Binomial Theorem · JEE Main previous year questions

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2025 7 questions

Q142025 · 4 Apr 2025 · Shift 1
For an integer $n \geq 2$ , if the arithmetic mean of all coefficients in the binomial expansion of $(x + y)^{2 n - 3}$ is $16$ , then the distance of the point $P (2 n - 1, n^{2} - 4 n)$ from the line $x + y = 8$ is
1. A. $2$
2. B. $22$
3. C. $52$
4. D. $32$
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Answer: D
Q192025 · 4 Apr 2025 · Shift 1
In the expansion of $(32 + \frac{1}{3 3})^{n}, n \in N$ , if the ratio of $1 5^{th}$ term from the beginning to the $1 5^{th}$ term from the end is $\frac{1}{6}$ , then the value of $^{n} C_{3}$ is
1. A. $4960$
2. B. $2300$
3. C. $1040$
4. D. $4060$
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Answer: B
Q152025 · 3 Apr 2025 · Shift 1
The sum of all rational terms in the expansion of $(2 + 3)^{8}$ is :
1. A.16923
2. B.18817
3. C.3763
4. D.33845
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Answer: B
Q192025 · 2 Apr 2025 · Shift 1
The term independent of $x$ in the expansion of $(\frac{( x + 1 )}{( x ^{2/3} + 1 - x ^{1/3} )} - \frac{( x - 1 )}{( x - x ^{1/2} )})^{10}, x > 1$ , is :
1. A.240
2. B.120
3. C.150
4. D.210
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Answer: D
Q42025 · 24 Jan 2025 · Shift 1
For some $n \neq = 10$ , let the coefficients of the $5 th$ , $6 th$ and $7 th$ terms in the binomial expansion of $(1 + x)^{n + 4}$ be in A.P. Then the largest coefficient in the expansion of $(1 + x)^{n + 4}$ is:
1. A. $10$
2. B. $35$
3. C. $70$
4. D. $20$
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Answer: B
Q92025 · 24 Jan 2025 · Shift 2
Suppose $A$ and $B$ are the coefficients of $3 0^{th}$ and $1 2^{th}$ terms respectively in the binomial expansion of $(1 + x)^{2 n - 1}$ . If $2 A = 5 B$ , then $n$ is equal to:
1. A.20
2. B.19
3. C.22
4. D.21
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Answer: D
Q152025 · 23 Jan 2025 · Shift 2
If in the expansion of $(1 + x)^{p} (1 - x)^{q}$ , the coefficients of $x$ and $x^{2}$ are $1$ and $- 2$ , respectively, then $p^{2} + q^{2}$ is equal to :
1. A.8
2. B.20
3. C.13
4. D.18
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Answer: C