List of top Questions asked in WBJEE- 2013

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

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

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

The value of the integral $ \int\limits^2_{1}e^{x} \left(log_{e} \,x + \frac{x+1}{x}\right)dx$ is

If $f(x) = e^x (x - 2)^2$ then

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

$S_1$ and $S_2$ are the two coherent point sources of light located in the $xy-plane$ at points $(0,0)$ and $(0,3?)$ respectively. Here $\lambda$ is the wavelength of light. At which one of the following points (given as coordinates), the intensity of interference will be maximum?

Two vectors are given by $\vec{A} = (\hat{i} + 2j + \hat{k})$ and $\vec{B} = (3\hat{i} + 6\hat{j} + 2\hat{k})$. Another vector $\vec{C}$ has the same magnitude as $\vec{B}$ but has the same direction as $\vec{A}$. Then which of the following vectors represents $\vec{C}$ ?

A small mass $m$ attached to one end of a spring with a negligible mass and an unstretched length $L$, executes vertical oscillations with angular frequency $\omega_0$. When the mass is rotated with an angular speed $\omega$ by holding the other end of the spring at a fixed point, the mass moves uniformly in a circular path in a horizontal plane. Then the increase in length of the spring during this rotation is

Suppose $z = x + iy$ where $x$ and $y$ are real numbers and $i = \sqrt{-1}$. The points $(x, y)$ for which $\frac{z - 1}{z - i} $ is real, lie on

At two different places the angles of dip are respectively $30^{\circ}$ and $45^{\circ}$. At these two places the ratio of horizontal component of earth?s magnetic field is

A planet moves around the sun in an elliptical orbit with the sun at one of its foci. The physical quantity associated with the motion of the planet that remains constant with time is

For the curve $x^2+4xy+8y^2=64$ the tangents are parallel to the x-axis only at the points

If $\alpha, \beta$ are the roots of the quadratic equation $x^2+ax+b=0, (b\ne 0)$; then the quadratic equation whose roots are $\alpha -\frac{1}{\beta}, \beta - \frac{1}{\alpha}$ is

A frictionless piston-cylinder based enclosure contains some amount of gas at a pressure of $400 \,kPa$. Then heat is transferred to the gas at constant pressure in a quasi-sta ic process. The piston moves up slowly through a height of $10\,cm$. If the piston has a cross-section area of $0.3 \,m^2$, the work done by the gas in this process is

A block of mass $m (= 0.1 kg)$ is hanging over a frictionless light fixed pulley by an inextensible string of negligible mass. The other end of the string is pulled by a constant force $F$ in the verticaly downward direction. The linear momentum of the block increase by $2\,kg$ $ms^{-1}$ in $1\,s$ after the block starts from rest. Then, (given $g \,= \,10\,ms^{-2}$)

A particle is moving with a uniform speed $v$ in a circular path of radius $r$ with the centre at $O$. When the particle moves from a point $P$ to $Q$ on the circle such that $? POQ=\theta$, then the magnitude of the change in velocity is

Correct statement(s) in cases of n-butanol and t-butanol is (are)