th terms in the expansion of  (x - 1/2x)ⁿ is 1:2 then find the value of n.

Q.18 The coefficients of three consecutive terms in the expansion of (1+a)nare in the ratio 1:7:42. Find n.

Q.19 Prove that ⁿ∑_r=0 3^{r n} C_r = 4_n

Q.20 Show that the coefficients of the middle term in the expansion of (1+x)²ⁿ is equal to the sum of the coefficients of two middle terms in the expansion of (1+x)^2n-1.