Binomial Theorem PYQs - Last 5 Years

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All Binomial Theorem PYQs Last 10 Years Create chapter test

Practice 46 AP EAPCET Mathematics questions from Binomial Theorem. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.

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Last 5 Years Binomial Theorem Questions

Showing 46 of 46 filtered questions.

1Binomial Theorem

If $x$ is positive real number and the first negative term in the expansion of $(1+x)^{\frac{27}{5}}$ is $t_k$, then $k=$

2Binomial Theorem

\(\frac{1}{81^n}-{ }^{2 n} C_1 \frac{10}{81^n}+{ }^{2 n} C_2 \frac{10^2}{81^n}-\ldots+\frac{10^{2 n}}{81^n}=\)

3Binomial Theorem

\(\sum_{r=1}^{15} r^2\left(\frac{{ }^{15} C_r}{{ }^{15} C_{r-1}}\right)=\)

4Binomial Theorem

The remainder obtained when $(2 m+1)^{2 n}(m, n \in N)$ is divided by 8 is

5Binomial Theorem

The numerically greatest term in the expansion of $(x+3 y)^{13}$, when $x=\frac{1}{2}$ and $y=\frac{1}{3}$ is

6Binomial Theorem

In the binomial expansion of $(p-q)^{14}$, if the sum of 7th term and 8 th term is zero, then $\frac{p+q}{p-q}=$

7Binomial Theorem

The coefficient of $x^{10}$ in the expansion of $\left(x+\frac{2}{x}-5\right)^{12}$ is

8Binomial Theorem

Let $S_1=\sum\limits_{j=1}^{10} j(j-1) \cdot{ }^{10} C_j, S_2=\sum\limits_{j=1}^{10} j \cdot{ }^{10} C_j$ and
\(S_3=\sum\limits_{j=1}^{10} j^2 \cdot{ }^{10} C_j\)
Assertion (A) $S_3=55 \times 2^9$
Reason (R) $S_1=90 \times 2^8$ and $S_2=1...

9Binomial Theorem

Sum of the coefficients of $x^4$ and $x^6$ in the expansion of $\left(1+x-x^2\right)^6$ is

10Binomial Theorem

If $y=\frac{3}{4}+\frac{3 \cdot 5}{4 \cdot 8}+\frac{3 \cdot 5 \cdot 7}{4 \cdot 8 \cdot 12}+\ldots+\infty$, then

11Binomial Theorem

If the coefficients of $x^{10}$ and $x^{11}$ in the expansion of $\left(1+\alpha x+\beta x^2\right)(1+x)^{11}$ are 396 and 144 respectively, then $\alpha^2+\beta^2=$

12Binomial Theorem

If $-\frac{2}{3} < x < \frac{2}{3}$, then the value of the 5 th term in the expansion of $\frac{1}{\sqrt[3]{2-3 x}}$ when $x=\frac{1}{2}$ is

13Binomial Theorem

The mean and variance of a binomial distribution are $x$ and 5 respectively. If $x$ is an integer, then the possible values for $x$ are

14Binomial Theorem

If $C_0, C_2, \ldots, C_n$ are the binomial coefficients in the expansion of $(1+x)^n$, then
\(\left(C_0+C_1\right)-\left(C_2+C_3\right)+\left(C_4+C_5\right)-\left(C_6+C_7\right)+\ldots=\)

15Binomial Theorem

If $11^{12}-11^2=k\left(5 \times 10^9+6 \times 10^9+33 \times 10^8\right. \left.+110 \times 10^7+\ldots+33\right)$, then $k=$

16Binomial Theorem

If $k$ is a positive integer and $10^k$ is a divisor of the number $9^{11}+11^9$, then the greatest value of $k$ is

17Binomial Theorem

The number of all possible values of $k$ for which the expansion $(\sqrt{x}+\sqrt[k]{y})^{10}$ will have exactly nine irrational terms is

18Binomial Theorem

The coefficient of $x^3$ in the power series expansion of $\frac{1+4 x-3 x^2}{(1+3 x)^3}$ is

19Binomial Theorem

The terms containing $x^r y^s$ (for certain $r$ and $s$ ) are present in both the expansions of $\left(x+y^2\right)^{13}$ and $\left(x^2+y\right)^{14}$. If $\alpha$ is the number of such terms, then the $\operatorname{sum} \alpha \sum_{r, s...

