List of top Mathematics Questions asked in WBJEE

The shortest distance from the point (1, 2, -1) to the surface of the sphere x² + y² + z² = 54 is

If $\sin \theta =\frac{2t}{1+t^2}$ and $\theta$ lies in the second quadrant, then $\cos \theta$ is equal to

Evaluate the integral: ${\int }_1^2\log xdx$

If $A=\left(\begin{array}{cc}3& x-1\\ 2x+3& x+2\end{array}\right)$ is a symmetric matrix, then the value of $x$ is

Directions: The following question has four choices, out of which one or more are correct.When photons of energy 4.25 eV strike the surface of a metal $A$, the ejected photoelectrons have minimum kinetic energy $T_A$ expressed in eV and de Broglie wavelength ${\lambda }_A.$ The maximum kinetic energy ofphotoelectrons liberated from another metal $B$ by photons of energy 4.70 eV is $T_B=(T_A-1.50eV)$. If the de Broglie wavelength of these photoelectrons is ${\lambda }_B=2{\lambda }_A$, then

If $\omega (\ne 1)$ is a cube root of unity and ${(1+{\omega }^2)}^n={(1+{\omega }^4)}^n,$ then the leastpositive value of $n$ is

If a particle moves in such a way that the displacement is proportional to the square of the velocity acquired, then its acceleration is

The value of $\sec [{\tan }^{-1}\left(\frac{b+a}{b-a}\right)-{\tan }^{-1}\left(\frac{a}{b}\right)]$

An integrating factor of the differential equation $x\frac{dy}{dx}+y\log x=x{e}^x{x}^{-\frac{1}{2}\log x},(x>0)$

The minimum value of $f(x)={\sin }^{4}x+{\cos }^{4}x,0\le x\le \frac{\pi }{2}$

The probability that in a family of 5 members, exactly 2 members have birthdays on Sunday, is

If A1, A2; G1, G2; and H1, H2 are two AMs, GMs and HMs between two quantities, then the value of $\frac{G_1{G}_2}{H_1{H}_2}$ is

If $\overrightarrow{A}=\hat{i}+2\overrightarrow{j}+3\hat{k},\overrightarrow{B}=-\hat{i}+2\hat{j}+\hat{k},\overrightarrow{C}=3\hat{i}+j$ and $\overrightarrow{A}+1\overrightarrow{B}$ is perpendicular to $\overrightarrow{\mathrm{C}},$ thent is equal to

ABCD is a parallelogram. If $P$ and $Q$ are the respective midpoints of$\overrightarrow{\mathrm{BC}}$ and $\overrightarrow{\mathrm{AD}},$ then $,\overrightarrow{\mathrm{AB}}+\overrightarrow{\mathrm{DC}}$ is equal to

The curve represented by the equation 4x² + 16y² - 24x - 32y - 12 = 0 is

The derivative of${\tan }^{-1}\left(\frac{\sqrt{1+x^2}-1}{x}\right)$ with respect to ${\tan }^{-1}\left(\frac{2x\sqrt{1-x^2}}{1-2x^2}\right)$ at $x=0$

If $x,\frac{3}{2},z$ are in $AP;x,3,z$ are in GP; then which one of the following will be in HP?

A coin is tossed again and again. If tail appears on first three tosses, then the chance that head appears on fourth toss is

If α and β are the roots of the equation x² + x + 1 = 0, then the equation whose roots are α¹⁹ and β⁷ is 

The locus of the middle points of all chords of the parabola y² = 4ax passing through the vertex is 

Let a , b, c be three real numbers such that a + 2b + 4c = 0. Then the equation ax² + bx + c = 0 

The equation  8x²+ 12y²– 4x + 4y – 1 = 0  represents