## NCERT Exemplar Problems Class 11 Mathematics Chapter 8 Binomial Theorem

**Short Answer Type Questions:
Q1. Find the term independent of x, where x≠0, in the expansion of **

**Q2. If the term free from x is the expansion of is 405, then find the value of k.**

**Sol:** Given expansion is

**Q3. Find the coefficient of x in the expansion of (1 – 3x + 1x ^{2})( 1 -x)^{16}.**

**Sol: **(1 – 3x + 1x^{2})( 1 -x)^{16}

**Q4. Find the term independent of x in the expansion of **

**Sol: **Given Expression

**Q5. Find the middle term (terms) in the expansion of**

**Q6. Find the coefficient of x ^{15} in the expansion of **

**Sol:** Given expression is ** **

**Q7. Find the coefficient of in the expansion of **

**Q8. Find the sixth term of the expansion (y ^{1/2} + x^{1/3})^{n}, if the binomial coefficient of the third term from the end is 45.**

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**Q9. 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.**

**Q10. If the coefficient of second, third and fourth terms in the expansion of (1 + x) ^{2}” are in A.P., then show that 2n^{2} – 9n + 7 = 0.**

**Q11. Find the coefficient of x ^{4} in the expansion of (1 + x + x^{2} + x^{3})^{11}.**

**Long Answer Type Questions**

**Q12. If p is a real number and the middle term in the expansion is 1120, then find the value of p.**

**Q15. In the expansion of (x + a) ^{n}, if the sum of odd term is denoted by 0 and the sum of even term by Then, prove that**

**Q17. Find the term independent ofx in the expansion of (1 +x + 2x ^{3})**

**Objective Type Questions**

**Q18. 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

**Q19. If 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**

**Q20. The two successive terms in the expansion of (1 + x) ^{24} whose coefficients are in the ratio 1 : 4 are
(a) 3^{rd} and 4^{th} **

**(b) 4**

^{th}and 5^{th}**(c) 5**

^{th}and 6^{th}**(d) 6**

^{th}and 7^{th}**Q21. The coefficients of x ^{n} in the expansion of (1 + x)^{2n} and (1 + x)^{2n} ~^{1} are in the ratio**

**(a) 1 : 2**

**(b) 1 : 3**

**(c) 3 : 1**

**(d) 2:1**

**Q22. If the coefficients of 2 ^{nd}, 3^{rd} and the 4^{th} terms in the expansion of (1 + x)^{n} are in A.P., then the value of n is**

(a) 2

**(b) 7**

**(c) 11**

**(d) 14**

**Q23. If A and B are coefficients of x ^{n }in the expansions of (1 + x)^{2n} and (1 + x)^{2n}–^{1 }**

^{ }

**respectively, then A/B equals to**