List of top Questions asked in WBJEE- 2013

The ore chromite is

A sphere of radius R has a volume density of charge $? = kr$, where r is the distance from the centre of the sphere and k is constant. The magnitude of the electric field which exists at the sur ace o the sphere is given by ($e_0$ = permittivity of the free space)

Treatment of with $NaNH_2/li \,NH_3$ gives

The increasing order of $O-N-O$ bond angle in the species $NO_2,\, NO_2^ +$ and $NO_2 ^-$ is

A point moves so that the sum of squares of its distances from the points (1,2) and (-2,1) is always 6. Then its locus is

A bar magnet has a magnetic moment of $200\, A \,m^2$. The magnet is suspended in a magnetic field of $0.30\, N\, A^{-1}\, m^{-1}$. The torque required to rotate the magnet from its equilibrium position through an angle of $30^{\circ}$, will be

A bullet of mass $m$ travelling with a speed $v$ hits a block of mass $M$ initially at rest and gets embedded in it. The combined system is free to move and there is no other force acting on the system. The heat generated in the process will be

The ionization energy of the hydrogen atom is $13.6\, eV$. The potential energy of the electron in $n = 2$ state of hydrogen atom is

Tautomerism is exhibited by

Amongst $\left[NiCl_{4}\right]^{2-}, \left[Ni\left(H_{2}O\right)_{6}\right]^{2+},\left[Ni\left(PPh_{3}\right)_{2}Cl_{2}\right], \left[Ni\left(CO\right)_{4}\right]$ and $\left[Ni\left(CN\right)_{4}\right]^{2-}$. the paramagnetic species are

Let $P = \begin{pmatrix}cos \frac{\pi}{4}&-sin \frac{\pi}{4}\\ sin \frac{\pi}{4}&cos \frac{\pi}{4}\end{pmatrix}$ and $X = \begin{pmatrix}\frac{1}{\sqrt{2}}\\ \frac{1}{\sqrt{2}}\end{pmatrix}$. Then $P^{3}X$ is equal to

A travelling acoustic wave of frequency $500\, Hz$ is moving along the positive $x$-direction with a velocity of $300 \,ms^{-1}$. The phase difference between two points $x_1$ and $x_2$ is 60$^{\circ}$. Then the minimum separation between the two pints is

In $SOCl_2$, the $Cl-S-Cl$ and $Cl-S-O$ bond angles are

$2$-Methylpropane on monochlorination under photochemical condition give

Pressure-volume $(PV)$ work done by an ideal gaseous system at constant volume is (where $E$ is internal energy of the system

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)

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 = $0.15, R = 8.314 \, J/K/mol)$

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 area of the region enclosed between parabola $y^2 = x$ and the line $y = mx$ is $\frac{1}{48}. $

If the distance between the foci of an ellipse is equal to the length of the latus rectum, then its eccentricity is

Let $f(?) = (1+sin^2?)(2-sin^2?)$. Then for all values of $?$