20Binomial Theorem

The coefficient of $x^3$ in the expansion of $\frac{x^4+1}{\left(x^2+1\right)(x-1)}$ when it is expressed in terms of positive integral powers of $x$, is

21Binomial Theorem

Coefficient of $x^2$ in the expansion of $\left(x^2+x-2\right)^5$ is

22Binomial Theorem

If $P_n$ denotes the product of the binomial coefficients in the expansion of $(1+x)^n$, then $\frac{P_{n+1}}{P_n}=$

23Binomial Theorem

If $x$ is so large that terms containing $x^{-3}, x^{-4}, x^{-5}, \ldots$ can be neglected, then the approximate value of $\left(\frac{3 x-5}{4 x^2+3}\right)^{-1 / 5}$ is

24Binomial Theorem

If $(1+x)^n=\sum_{r=0}^n C, x^r$, then the value of $C_0+\left(C_0+C_1\right)+\left(C_0+C_1+C_2\right)+\ldots+ \left(C_0+C_1+C_2+\ldots+C_n\right)$ is

25Binomial Theorem

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

26Binomial Theorem

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

27Binomial Theorem

If $|x|<1$, then the number of terms in the expansion of $\left[\frac{1}{2}\left(1 \cdot 2+2 \cdot 3 x+3 \cdot 4 x^2+\ldots . \infty\right)\right]^{-25}$

28Binomial Theorem

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 $a+x=$

29Binomial Theorem

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

30Binomial Theorem

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

31Binomial Theorem

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

32Binomial Theorem

The sum of the rational terms in the binomial expansion of $\left(\sqrt{2}+3^{1 / 5}\right)^{10}$ is

33Binomial Theorem

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

34Binomial Theorem

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

35Binomial Theorem

The coefficient of $x^5$ in the expansion of $\left(2 x^3-\frac{1}{3 x^2}\right)^5$ is

36Binomial Theorem

If $|x|<\frac{2}{3}$, then the 4th term in the expansion of $(3 x-2)^{\frac{2}{3}}$ is :

37Binomial Theorem

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.

38Binomial Theorem

Numerically greatest term in the expansion of $(5+3 x)^6$ When, $x=1$, is

39Binomial Theorem

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

40Binomial Theorem

The coefficient of $x^5$ in $\left(3+x+x^2\right)^6$ is

41Binomial Theorem

The square root of independent term in the expansion of $ \left( 2x^2 + \frac{5}{x} \right)^5 $ is

42Binomial Theorem

If $C_j$ stands for ${ }^n C_j$, then
\(\frac{C_1}{C_0}+\frac{2 \times C_2}{C_1}+\frac{3 \times C_3}{C_2}+\ldots+\frac{n \times C_n}{C_{n-1}}=\)

43Binomial Theorem

If $(2-5 x)^{\frac{-1}{5}}=a_0+a_1 x+a_2 x^2+\ldots$, then $\frac{a_1}{a_2}=$

44Binomial Theorem

If $C_j={ }^n C_j$, then $C_0 C_r+C_1 C_{r+1}+C_2 C_{r+2}+\ldots+C_{n-r} C_n=$

45Binomial Theorem

The coefficient of the highest power of $x$ in the expansion of $\left(x+\sqrt{x^2-1}\right)^8+\left(x-\sqrt{x^2-1}\right)^8$ is

46Binomial Theorem

The least value of \(n\) so that \({ }^{(n-1)} C_3+{ }^{(n-1)} C_4>{ }^n C_3\)