List of top Questions asked in WBJEE

Suppose $M=\int\limits_{0}^{\pi / 2} \frac{\cos x}{x+2} d x$, $N=\int\limits_{0}^{\pi / 4} \frac{\sin x \cos x}{(x+1)^{2}} d x$ Then, the value of $(M-N)$ equals

Out of $7$ consonants and $4 $ vowels, the number of words (not necessarily meaningful) that can be made, each consisting of $3$ consonants and $2 $ vowels, is

The angle of intersection between the curves $y=\left[\left|\sin\,x\right|+\left|\cos\,x\right|\right]$ and $x^{2}+y^{2}=10, $ where $[x]$ denotes the greatest integer $= x,$ is

The minimum value of $2^{\sin\, x} + 2^{\cos\, x}$ is

The hydrides of the first elements in groups $15 - 17$, namely $NH_3, H_2O$ and $HF$ respectively show abnormally high values for melting and boiling points. This is due to

The coefficient of $x^3$ in the infinite series expansion of $\frac{2}{\left(1-x\right)\left(2-x\right)},$ for $\left|x\right|< 1,$ is

To observe an elevation of boiling point of $0.05^?C$, the amount of solute (Mol. $Wt. = 100$) to be added to $100\, g$ of water $(K_b=0.5)$ is

Metal ion responsible for the Minamata disease is

The compound that will have a permanent dipole moment among the following is

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

The equation of the common tangent with positive slope to the parabola $y^{2}=8\sqrt{3x}$ and the hyperbola $4x^2 - y^2 = 4$ is

To determine the coefficient of friction between a rough surface and a block, the surface is kept inclined at $45^{\circ}$ and the block is released from rest. The block takes a time $t$ in moving a distance $d$. The rough surface is then replaced by a smooth surface and the same experiment is repeated. The block now takes a time $t / 2$ in moving down the same distance $d$. The coefficient of friction is

Three capacitors $3\, \mu F , 6 \, \mu F$ and $6\, \mu F$ are connected in series to a source of $120 \, V$. The potential difference, in volt, across the $3 \, \mu F$ capacitor will be

The remainder obtained when \(1!+2!+3!+.....+11!\) is divided by 12 is

The point on the parabola $y^2 = 64x$ which is nearest to the line $4x + 3y + 35 = 0$ has coordinates

The bond angle in $NF _{3}\left(102.3^{\circ}\right)$ is smaller than $NH _{3} (107.2 \left.^{\circ}\right)$. This is because of

When phenol is treated with $D_2SO_4/D_2O$, some of the hydrogens get exchanged. The final product in this exchange reaction is

Two gases $X$ (Mol. Wt. $M_x$) and $Y$ (Mol. Wt. $M_Y; M_Y > M_x$) are at the same temperature T in two different containers. Their root mean square velocities are $C_X$ and $C_Y$ respectively. If the average kinetic energies per molecule of two gases $X$ and $Y$ are $E_x$ and $E_Y$ respectively, then which of the following relation (s) is (are) true?

The number of amino acids and number of peptide bonds in a linear tetrapeptide (made of different amino acids) are respectively

The energy of gamma $(?)$ ray photon is $E_?$ and that of an X-ray photon is $E_x$. If the visible light photon has an energy of $E_v$ , then we can say that

A particle moves with constant acceleration along a straight line starting from rest. The percentage increase in its displacement during the $4^{th}$ second compared to that in the $3^{rd}$ second is

A solid uniform sphere resting on a rough horizontal plane is given a horizontal impulse directed through its center so that it starts sliding with an initial velocity $v_0$. When it finally starts rolling without slipping the speed of its center is

A uniform solid spherical ball is rolling down a smooth inclined plane from a height $h$. The velocity attained by the ball when it reaches the bottom of the inclined plane is $v$. If the ball is now thrown vertically upwards with the same velocity $v$, the maximum height to which the ball will rise is

For a spontaneous process, the correct statement(s) is (are)

A whistle whose air column is open at both ends has a fundamental frequency of $5100 \,Hz$. If the speed of sound in air is $340\, ms^{-1}$, the length of the whistle, in cm, is