List of top Questions asked in WBJEE

$58.4\, gm$ of $NaCl$ and $180\,gm$ of glucose were separately dissolved in $1000 \,mL$ of water. Identify the correct statement regarding the elevation of boiling point ($b.pt$) of the resulting solutions.

The sum $1\times 1! + 2 \times 2! + ... + 50 \times 50!$ equals

The magnetic flux linked with a coil satisfies the relation $\phi= (4t^2 + 6t + 9) Wb$, where $t$ is the time in second. The e.m.f. induced in the coil at $t\, =\, 2$ second is

In a mercury thermometer, the ice point (lower fixed point) is marked as $10^{\circ}$ and the steam point (upper fixed point) is marked as $130^{\circ}$. At $40^{\circ} C$ temperature, what will this thermometer read?

From the top of a tower, $80\, m$ high from the ground, a stone is thrown in the horizontal direction with a velocity of $8\, ms^{-1}.$ The stone reaches the ground after a time ?t? and falls at a distance of ?d? from the foot of the tower. Assuming $g=10\, ms^{-2},$ the time t and distance d are given respectively by

Water is flowing through a very narrow tube. The velocity of water below which the flow remains a streamline flow is known as

The line $x=2 y$ intersects the ellipse $\frac{x^{2}}{4}+y^{2}=1$ at the points $P$ and $Q$. The equation of the circle with $P Q$ as diameter is

If $\sin ^{-1} x+\sin ^{-1} y+\sin ^{-1} z=\frac{3 \pi}{2}$, then the value of $x^{9}+y^{9}+z^{9}-\frac{1}{x^{9} y^{9} z^{9}}$ is equal to

There are $100$ students in a class. In an examination, $50$ of them failed in Mathematics, $45$ failed in Physics, $40$ failed in Biology and $32$ failed in exactly two of the three subjects. Only one student passed in all the subjects. Then the number of students failing in all the three subjects.

The number of integer values of $m$, for which the $x$-coordinate of the point of intersection of the lines $3x + 4y = 9$ and $y = mx + 1$ is also an integer, is

In a slide callipers, $(m + 1)$ number of vernier divisions is equal to m number of smallest main scale divisions. If d unit is the magnitude of the smallest main scale division, then the magnitude of the vernier constant is

Let $A$ and $B$ be two events with $P\left(A^{c}\right)=0.3, P\left(B\right)=0.4$ and $P\left(A\cap B^{c}\right)=0.5$ Then $P\left(B|A \cup B^{c} \right) $ is equal to

Rolle's theorem is applicable in the interval $[-2, 2]$ for the function

If $\log _{e}\left(x^{2}-16\right) \leq \log _{e}(4 x-11)$, then

The coefficient of $x^{10}$ in the expansion of $1+\left(1+x\right)+\ldots+\left(1+x\right)^{20}$ is

The incentre of an equilateral triangle is $(1,1)$ and the equation of one side is $3 x+4 y+3=0$ Then, the equation of the circumcircle of the triangle is

An urn contains $8$ red and $5$ white balls. Three balls are drawn at random. Then the probability that balls of both colours are drawn is

If the first ionization energy of $H$ atom is $13.6\, eV$, then the $2^{nd}$ ionization energy of He atom is

The eccentric angle in the first quadrant of a point on the ellipse $\frac{x^{2}}{10}+\frac{y^{2}}{8}=1$ at a distance $3$ units from the centre of the ellipse is

The value of $\displaystyle \lim_{n \to \infty}\frac{\left(n!\right)^{\frac{1}{n}}}{n}$ is

Let $p, q$ and $r$ be the side4s opposite to the angles $P, Q$ and $R$, respectively in a $\Delta P Q R$. Then, $2 p r \sin \left(\frac{P-Q+R}{2}\right)$ equals

The area of the region bounded by the curves $y=x^{3}, y=\frac{1}{x}, x=2$ is

The solution of $25\frac{d^{2}y}{dx^{2}}-10 \frac{dy}{dx}+y=0, \, y\left(0\right) =1, \, y\left(1\right)=2e^{\frac{1}{5}} $ is

The value of the integral $\int\limits_{0}^{\pi / 2} \frac{1}{1+(\tan x)^{101}} d x$ is equal to