List of top Mathematics Questions

Let the following system of equations kx + y + z =1x + ky + z = kx + y + kz=k2Has no solution. Find

Area bounded by\( y=x^3 , y=8\) and \(x=0\) is

You have a 9 x 9 x 9 cm box. How many cubes of side 5 cm will you be able to fit inside it?

A determinant is chosen at random from the set of order 2 with elements 0 or 1 only. The probability that the determinant chosen non zero is

The third term of a G.P. is 9. The product of its first five terms is

A man speaks truth 2 out of 3 times. He picks one of the natural numbers in the set S = {1, 2, 3, 4, 5, 6, 7} and reports that it is even. The probability that it is actually even is

If cos x = |sin x| then, the general solution is

If $A = \{ x | x \in N, x \le 5 \}, B = \{ x | x \in Z, x^2 - 5x + 6 = 0\}$, then the number of onto functions from A to B is

If $| 3x -5| \le 2$, then

$\sqrt{3}\, cosec \,20^{\circ} - \sec\, 20^{\circ}$ =

The interval in which the function $f(x) = x^3 - 6x^2 + 9x + 10$ is increasing in

If $a + \frac{\pi}{2} < 2 \tan^{-1} x + 3 \cot^{-1} x < b $ then 'a' and 'b' are respectively.

The domain of the function f : R $\to$ R defined by $f(x) = \sqrt{x^2 - 7x + 12} $ is

On the set of positive rationals, a binary operation * is defined by a * b = $\frac{2ab}{5}$ . If 2 * x = $3^{-1}$ then x =

If $P$ and $Q$ are symmetric matrices of the same order then $PQ - QP$ is

The eccentricity of the ellipse $9x^2 + 25y^2 = 225$ is

Let $D=R-\{0,1\}$ and $f: D \rightarrow D, g: D \rightarrow D$ and $h: D \rightarrow D$ be three functions defined by $f(x)=\frac{1}{x} ; g(x)=1-x$ and $h(x)=\frac{1}{1-x} .$ If $j: D \rightarrow D$ is such that $(gojof)$ $(x)=f(x)$ for all $x \in D$, then which one of the following is $j(x) ?$

The distance of the point (1, 2, 1) from the line $\frac{x-1}{2} = \frac{ y-2}{1}=\frac{ z-3}{2} $ is

If $y = f(x)$ is twice differentiable function such that at a point $P , \frac{dy}{dx} = 4 , \frac{d^2 y}{dx^2} = - 3$ , then $\left( \frac{d^2 x}{dy^2} \right)_P = $

Let a, b, c be real numbers such that $a + b + c < 0$ and the quadratic equation $ax^2 + bx + c = 0$ has imaginary roots. Then

Let S, T, U be three non-void sets and f : S $\to$ T,g : T $\to$ U is surjective. Then

Let $f(x) = x^{4} - 4x^{3} + 4x^{2} +c, c \in \mathbb{R}.$ Then

T$\displaystyle\lim_{x \to 0+}$ $\left(x^{n} \,ln\, x\right), n > 0$

Let A be a square matrix of order 3 whose all entries are 1 and let $I_3$ be the identity matrix of order 3. Then the matrix $A - 3I_3$ is