Functions 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 Functions with explanations for effective preparation. Practice of WBJEE Mathematics PYQs including Functions questions regularly will improve accuracy, speed, and confidence in the WBJEE 2026 exam.
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WBJEE PYQs for Functions with Solutions
1.
Let f(x)=\(\begin{Bmatrix} x+1&\,\,\,-1\leq x\leq 0\\ -x&\,\,\,\,\,0<x\leq1 \end{Bmatrix}\)- f(x) is discontinuous in [-1,1] and so has no maximum value or minimum value in [-1,1].
- f(x) is continuous in [-1,1] and so has maximum and minimum value
f(x) is bounded in[-1,1] and doesn't attain maximum or minimum value
f(x) is discontinuous in [-1,1] but still has the maximum and minimum value
2.
Let \(R\) be the set of all real numbers and \(f : R \rightarrow R\) be given by \(f(x) = 3x^2 + 1\).Then the set \(f ^{-1}\left(\left[1, 6\right]\right)\) is- $\left\{-\sqrt{\frac{5}{3}},0, \sqrt{\frac{5}{3}}\right\}$
- $\left[-\sqrt{\frac{5}{3}}, \sqrt{\frac{5}{3}}\right]$
- $\left[-\sqrt{\frac{1}{3}}, \sqrt{\frac{1}{3}}\right]$
- $\left(-\sqrt{\frac{5}{3}}, \sqrt{\frac{5}{3}}\right)$
3.
Let $R$ be a relation defined on the set $Z$ of all integers and $xRy$ when $x + 2y$ is divisible by $3$. Then- $R$ is not transitive
- $R$ is symmetric only
- $R$ is an equivalence relation
- $R$ is not an equivalence relation
4.
Let $f(x) = x^{4} - 4x^{3} + 4x^{2} +c, c \in \mathbb{R}.$ Then- f(x) has infinitely many zeros in (1, 2) for all c
- f(x) has exactly one zero in (1, 2) if -1 < c < 0
- f(x) has double zeros in (1, 2) if -1 < c < 0
- Whatever be the value of c, f(x) has no zero in (1, 2)
5.
Suppose f:R\(\rightarrow\)R be given by f(x)={\(e^{(x^{10}-1)}+(x-1)^2sin\frac{1}{1-x},if\,\,\,x\neq1\)}, then- f'(1) does not exist
- f'(1) exists and is zero
- f'(1) exist and is 9
- f'(1) exists and is 10
6.
The function $f\left(x\right) = \sec \left[\log\left(x+\sqrt{1+x^{2}}\right)\right]$ is- odd
- even
- neither odd nor even
- constant
7.
If $log_{2}\,6+\frac{1}{2x} = log_{2}\left(2^{\frac{1}{x}} + 8\right)$, then the values of x are- $\frac{1}{4}, \frac{1}{3}$
- $\frac{1}{4}, \frac{1}{2}$
- $-\frac{1}{4}, \frac{1}{2}$
- $\frac{1}{3}, \frac{1}{^{-}2}$
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