SATHEE: Binomial Theorem 1 Question 24

Binomial Theorem 1 Question 24

26.

Given positive integers $r > 1, n > 2$ and the coefficient of $(3 r)$ th and $(r + 2)$ th terms in the binomial expansion of $(1 + x)^{2 n}$ are equal. Then,

(1980, 2M)

(a) $n = 2 r$

(b) $n = 2 r + 1$

(d) None of these

Show Answer

Answer:

Correct Answer: 26. (a)

Solution:

In the expansion $(1 + x)^{2 n}, t_{3 r} =^{2 n} C_{3 r - 1} (x)^{3 r - 1}$

and $t_{r + 2} =^{2 n} C_{r + 1} (x)^{r + 1}$

Since, binomial coefficients of $t_{3 r}$ and $t_{r + 2}$ are equal.

$\begin{aligned} ∴^{2 n} C_{3 r - 1} =^{2 n} C_{r + 1} \\ \Rightarrow 3 r - 1 = r + 1 or 2 n = (3 r - 1) + (r + 1) \\ \Rightarrow 2 r = 2 or 2 n = 4 r \\ \Rightarrow r = 1 or n = 2 r \\ But r > 1 \end{aligned}$

$∴$ We take, $n = 2 r$

Binomial Theorem 1 Question 24

26.

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

Binomial Theorem 1 Question 24

26.

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

Menu