WBJEE PYQs for Limits and Derivatives with Solutions: Practice WBJEE Previous Year Questions

Updated 3+ months ago

Limits and Derivatives 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 Limits and Derivatives with explanations for effective preparation. Practice of WBJEE Mathematics PYQs including Limits and Derivatives questions regularly will improve accuracy, speed, and confidence in the WBJEE 2026 exam.

WBJEE PYQs for Limits and Derivatives with Solutions

1.
Let $x_{n}=\left(1-\frac{1}{3}\right)^{2}\left(1-\frac{1}{6}\right)^{2}\left(1-\frac{1}{10}\right)^{2} ........ \left(1-\frac{1}{\frac{n\left(n+1\right)}{2}}\right)^2, n \ge 2.$ Then the value of $\displaystyle \lim_{n \to \infty} x_n$ is
- 44564
- 44570
- Jan-81
- 0
View Solution
2.
If $f(5)=7$ and $f^{'}(5)=7$ then $\displaystyle\lim _{x \rightarrow 5} \frac{x f(5)-5 f(x)}{x-5}$ is given by
- 35
- -35
- 28
- -28
View Solution
3.
$f A + B + C =,$ then $\tan (\frac{A}{2}) \tan (\frac{B}{2}) + \tan (\frac{B}{2}) \tan (\frac{C}{2}) + \tan (\frac{C}{2}) \tan (\frac{A}{2})$ is equal to
- (A) π/6
- (B) 3
- (C) 2
- (D) 1
View Solution
4.
The limit of $ \sum\limits^{1000}_{ n-1} (-1)^n \, x^n $ as $x?8$
- does not exist
- exists and equals to 0
- exists and approaches to $+\propto$
- exists and approaches $-8$
View Solution
5.
It $\displaystyle \lim_{x \to 0}$$\frac{axe^{x}-b\, \log\left(1+x\right)}{x^{2}}=3$ then the values of $a, b$ are respectively
- 44594
- 44563
- 44593
- 2, 0
View Solution
6.
Let f(x) = x³e^–3x, x ^gt 0. Then the maximum value of f(x) is
- (A) e^–3
- (B) 3e^–3
- (C) 27e^–9
- (D) ∞
View Solution
7.
The sum of n terms of an AP is n² + n; the common difference will be:
- (A) n - 1
- (B) 1
- (C) 2
- (D) -4
View Solution
8.
$\displaystyle\lim _{x \rightarrow 0} \frac{\sin |x|}{x}$ is equal to
- 1
- 0
- positive infinity
- does not exist
View Solution
9.
$\displaystyle\lim _{x \rightarrow 0} \frac{\pi^{x}-1}{\sqrt{1+x}-1}$
- does not exist
- equals $\log_{e} \left(\pi^{2}\right)$
- equals $1$
- lies between $10$ and $11$
View Solution

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WBJEE PYQs for Limits and Derivatives with Solutions

1.Let $x_{n}=\left(1-\frac{1}{3}\right)^{2}\left(1-\frac{1}{6}\right)^{2}\left(1-\frac{1}{10}\right)^{2} ........ \left(1-\frac{1}{\frac{n\left(n+1\right)}{2}}\right)^2, n \ge 2.$ Then the value of $\displaystyle \lim_{n \to \infty} x_n$ is

2.If $f(5)=7$ and $f^{'}(5)=7$ then $\displaystyle\lim _{x \rightarrow 5} \frac{x f(5)-5 f(x)}{x-5}$ is given by

3.fA+B+C=, then tan⁡(A2)tan⁡(B2)+tan⁡(B2)tan⁡(C2)+tan⁡(C2)tan⁡(A2) is equal to

4.The limit of $ \sum\limits^{1000}_{ n-1} (-1)^n \, x^n $ as $x?8$

5.It $\displaystyle \lim_{x \to 0}$$\frac{axe^{x}-b\, \log\left(1+x\right)}{x^{2}}=3$ then the values of $a, b$ are respectively

6.Let f(x) = x3e–3x, x ^gt 0. Then the maximum value of f(x) is

7.The sum of n terms of an AP is n2 + n; the common difference will be:

8.$\displaystyle\lim _{x \rightarrow 0} \frac{\sin |x|}{x}$ is equal to

9.$\displaystyle\lim _{x \rightarrow 0} \frac{\pi^{x}-1}{\sqrt{1+x}-1}$

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1.
Let $x_{n}=\left(1-\frac{1}{3}\right)^{2}\left(1-\frac{1}{6}\right)^{2}\left(1-\frac{1}{10}\right)^{2} ........ \left(1-\frac{1}{\frac{n\left(n+1\right)}{2}}\right)^2, n \ge 2.$ Then the value of $\displaystyle \lim_{n \to \infty} x_n$ is

2.
If $f(5)=7$ and $f^{'}(5)=7$ then $\displaystyle\lim _{x \rightarrow 5} \frac{x f(5)-5 f(x)}{x-5}$ is given by

3.
$f A + B + C =,$ then $\tan (\frac{A}{2}) \tan (\frac{B}{2}) + \tan (\frac{B}{2}) \tan (\frac{C}{2}) + \tan (\frac{C}{2}) \tan (\frac{A}{2})$ is equal to

4.
The limit of $ \sum\limits^{1000}_{ n-1} (-1)^n \, x^n $ as $x?8$

5.
It $\displaystyle \lim_{x \to 0}$$\frac{axe^{x}-b\, \log\left(1+x\right)}{x^{2}}=3$ then the values of $a, b$ are respectively

6.
Let f(x) = x³e^–3x, x ^gt 0. Then the maximum value of f(x) is

7.
The sum of n terms of an AP is n² + n; the common difference will be:

8.
$\displaystyle\lim _{x \rightarrow 0} \frac{\sin |x|}{x}$ is equal to

9.
$\displaystyle\lim _{x \rightarrow 0} \frac{\pi^{x}-1}{\sqrt{1+x}-1}$