Binomial Theorem PYQs - Last 5 Years

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All Binomial Theorem PYQs Last 10 Years Create chapter test

Practice 47 TS EAMCET 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 47 of 47 filtered questions.

1Binomial Theorem

When $|x|<\frac{1}{2}$ the coefficient of $x^6$ in the expansion of $\left(\frac{2-x}{1+2 x}\right)^2$ is

2Binomial Theorem

If $C_0, C_1, C_2, \ldots, C_{10}$ represent the binomial coefficients in the expansion of $(1+x)^{10}$, then
\(C_0 C_6+C_1 C_7+C_2 C_8+C_3 C_9+C_4 C_{10}=\)

3Binomial Theorem

Let $K$ be the number of rational terms in the expansion of $(\sqrt{2}+\sqrt[3]{3})^{6144}$. If the coefficient of $x^P(P \in N)$ in the expansion of $\frac{1}{(1+x)\left(1+x^2\right)\left(1+x^4\right)\left(1+x^8\right)\left(1+x^{16}\right)...

4Binomial Theorem

Numerically greatest term in the expansion of $(3 x-4 y)^{23}$ when $x=\frac{1}{6}$ and $y=\frac{1}{8}$ is

5Binomial Theorem

If $C_0, C_1, C_2, \ldots, C_8$ are the binomial coefficients in the expansion of $(1+x)^8$, then $\sum\limits_{r = 1}^8 {} r^3 \frac{C_r}{C_{r-1}}=$

6Binomial Theorem

Numerically greatest term in the expansion of $(2 x-3 y)^n$ when $x=\frac{7}{2}, y=\frac{3}{7}$ and $n=13$ is

7Binomial Theorem

The coefficient of $x^{12}$ in the expansion of $\left(x^2+2 x+2\right)^8$ is

8Binomial Theorem

If $C_0, C_1, C_2, \ldots, C_n$ are the binomial coefficients in the expansion of $(1+x)^n$ then the value of $\Sigma r^3 \cdot C_r$ when $n=5$ is

9Binomial Theorem

If $X \sim B(7, P)$ is a binomial variate and $P(X=3)=P(X=5)$, then $P=$

10Binomial Theorem

If the expression $5^{2 n}-48 n+k$ is divisible by 24 for all $n \in N$, then the least positive integral value of $k$ is

11Binomial Theorem

If the coefficient of 3rd term from the beginning in the expansion of $\left(a x^2-\frac{8}{b x}\right)^9$ is equal to the coefficient of 3rd term from the end in the expansion of $\left(a x-\frac{2}{b x^2}\right)^9$, then the relation betw...

12Binomial Theorem

When $|x|>3$, then coefficient of $\frac{1}{x^n}$ in the expansion of $x^{3 / 2}(3+x)^{1 / 2}$ is

13Binomial Theorem

The constant term in the expansion of $\left(1+\frac{1}{x}\right)^{20}\left(30 x(1+x)^{29}+(1+x)^{30}\right)$ is

14Binomial Theorem

For $n \in N$ the largest positive integer that divides $81^n+20 n-1$ is $k$. If $S$ is the sum of all positive divisors of $k$, then $S-k=$

15Binomial Theorem

The numerically greatest term in the expansion of $(3 x-16 y)^{15}$, when $x=\frac{2}{3}$ and $y=\frac{3}{2}$, is

16Binomial Theorem

If the coefficients of 3 consecutive terms in the expansion of $(1+x)^{23}$ are in arithmetic progression, then those terms are

17Binomial Theorem

The set of all real values of $x$ for which the expansion of $\left(125 x^{2}-\frac{27}{x}\right)^{\frac{-2}{3}}$ is valid, is

18Binomial Theorem

The coefficient of $x y^{2} z^{3}$ in the expansion of $(x-2 y+3 z)^{6}$ is

19Binomial Theorem

If $p$ and $q$ are the real numbers such that the 7 th term in the expansion of $\left(\frac{5}{p^3}-\frac{3 q}{7}\right)^8$ is 700 , then $49 p^2=$

20Binomial Theorem

If $T_4$ represents the 4 th term in the expansion of $\left(5 x+\frac{7}{x}\right)^{\frac{-3}{2}}$ and $x \notin\left[-\sqrt{\frac{7}{5}}, \sqrt{\frac{7}{5}}\right]$, then $\left(x^7 \sqrt{5 x}\right) T_4=$

21Binomial Theorem

If $X \sim B(6, p)$ is a binomial variate and $\frac{P(X=4)}{P(X=2)}=\frac{1}{9}$, then $p=$

22Binomial Theorem

If $3^{2 n+2}-8 n-9$ is divisible by $2^{p}, \forall n \in \mathrm{~N}$, then the maximum value of $P$ is

23Binomial Theorem

If the coefficient fo $x^{r}$ in the expansion of $\left(1+x+x^{2}+x^{3}\right)^{100}$ is $a_{r}$ and $S=\sum_{r=0}^{300} a_{r}$ then $\sum_{r=0}^{300} r \cdot a_{r}=$

