List of top Questions asked in KCET, WBJEE

$2\,gm$ of metal carbonate is neutralized completely by $100 \,mL$ of $0.1 \,(N) \,HCl$. The equivalent weight of metal carbonate is

If the focal length of the eye-piece of a telescope is doubled, its magnifying power $(m)$ will be

A body floats in water with $40\%$ of its volume outside water. When the same body floats in an oil, $60\%$ of its volume remains outside oil. The relative density of oil is

The sequence $\log \,a$, $\log \frac{a^{2}}{b}, \,\log \frac{a^{3}}{b^{2}}, ...........$ is

Two soap bubbles of radii $x$ and $y$ coalesce to constitute a bubble of radius $z$. Then $z$ is equal to

If the equilibrium constants of the following equilibria ${SO_{2(g)} +\frac{1}{2}O2 <=> SO3$ $ and\, 2SO_{3(g)} <=> 2SO_{2(g)} +O_{2(g)}}$ are given by $K_1$ and $K_2$ respectively, which of the following relations is correct

A planoconvex lens has a maximum thickness of $6\,cm$. When placed on a horizontal table with the curved surface in contact with the table surface, the apparent depth of the bottommost point of the lens is found to be $4 \,cm$. If the lens is inverted such that the plane face of the lens is in contact with the surface of the table, the apparent depth of the center of the plane face is found to be $\left(\frac{17}{4}\right)\, cm$ .The radius of curvature of the lens is

Two cells with the same e.m.f. $E$ and different internal resistances $r_1$ and $r_2$ are connected in series to an external resistance $R$. The value of $R$ so that the potential difference across the first cell be zero is

$^{15}C_{3} +\,^{15}C_{5} + .. ...+\,^{15}C_{15} $ will be equal to

An ideal gas is compressed isothermally until its pressure is doubled and then allowed to expand adiabatically to regain its original volume ($? = 1.4$ and $2^{-1.4} = 0.38$). The ratio of the final to initial pressure is

The amount of heat evolved when $500 \, cm^3$ of $0.1 \, M \, HCl$ is mixed with $200\,cm^3$ of $0.2 \, M \, NaOH$ is

Effective filtration pressure in glomerulus is caused due to...................

The following is the diagram of T.S. of Anther. Identify the parts labelled A, B, C.

$G = \left\{\begin{bmatrix} x&x \\[0.3em] x & x \end{bmatrix} , x \text{ is a nonzero real number} \right\}$ is a group with respect to matrix multiplication. In this group, the inverse of $\begin{bmatrix} \frac{1}{3} &\frac{1}{3} \\[0.3em] \frac{1}{3} & \frac{1}{3} \end{bmatrix}$ is

$\begin{vmatrix} {Sin \alpha}&{ \cos\alpha} &Sin ({\alpha+ \delta })\\ {Sin \beta}&{ Cos \beta}& Sin ({\beta+\delta}) \\ {Sin \gamma}&{ Cos \gamma}&Sin ({\gamma+\delta})\\ \end{vmatrix} $ is equal to

Suppose $ P(2,\,y,\,z) $ lies on the line through $ A(3,-1,4) $ and $ B(-4,2,1) $ . Then, the value of z is equal to

Angles of elevation of the top of a tower from three points (collinear) $A, B$ and $ C$ on a road leading to the foot of the tower are $30^\circ$, $45^\circ$ and $60^\circ$ respectively. The ratio of $AB$ to $BC$ is

The derivative of $tan ^{-1}[\frac{Sin x}{1+ Cos x}]$ with respect to $tan^{-1}[\frac{Cos x}{1+Sin x}]$ is

In $n$ is an odd positive integer and $(1+x +x^2 +x^3)^n =\displaystyle\sum_{r=0}^{3n} a_rx^r$ then $a_0 -a_1+a_2-a_3 +\dots -a_{3n}$ is equal to

The value of $\left| \frac{1+ i \sqrt{3}}{\left( 1 + \frac{1}{i+1}\right)^2} \right|$ is

The sum of the first n terms $ \frac {1^2}{1} +\frac {1^2+2^2}{1+2}+ \frac {1^2 +2^2+3^2}{1+2+3}+$ $\dots$ is

The rms velocity of hydrogen is $\sqrt {7}$ times the rms velocity of nitrogen. If $T$ is the temperature of the gas, which of the following is true?

A particle of charge $e$ and mass $m$ moves with a velocity $v$ in a magnetic field $B$ applied perpendicular to the motion of the particle. The radius $r$ of its path in the field is

If $\alpha , \beta ,\gamma$ are the roots of $x^3-2x+1=0$, then the value of $(\sum \frac {1} {\alpha +\beta -\gamma}$) is

If the focii of $\frac {x^2}{16}+\frac{y^2}{4}=1 $ and $\frac {x^2}{a^2}-\frac{y^2}{3}=1 $ coincide, then value of $a$ is