List of top Mathematics Questions

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

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 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

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 $x=0$

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

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 

If the straight line  y = mx lies outside of the circle x²+ y²– 20y + 90 = 0, then the value of m will satisfy 

The order and degree of the differential equation ${(1+3{\mathrm{y}}_1)}^{\frac{2}{3}}$ respectively is:

If $\omega \ne 1$ is a cube root of unity, then the sum of the series $S=1+2\omega +3{\omega }^2+\dots \dots \dots +3n{\omega }^{3n}-1$ is

4 boys and 2 girls occupy seats in a row at random. Then the probability that the two girls occupy seats side by side is

If sin θ and cos θ are the roots of the equation  ax² – bx + c = 0, then a, b and c satisfy the relation 

The value of cos 15° – sin 15° is

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

If  A and B are two matrices such that A+B and AB are both defined, then 

Let R be the relation on Z defined by R = {(a, b): a, b ∈ Z, a - b is an integer}. Find the domain and range of R.

The general solution of the differential equation $\frac{d^{2}y}{d{x}^2}+8\frac{dy}{dx}+16y=0$ is

Find the sum of :
(a) 137 and – 354
(b) – 52 and 52
(c) – 312, 39 and 192
(d) – 50, – 200 and 300