24Binomial Theorem

If $(-c, c)$ is the set of all values of $x$ for which the expansion of $(7-5 x)^{\frac{-2}{3}}$ is valid, then $5 c+7=$

25Binomial Theorem

If $n$ is a positive integer and $f(n)$ is the coefficient of $x^n$ in the expansion of $(1+x)(1-x)^n$, then $f(2023)=$

26Binomial Theorem

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

27Binomial Theorem

The term independent of $x$ in the expansion of $\left(1-3 x+2 x^3\right)\left(\frac{3 x^2}{2}-\frac{1}{3 x}\right)^9$ is

28Binomial Theorem

If $\sum_{r=0}^{20}{ }^{20+r} C_r=\frac{p}{q}{ }^{40} C_{20}$ and GCD of $(p, q)=1$, then $p^2-q^2=$

29Binomial Theorem

If $x=\frac{2 \cdot 5}{2!3}+\frac{2 \cdot 5 \cdot 7}{3!3^2}+\frac{2 \cdot 5 \cdot 7 \cdot 9}{4!3^3}+\ldots$, then $x^2+8 x+8=$

30Binomial Theorem

If the coefficient of $x^4$ in the expansion of $\frac{x}{(x-1)^2(x-2)}$ is $\frac{m}{n}$ and $|m|,|n|$ are coprimes, then $\sqrt{|m+n|}=$

31Binomial Theorem

Let $C_0, C_1, C_2, \ldots, C_n$ be the binomial coefficients in the expansion of $(1+x)^n$. If $S_{n+1}=5 \cdot C_0+8 \cdot C_1+11 \cdot C_2+\ldots(n+1)$ terms, then $S_{11}=$

32Binomial Theorem

If $|x|$ is so small that $x^3$ and higher powers of $x$ can be neglected, then an approximate value of $\frac{1}{\sqrt{4-x}(2+x)^3}$ is

33Binomial Theorem

In the expansion of $(x-2 y+3 z)^5$, if the total number of terms is $p$ and the coefficient of $x^2 y z^2$ is $q$, then $\frac{q}{p}=$

34Binomial Theorem

The numerically greatest term in the binomial expansion of $(2 x-3 y)^5$, when $x=\frac{3}{2}$ and $y=\frac{2}{3}$ is

35Binomial Theorem

If $\frac{2 x^3+3 x^2+3 x+5}{\left(x^2+1\right)\left(x^2+2\right)}$ is expanded in terms of the powers of $x$, then the coefficient of $x^5$ is

36Binomial Theorem

If the term independent of $x$ in the expansion of $\left(\sqrt{x}-\frac{k}{x^2}\right)^{10}$ is 405 , then $k=$

37Binomial Theorem

The coefficient of $x^{50}$ in the expansion of $(1+x)^{101}\left(1-x+x^2\right)^{100}$ is

38Binomial Theorem

The number of rational terms in the binomial expansion $(\sqrt[4]{5}+\sqrt[5]{4})^{100}$ is

39Binomial Theorem

The expansion of $\left(1+x+x^2\right)^{-3 / 2}$ in powers of $x$ is valid, if

40Binomial Theorem

The number of integral terms in the expansion of $(\sqrt{3}+\sqrt[8]{5})^{256}$ is

41Binomial Theorem

If $(1+x)^n=c_0+c_1 x+c_2 x^2+\ldots \ldots+c_n x^n$ for $n \in N$, then $c_0+\frac{c_1}{2}+\frac{c_2}{3}+\ldots \ldots+\frac{c_n}{n+1}=$

42Binomial Theorem

$\frac{1}{8}-\frac{7}{8 \cdot 12}+\frac{7 \cdot 10}{8 \cdot 12 \cdot 16}-\ldots=$

43Binomial Theorem

Numerically greatest term in the expansion of $(2 x-3 y)^{11}$ when $x=\frac{1}{3}$ and $y=\frac{1}{2}$ is

44Binomial Theorem

If $k$ is the coefficient of $x^5$ in the expansion of $\left(2 x^2-\frac{1}{3 x^3}\right)^5$, then $\frac{3 k}{2}=$

45Binomial Theorem

The expansion of $(a+x)^n$ contains 15 terms. When $x=1$ the ratio of the neighbouring terms to the middle term in this expansion is 16 . Then, the positive integral value of ' $a$ ' is

46Binomial Theorem

If $L$ and $M$ are respectively the coefficient of $x^{-7}$ in $\left(a x+\frac{b}{x^2}\right)^{11}$ and the coefficient of $x^7$ in $\left(b x^2+\frac{a}{x^2}\right)^{11}$, then $L+M=$

47Binomial Theorem

If the 4 th term in the expansion of $\left(\frac{x}{2}-\frac{2 y}{3}\right)^6$ is -20, then $x y=$