# NCERT Solutions for Class 11 Maths

Find 100% accurate solutions for NCERT Class XI Maths. All questions have been explained and solved step-by-step, to help you understand thoroughly. Free Download option available!

# Binomial Theorem

1.    (1 – 2x)5

2.

3.    (2x – 3)6

4.

5.

6.     (96)3

7.     (102)5

8.     (101)4

9.     (99)5

10.   Using binomial theorem, indicate which number is larger (1.1)1000 or 1000.

11.   Find (a + b)4 – (a – b)4. Hence evaluate:

12.   Find (x + 1)6 + (x – 1)6. Hence or otherwise evaluate

13.   Show that 9n+1 – 8n – 9 is divisible by 64 whenever n is a positive integer.

14.   Prove that

Exercise 2

15.   x5 in (x + 3)8

16.   a5b7 in (a – 2b)12

17.   (x2 – y)6

18.   (x2 – yx)12, x ≠ 0

19.   Find the 4th term in the expansion of (x – 2y)12.

20.   Find the 13th term in the expansion of

Find the middle terms in the expansion of:

21.

22.

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

24.   The coefficients of the (r – 1)th, rth and (r + 1)th terms in the expansion of (x + 1)n are in the ratio 1 : 3 : 5. Find n and r.

25.   Prove that the coefficient of xn in the expansion of (1 + x)2n is twice the coefficient of xn in the expansion of (1 + x)2n-1.

26.   Find a positive value of m for which the coefficient of x2 in the expansion (1 + x)m is 6.

27.   Find a, b and n in the expansion of (a + b)n if the first three terms of the expansion are 729, 7290 and 30375 respectively.

28.   Find a if the coefficient of x2 and x3 in the expansion of (3 + ax)9 are equal.

29.   Find the coefficient of x5 in the product (1 + 2x)6 (1 – x)7 using binomial theorem.

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

31.   Evaluate:

32.   Find the value of

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

34.   Find n, if the ratio of the fifth term from the beginning to the fifth term from the end in the expansion of

35.   Expand using binomial theorem

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

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