NCERT solution Class 11 binomial theorem

NCERT Solutions

Class 11 Maths

Binomial Theorem

NCERT Questions

Ex.8.1 Q.1
Ex.8.1 Q.2
Ex.8.1 Q.3
Ex.8.1 Q.4
Ex.8.1 Q.5
Ex.8.1 Q.6
Ex.8.1 Q.7
Ex.8.1 Q.8
Ex.8.1 Q.9
Ex.8.1 Q.10
Ex.8.1 Q.11
Ex.8.1 Q.12
Ex.8.1 Q.13
Ex.8.1 Q.14
Ex.8.2 Q.1
Ex.8.2 Q.2
Ex.8.2 Q.3
Ex.8.2 Q.4
Ex.8.2 Q.5
Ex.8.2 Q.6
Ex.8.2 Q.7
Ex.8.2 Q.8
Ex.8.2 Q.9
Ex.8.2 Q.10
Ex.8.2 Q.11
Ex.8.2 Q.12
Ex.Misc Q.1
Ex.Misc.Q.2
Ex.Misc.Q.3
Ex.Misc.Q.4
Ex.Misc.Q.5
Ex.Misc.Q.6
Ex.Misc.Q.7
Ex.Misc.Q.8
Ex.Misc.Q.9
Ex.Misc.Q.10

Ex.Misc.Q.2

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

It is known that (r + 1)^th term, (T_r+1), in the binomial expansion of (a + b)ⁿ is given by

T_r+1 = ⁿC_r a^n-r b^r

Assuming that x² occurs in the (r + 1)^th term in the expansion of (3 + ax)⁹, we obtain

T_r+1 = ⁹C_r (3)^{9 - r}(ax)^r= ⁹C_r a^r x^r

Comparing the indices of x in x² and in T_{r + 1}, we obtain r = 2

Thus, the coefficient of x² is

⁹C₂ 3^9-2 a²= {9! ÷ (2! × 7!)} × 3⁷ a²= 36 × 3⁷ a²

Assuming that x³ occurs in the (k + 1)^th term in the expansion of (3 + ax)⁹, we obtain

T_k+1 = ⁹C_k (3)^{9 - r}(ax)^k= ⁹C_r (3)^{9 - k}a^k x^k

Comparing the indices of x in x³ and in T_{k+ 1}, we obtain k = 3

Thus, the coefficient of x³ is

⁹C₃ 3^9-3 a³= {9! ÷ (3! × 6!)} × 3⁶ a³= 84 × 3⁶ a³

It is given that the coefficients of x² and x³ are the same.

=> 84 × 3⁶ a³= 36 × 3⁷ a²

=> 84a = 36 × 3

=> a =

Thus, the required value of a is .

Video solution:

Binomial Theorem Class 11 Maths NCERT Chapter 7 NCERT Solutions

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NCERT solutions of Binomial Theorem Class 11 Maths - all questions of all exercises are solved. Q. No. 1, 2, 3, and so on. Complete explanation and detailed solution makes them the best videos for Class 11 Maths Binomial Theorem NCERT solutions.