List of top Questions asked in WBJEE- 2026

Let domain and range of \(f(x)\) and \(g(x)\) is \([0,\infty)\). If \(f(x)\) is an increasing function, \(g(x)\) is a decreasing function, \(h(x)=f\{g(x)\}\), \(h(0)=0\) and \(p(x)=h(x^{3}-2x^{2}+2x)-h(4)\) then for all \(x\in(0,2)\):

Let 10 Bags \(B_{1},B_{2},\dots,B_{10}\) which contain 21, 22, \dots, 30 different articles respectively. Then the total number of ways to bring out 10 articles from a Bag is:

Number of elements in the range set of $f(x)=\left[\frac{x}{15}\right]\left[-\frac{15}{x}\right]$, for all $x \in (0,90)$; (where $[\cdot]$ denotes the greatest integer function) is:

If \(\vec{a}=\hat{i}+\hat{j}+\hat{k}\), \(\vec{b}=\hat{i}-\hat{j}+\hat{k}\), \(\vec{c}=\hat{i}+2\hat{j}-\hat{k}\) then the value of \(\left|\begin{matrix}\vec{a}\cdot\vec{a}&\vec{a}\cdot\vec{b}&\vec{a}\cdot\vec{c}\\ \vec{b}\cdot\vec{a}&\vec{b}\cdot\vec{b}&\vec{b}\cdot\vec{c}\\ \vec{c}\cdot\vec{a}&\vec{c}\cdot\vec{b}&\vec{c}\cdot\vec{c}\end{matrix}\right|\) is equal to:

The general solution of the equation \(\sin^{100}x-\cos^{100}x=1\) is:

Intercepts of the plane \(\vec{r}\cdot\vec{n}=d \ (\ne0)\) on the coordinate axes respectively are:

The minimum length of intercept on any tangent to the ellipse \(\frac{x^{2}}{4}+\frac{y^{2}}{9}=1\) cut by the circle \(x^{2}+y^{2}=25\) is:

Let \(a_{1},a_{2},a_{3},\dots\) are in G.P. such that \(n>m\), \(a_{n}>a_{m}\) and \(a_{1}+a_{n}=66\), \(a_{2}\cdot a_{n-1}=128\). If \(\sum_{r=1}^{n}a_{r}=126\), then \(n\) is:

The point of intersection of \(\vec{r}\times\vec{a}=\vec{b}\times\vec{a}\) and \(\vec{r}\times\vec{b}=\vec{a}\times\vec{b}\), where \(\vec{a}=\hat{i}+\hat{j}\) and \(\vec{b}=2\hat{i}-\hat{k}\) is:

The position vectors of two adjacent sides of a rectangle \(OACB\) are \(\vec{a}\) and \(\vec{b}\) respectively, where \(O\) is the origin. If \(16|\vec{a}\times\vec{b}|=3(|\vec{a}|+|\vec{b}|)^{2}\) and \(\theta\) be the acute angle between the diagonals \(OC\) and \(AB\), then the value of \(\tan\left(\frac{\theta}{2}\right)\) is:

If \(a=\lim_{n\rightarrow\infty}\cos^{2n}x\), \((x=n\pi)\) and \(b=\lim_{n\rightarrow\infty}\cos^{2n}x\), \((x\ne m\pi)\), then numerical value of the area of the triangle whose vertices are \((a,b)\), \((-2,1)\) and \((2,1)\) is:

Let \(A=[a,\infty)\) denotes the domain, then \(f:[a,\infty)\rightarrow B\) which is defined by \(f(x)=2x^{3}-3x^{2}+6\) will have an inverse for the smallest real value of \(a\) if:

A mapping is selected at random from all mappings \(f:A\rightarrow A\) where set \(A=\{1,2,3,\dots,n\}\). If the probability that the mapping is injective is \(\frac{3}{32}\), then the value of \(n\) is:

The true set of values of \(K\) for which \(\sin^{-1}\left(\frac{1}{1+\sin^{2}x}\right)=\frac{K\pi}{6}\) may have a solution is:

If the locus of mid point of any normal chord of the parabola \(y^{2}=4x\) is \(x-\lambda=\frac{\mu}{y^{2}}+\frac{y^{2}}{\nu}\), \(\lambda,\mu,\nu\in\mathbb{N}\), then \((\lambda+\mu+\nu)\) equals to:

If \(\int\frac{\csc^{2}x-2010}{\cos^{2010}x}dx=-\frac{f(x)}{(g(x))^{2010}}+c\), where \(f\left(\frac{\pi}{4}\right)=1\), then the number of solutions of the equation \(\frac{f(x)}{g(x)}=\{x\}\) in \([0,2\pi]\) is/are (where \(\{\cdot\}\) represents fractional part function):

On the set \(\mathbb{R}\) of real numbers the relation \(\rho\), defined by \(x\rho y\) \((x,y\in\mathbb{R})\) iff:

If \(0<\alpha<\beta<\gamma<\frac{\pi}{2}\) then the equation \(\frac{1}{x-\sin\alpha}+\frac{1}{x-\sin\beta}+\frac{1}{x-\sin\gamma}=0\) has:

Which of the following statements is always true?

If \[ f(x)=\frac{1+x}{1-x} \] and \(A\) is a matrix such that \(A^{3}=0\), then \[ f(A)= \]

\(t_n\) denotes the nth term of an A.P. and \[ t_p=\frac{1}{q}, \qquad t_q=\frac{1}{p}. \] Then which one of the following options is a root of the equation \[ (p+2q-3r)x^{2}+(q+2r-3p)x+(r+2p-3q)=0? \]