List of top Mathematics Questions

Let relation defined as $(x_1, y_1) \,R (x_2, y_2)\, x_1 ≤ x_2,\, y_1 ≤ y_2$ and given that
(a) R is reflexive but not symmetric.
(b) R is transitive. then

If a, b, c are in A. P. and a + 1, b, c + 3 are in G. P., arithmetic mean of a, b, c is 8, then the value of cube of geometric mean of a, b, c is:

If $ f(x) =\begin{cases}\frac{(72)^x - 9^x -8^x+1}{\sqrt2-\sqrt{1+cosx}} &; x ≠0\\a\,log2\,log3 &  ; x=0\end{cases} $ is continuous at x = 0. Then $a^2$ equals to

The radius of a circle is $\sqrt{10} .\,\, x + y = 4$ is the line intersecting the circle at P & Q. A chord MN is of length 2 m having slope –1. Find perpendicular distance between the two chords PQ and MN.

$(x^2 + 1)2dy + (y(2x^3 + x) – 2)dx = 0, y(0) = 0,$ then y(2) is equal to

If $f(x)= 3\sqrt{(x-2)}+\sqrt{4-x }$ If minimum value = α Maximum value = β find $α2 + β2 $.

In group A there are 4 men and 5 women and in group B there are 5 men and 4 women, if 4 people are selected from each group. Find a number of ways to select 4 men and 4 women.

$(x^2 + 1)2dy + (y(2x^3 + x) – 2)dx = 0, y(0) = 0,$ then y(2) is equal to

Find area bounded by $y^2 ≤ 2x$ and $y ≥ 4x – 1$

For a hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2}=1, C_1$ is a circle touching hyperbola having centre at origin and $C_2$ is circle centred at four and touching hyperbola at vertices, if area of $C_1= 36π$ and area of $C_2 = 4π$. Find $a_2 + b_2 $= ?

Team A plays 10 matches, probability of winning is $\frac1{3}$ and losing is $\frac2{3}$. They win x matches and lose y matches. Probability such that $|x – y| ≤ 2$ is P then find 3$^9P$.

A parabola $y^2 = 12x$ has a chord PQ with mid-point (4, 1) then equation of PQ passes through

The value of $\frac{1\times 2^2+2\times3^2+...+100\times (101)^2}{1^2 \times 2\times2^2 \times3+...+100^2 \times 101}$

if  $∫_{-1}^1 \frac{cos \, \alpha x}{1+3^x} dx = \frac2{\pi} $ then $\alpha$ is

If a, b, c are in increasing A.P. and a + 1, b, c + 3 are in G.P. If A.M. of a, b, c is 8. Find cube of G.M. of a, b, c.

Find the numbers of distinct real roots $|x||x + 2| - 5|x + 1| - 1$ =0

$ \lim_{t \rightarrow x} \frac{t^2f(x) - x^2 f(t)}{t-x} = 1$, then 2f(2) + 3f(3) equals to:

Two lines passing through (2, 3) parallel to coordinate axes. A circle of unit radius touches both the lines and lies on the origin side. Then the shortest distance of point (5,5) from the circle is:

The value of $∫_0^{\frac{\pi}{4}} \frac{dx}{1+tanx} $

A rectangle ABCD with ABCD with AB = 2 and BC = 4 is inscribed in rectangle PQRS such that vertices of ABCD lie on sides of PQRS then maximum possible area(in sq. unit) of rectangle PQRS is :

When 4 dice are rolled, then the probability of 16 as a sum is:

Let f(x) = $x^2 - 5x$ and $g(x) = 7x - x^2$, then the area between the curves equals to:

$∫_{-\pi}^{\pi} \frac{2x(1+sinx)}{1+cos^2x}dx $ is equal to?

If $\frac{dy}{dx} +2y = sin 2x$ and $y(0) = \frac{3}4$ , then $y (\frac{π}{8})$ is equal to: