List of top Mathematics Questions

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 

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

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

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

Which one is different from the others ? (i) empty (ii) void (iii) zero (iv) null :

The number of solutions of log2(x – 1) = 2 log2(x – 3) is

$\sum _{r=0}^{m}n+r{c}_r$ is equal to

The locus of the centre of a circle which passes through two variable points (a, 0), (–a, 0) is 

Evaluate the definite integral as limit of sums: \(∫^3_2 x^2dx\)

Find the intervals in which the function f given by f(x) = 2x³ − 3x² − 36x + 7 is (a) strictly increasing (b) strictly decreasing

Sand is pouring from a pipe at the rate of \(12 cm^3 /s\). The falling sand forms a cone on the ground in such a way that the height of the cone is always one-sixth of the radius of the base. How fast is the height of the sand cone increasing when the height is \(4 cm\)?

If $y = \sec\, x^?$, then $\frac{dy}{dx}$ is equal to:

If I =$ \int sec ^4x \, cosec ^2x \,dx$ =K tan ^3x +L tan x+M cot x + const, then