List of top Questions asked in KCET, WBJEE

If $\alpha$ and $\beta$ are the roots of $x^2 + x + 1 = 0$ then $\alpha^{16}+\beta^{16}$=

If one side of a triangle is double the other and the angles opposite to these sides differ by $60^\circ$, then the triangle is

In the group $G= \{0, 1,2, 3,4, 5\}$ under addition modulo $6,(2 +_6 3^{-1} +_6 4)^{-1}$=

A bivalent metal has an equivalent mass of $32$. The molecular mass of the metal nitrate is

The smallest positive integral value of $'n'$ such that $\left[\frac {1+\sin \frac {\pi}{8}+\,i\,\cos \frac {\pi}{8}}{1+\sin \frac {\pi}{8}-\,i\,\cos \frac {\pi}{8}} \right]^n$ is purely imaginary is, $n$ =

If $\begin{vmatrix} {1+\sin^2}&{\cos^2 \theta } &{4\sin 2\theta}\\ {\sin^2}&{1+\cos^2}& {4\sin2\theta} \\ {\sin^2\theta}&{\cos^2\theta}&{4\sin2\theta-1}\\ \end{vmatrix} =0 $ and $ 0< \theta

If$\vec{a}.\vec{b}\, = \,- |\vec{a}| \, |\vec{b}|$ then the angle between $\vec{a}$ and $ \vec{b}$ is

If the volume of the parallelopiped with $ \vec{a},\vec{b} $ and $ \vec{c}$ as coterminous edges is $40 \,cubic$ units, then the volume of the parallelopiped having $ \vec{b}+\vec{c} , \vec{c}+ \vec{a} $ and $ \vec{a}+ \vec{b}$ as coterminous edges in cubic units is

Among the following, the compound that contains ionic, covalent and coordinate linkage is

The enthalpy of formation of $NH_3$ is $- 4 6\, kJ \, mol^{-1}$. The enthalpy change for the reaction : $2 NH _{3}(g) \longrightarrow N _{2}(g)+3 H _{2}(g)$ is

The magnetic Lorentz force experienced by a charge q, entering a magnetic field B with a velocity v is

Which of the following prevents the conversion of prothrombin to thrombin in an undamaged blood vessel ?

The foot of the perpendicular from the point $(2, 4)$ upon $x + y = 4$ is

The r.m.s. velocity of molecules of a gas of density $4 \,kg \,m^{-3}$ and pressure $1.2 \times10^{5} Nm^{-2}$ is

Which one of the following is called a carbylamine?

$1$ mole of photon, each of frequency $2500\,s^{-1},$ would have approximately a total energy of :

For any complex number $z$, the minimum value of $\left|z\right|+\left|z-1\right|$ is

Two sources are said to be coherent if they produce waves

An $L C R$ series circuit containing a resistance of $120 \,\Omega$ has angular resonance frequency $4 \times 10^{5} \,rad \,s ^{-1}$. At resonance the voltage across resistance and inductance are $60\, V$ and $40 \,V$ respectively. The values of $L$ and $C$ are

The distance between an object and a divergent lens is $m$ times the focal length of the lens. The linear magnification produced by the lens is

If the charge on a capacitor is increased by $2$ coulomb, the energy stored in it increases by $21\%$. The original charge on the capacitor is

$30\, cc$ of $\frac {M}{3}\, HCl, 20\, cc$ of $\frac {M}{N} HNO_3$ and $40\, cc$ of $\frac {M}{4}$ $NaOH$ solutions are mixed and the volume was made up to $1\, dm^3$. The $pH$ of the resulting solution is

The time taken for $10\%$ completion of a first order reaction is $20$ minutes. Then for $19\%$ completion the reaction will take

An organic compound made of $C, H$ and $N$ contains $20\%$ nitrogen. Its molecular weight is :