 # NCERT Exemplar Solutions for Class 11 Maths Chapter 8 Binomial Theorem

NCERT Exemplar Solutions Class 11 Maths Chapter 8 Binomial Theorem contains all the solutions to the Maths problems provided in the NCERT Exemplar textbook. The questions from every section are framed and solved accurately by the subject experts. NCERT Exemplar Solutions for Class 11 is a detailed and step-by-step guide to all the queries of the students. The exercises present in the chapter should be dealt with utmost sincerity, if one wants to score well in the examinations.

NCERT Exemplar Solutions for Class 11 Maths are focused on learning various Mathematics tricks and shortcuts for quick and easy calculations. Students can easily get the PDF of NCERT Exemplar Solutions for Class 11 Maths Chapter 8 Binomial Theorem from the given links. Let us have a look at some of the important concepts that are discussed in this chapter.

• Binomial theorem
• Some important observations on binomial theorem
• The p th term from the end
• Middle terms
• Binomial coefficient

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Exercise Page no: 296

1. Find the term independent of x, x ≠ 0, in the expansion of

Solution:

2. If the term free from x in the expansion of is 405, find the value

of k.

Solution:

3. Find the coefficient of x in the expansion of
(1 – 3x + 7x2) (1 – x)16.

Solution:

Given (1 – 3x + 7x2) (1 – x)16

Coefficient of x = -19

4.

Solution:

5. Find the middle term (terms) in the expansion of

Solution:

6. Find the coefficient of x15 in the expansion of
(x – x2)10.

Solution:

Given (x – x2)10

7. Find the coefficient of 1/x17 in the expansion of

Solution:

8. Find the sixth term of the expansion if the binomial coefficient of

the third term from the end is 45.

Solution:

9. Find the value of r, if the coefficients of (2r + 4)th and (r – 2)th terms in the expansion of (1 + x)18 are equal.

Solution:

10. If the coefficient of second, third and fourth terms in the expansion of (1 + x)2n are in A.P. Show that 2n2 – 9n + 7 = 0.

Solution:

11. Find the coefficient of x4 in the expansion of (1 + x + x2 + x3)11.

Solution:

12. If p is a real number and if the middle term in the expansion of

Is 1120, find p.

Solution:

Solution:

Solution:

15. In the expansion of (x + a)n if the sum of odd terms is denoted by O and the sum of even term by E. Then prove that

(i) O2 – E2 = (x2 – a2)n

(ii) 4OE = (x + a)2n – (x – a)2n

Solution:

(ii) 40 E = (O + E)2 – (O – E)2

= (x – a)2n – (x – a)2n

16. If xp occurs in the expansion of

Prove that its coefficient is

Solution:

17. Find the term independent of x in the expansion of

Solution:

Objective TYPE questions:

Choose the correct answer from the given options in each of the Exercises 18 to 24 (M.C.Q.).

18. The total number of terms in the expansion of
(x + a)100 + (x – a)100 after simplification is

(A) 50 (B) 202 (C) 51 (D) none of these

Solution:

(C) 51

Explanation:

Given (x + a)100 + (x – a)100

So, there are 51 terms

Hence option c is the correct answer.

19. Given the integers r > 1, n > 2, and coefficients of (3r)th and (r + 2)nd terms in the binomial expansion of (1 + x)2n are equal, then

(A) n = 2r (B) n = 3r (C) n = 2r + 1 (D) none of these

Solution:

(A) n = 2r

Explanation:

Given (1 + x)2n

Hence option A is the correct answer.

20. The two successive terms in the expansion of (1 + x)24 whose coefficients are in the ratio 1: 4 are

(A) 3rd and 4th (B) 4th and 5th (C) 5th and 6th (D) 6th and 7th

Solution:

(C) 5th and 6th

Explanation: