Binomial Theorem · Mathematics · AP EAPCET
MCQ (Single Correct Answer)
1
The independent term in the expansion of $\left(1+x+2 x^2\right)\left(\frac{3 x^2}{2}-\frac{1}{3 x}\right)^9$ is
AP EAPCET 2024 - 23th May Morning Shift
2
For $|x|<\frac{1}{\sqrt{2}}$, the coefficient of $x$ in the expansion of $\frac{(1-4 x)^2\left(1-2 x^2\right)^{1 / 2}}{(4-x)^{3 / 2}}$ is
AP EAPCET 2024 - 23th May Morning Shift
3
If $P$ is the greatest divisor of $49^n+16 n-1$ for all $n \in N$, then the number of factors of $P$ is
AP EAPCET 2024 - 22th May Evening Shift
4
If the coefficients of $r$ th, $(r+1)$ th and $(r+2)$ th terms in the expansion of $(1+x)^n$ are in the ratio of $4: 15: 42$, then $n-r$ is equal to
AP EAPCET 2024 - 22th May Evening Shift
5
If the coefficients of $(2 r+6)$ th and $(r-1)$ th terms in the expansion of $(1+x)^{21}$ are equal, then the value of $r$ is equal to
AP EAPCET 2024 - 22th May Evening Shift
6
If the $2 \mathrm{nd}, 3 \mathrm{rd}$ and 4 th terms in the expansion of $(x+a)^n$ are $96,216,216$ respectively and $n$ is a positive integer, then $a+x=$
AP EAPCET 2024 - 22th May Morning Shift
7
If $|x|<1$, then the number of terms in the expansion of $\left[\frac{1}{2}\left(1 \cdot 2+2 \cdot 3 x+3 \cdot 4 x^2+\ldots . \infty\right)\right]^{-25}$
AP EAPCET 2024 - 22th May Morning Shift
8
If the ratio of the terms equidistant from the middle term in the expansion of $(l+x)^{12}$ is $\frac{1}{256}(x \in N)$, then sum of all the terms of the expansion $(1+x)^{12}$ is
AP EAPCET 2024 - 21th May Evening Shift
9
If the eleventh term in the binomial expansion of $(x+a)^{15}$ is the geometric mean of the eighth and twelfth terms, then the greatest term in the expansion is
AP EAPCET 2024 - 21th May Morning Shift
10
The sum of the rational terms in the binomial expansion of $\left(\sqrt{2}+3^{1 / 5}\right)^{10}$ is
AP EAPCET 2024 - 21th May Morning Shift
11
If the coefficients of $x^5$ and $x^6$ are equal in the expansion of $\left(a+\frac{x}{5}\right)^{65}$, then the coefficient of $x^2$ in the expansion of $\left(a+\frac{x}{5}\right)^4$ is.
AP EAPCET 2024 - 20th May Evening Shift
12
If $|x|<\frac{2}{3}$, then the 4th term in the expansion of $(3 x-2)^{\frac{2}{3}}$ is :
AP EAPCET 2024 - 20th May Evening Shift
13
The coefficient of $x^5$ in the expansion of $\left(2 x^3-\frac{1}{3 x^2}\right)^5$ is
AP EAPCET 2024 - 20th May Morning Shift
14
Numerically greatest term in the expansion of $(5+3 x)^6$ When, $x=1$, is
AP EAPCET 2024 - 19th May Evening Shift
15
The square root of independent term in the expansion of $ \left( 2x^2 + \frac{5}{x} \right)^5 $ is
AP EAPCET 2024 - 18th May Morning Shift
16
The coefficient of $x^5$ in $\left(3+x+x^2\right)^6$ is
AP EAPCET 2024 - 18th May Morning Shift
17
The absolute value of the difference of the coefficients of $x^4$ and $x^6$ in the expansion of $x^2 - 2x^2 + (x + 1)^4(x^2 - 1)^2$, is
AP EAPCET 2024 - 18th May Morning Shift
18
The least value of $$n$$ so that $${ }^{(n-1)} C_3+{ }^{(n-1)} C_4>{ }^n C_3$$
AP EAPCET 2022 - 4th July Evening Shift