Binomial theorem is an important topic in the Mathematics section in WBJEE exam. Practising this topic will increase your score overall and make your conceptual grip on WBJEE exam stronger.
This article gives you a full set of WBJEE PYQs for Binomial theorem with explanations for effective preparation. Practice of WBJEE Mathematics PYQs including Binomial theorem questions regularly will improve accuracy, speed, and confidence in the WBJEE 2026 exam.
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WBJEE PYQs for Binomial theorem with Solutions
1.
If \( (1 + x - 2x^2)^6 = 1 + a_1x + a_2x^2 + \ldots + a_{12}x^{12} \), then the value of \( a_2 + a_4 + a_6 + \ldots + a_{12} \) is:- \( 21 \)
- \( 31 \)
- \( 32 \)
- \( 64 \)
2.
The coefficient of $ x^{-10}$ in $\left(x^{2} - \frac{1}{x^{3}}\right)^{10}$ is- $-252$
- $-210$
- $-(5!)$
- $-120$
3.
The coefficient of \(a^{10}b^7c^3\) in the expansion of \((bc + ca + ab)^{10}\) is:- 140
- 150
- 120
- 160
4.
The remainder obtained when \(1!+2!+3!+.....+11!\) is divided by 12 is- 9
- 8
- 7
- 6
5.
If \( n = 1, 2, 3, \dots \), then \( \cos \alpha \cos 2\alpha \cos 4\alpha \dots \cos^{2n - 1} \alpha \) is equal to:- (A)
- (B)
- (C)
- (D)
6.
If $C_{0}, C_{1}, C_{2}, \ldots, C_{n}$ denote the coefficients in the expansion of $(1+x)^{n}$, then the value of $C_{1}+2C_{2}+3C_{3}+\ldots+nC_{n}$ is- $n\cdot2^{n-1}$
- $(n+1)2^{n-1}$
- $(n+1)2^{n}$
- $(n+2)2^{n-1}$
7.
If sin θ and cos θ are the roots of the equation ax2 – bx + c = 0, then a, b and c satisfy the relation- (A) a2 + b2 + 2ac = 0
- (B) a2 – b2 + 2ac = 0
- (C) a2 + c2 + 2ab = 0
- (D) a2 – b2 – 2ac = 0
8.
The coordinates of a moving point p are (2t2 + 4, 4t + 6). Then its locus will be a- (A) circle
- (B) straight line
- (C) parabola
- (D) ellipse
9.
If \((1 + x + x^2 + x^3)^5 = \sum_{k=0}^{15} a_k x^k\), then \(\sum_{k=0}^{7} (-1)^k \cdot a_{2k}\) is equal to:- \(2^5\)
- \(4^5\)
- \(0\)
- \(4^4\)
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