21
MCQ (Single Correct Answer)
The coefficient of $x^n$ in the expansion of $(1+x)^{2 n}$ and $(1+x)^{2 n-1}$ are in the ratio
A
$1: 2$
B
$1: 3$
C
$3: 1$
D
$2:1$
22
MCQ (Single Correct Answer)
If the coefficients of 2 nd , 3 rd and the 4 th terms in the expansion of $(1+x)^n$ are in AP, then the value of $n$ is
A
2
B
7
C
11
D
14
23
MCQ (Single Correct Answer)
If $A$ and $B$ are coefficient of $x^n$ in the expansions of $(1+x)^{2 n}$ and $(1+x)^{2 n-1}$ respectively, then $\frac{A}{B}$ equals to
A
1
B
2
C
$\frac{1}{2}$
D
$\frac{1}{n}$
24
MCQ (Single Correct Answer)
If the middle term of $\left(\frac{1}{x}+x \sin x\right)^{10}$ is equal to $7 \frac{7}{8}$, then the value of $x$ is
A
$2 n \pi+\frac{\pi}{6}$
B
$n \pi+\frac{\pi}{6}$
C
$n \pi+(-1)^n \frac{\pi}{6}$
D
$n \pi+(-1)^n \frac{\pi}{3}$
25
The largest coefficient in the expansion of $(1+x)^{30}$ is .............. .
Explanation
Largest coefficient in the expansion of $(1+x)^{30}={ }^{30} \mathrm{C}_{30 / 2}={ }^{30} \mathrm{C}_{15}$