List of top Questions asked in WBJEE

The standard Gibbs free energy change $(\Delta G^\circ)$ at 25$^{\circ}$C for the dissociation of $N_2O_4(g)$ to $NO_2(g)$ is (given, equilibrium constant = $0.15, R = 8.314 \, J/K/mol)$
The best method for preparation of $Me_3CCN$ is
In basic medium the amount of $Ni^{2+}$ in a solution can be estimated with the dimethylglyoxime reagent. The correct statement(s) about the reaction and the product is(are)
In $SOCl_2$, the $Cl-S-Cl$ and $Cl-S-O$ bond angles are
$2$-Methylpropane on monochlorination under photochemical condition give
Four small objects each of mass m are fixed at the corners of a rectangular wire-frame of negligible mass and of sides $a$ and $b (a > b)$. If the wire frame is now rotated about an axis passing along the side of length b, then the moment of inertia of the system for this axis of rotation is
An equilateral triangle is made by uniform wires $AB, BC, CA. A$ current $I$ enters at $A$ and leaves from the mid point of $BC$. If the lengths of each side of the triangle is $L$, the magnetic field $B$ at the centroid $O$ of the triangle is
An electron of charge $e$ and mass $m$ is moving in circular path of radius $r$ with a uniform angular speed $\omega$. Then which of the following statements are correct ?
An alpha particle (He)has a mass of 4.00300 amu. A proton has mass of 1.00783 amu and a neutron has mass of 1.00867 amu respectively. The binding energy of alpha particle estimated from these data is the closest to
The limit of $ \sum\limits^{1000}_{ n-1} (-1)^n \, x^n $ as $x?8$
If the distance between the foci of an ellipse is equal to the length of the latus rectum, then its eccentricity is
The area of the region enclosed between parabola $y^2 = x$ and the line $y = mx$ is $\frac{1}{48}. $
There are two coins, one unbiased with probability $\frac{1}{2}$ of getting heads and the other one is biased with probability $\frac{3}{4}$ of getting heads. A coin is selected at random and tossed. It shows heads up. Then the probability that the unbiased coin was selected is
Let $f(?) = (1+sin^2?)(2-sin^2?)$. Then for all values of $?$
The value of the determinant $\begin{vmatrix}1+a^{2}-b^{2}&2ab&-2b\\ 2ab&1-a^{2}+b^{2}&2a\\ 2b&-2a&1-a^{2}-b^{2}\end{vmatrix}$ is equal to
Silicone oil is obtained from the hydrolysis and polymerisation of
?Sulphan? is
The value of the integral is equal to $\int\limits^{\frac{\pi}{3}}_{\frac{\pi}{6}} \frac{\left(sin\,x - xcos\, x\right)}{x\left(x+sin\,x\right)}dx$ is
If $f(x) = e^x (x - 2)^2$ then
The value of the integral $ \int\limits^2_{1}e^{x} \left(log_{e} \,x + \frac{x+1}{x}\right)dx$ is
A car moving at a velocity of 17 $ms^{-1}$ towards an approaching bus that blows a horn at a frequency of $640\ Hz$ on a straight track. The frequency of this horn appears to be $680\, Hz$ to the car driver. If the velocity of sound in air is $340\,m\,s^{-1}$, then velocity of the approaching bus is
$3$ moles of a mono-atomic gas $(\gamma = 5/3)$ is mixed with $1$ mole of a diatomic gas $(\gamma = 7/5)$. The value of $?$ for the mixture will be
The value of $I = \int \limits^ \frac{\pi}{4}_{0}\left(tan^{n+1} x\right)dx + \frac{1}{2} \int \limits^ \frac{\pi}{2}_{0} tan^{n-1} \left(x / 2\right)dx$ is equal to
Ribose and 2-deoxyribose can be differentiated by
Identify the CORRECT statement