List of top Mathematics Questions

The value of $\sin \left[\cot^{-1}\{{\cos(tan^{-1}\,x)\}}\right]$ is

If the line px + qy = 0 coincides with one of the lines given by $ax^2 + 2hxy + by^2 = 0$, then

If the circle $x^2+y^2+2\,gx+2fy+=0,$ and $x^2+y^2+2g'x+2f'y$ touch each other, then

Which of the following is an empty set?

The number of proper subsets of a set having $n + 1$ elements is

The interval I such that $\int^1_0\frac{dx}{\sqrt{1+x^4}}\in \,I$ is given by

A card is picked at random from a pack of cards. Given that the picked card is a Queen, what is the probability that it is a spade ?

The curve $x^2 - xy + y^2 =27$ has tangents parallel to $x-axis$ at

Let $x$ be a number which exceeds its square by the greatest possible quantity, then $x$ =

The value of $\int^2_{-2}(ax^3+bx +c)dx$ depends on the

The value of $\frac{\tan 330^{\circ} \sec 420^{\circ} \sin 300^{\circ}}{\tan 135^{\circ} \sin 210^{\circ} \sec 315^{\circ} } $ is equal to

Find the length of the diagonal of the parallelepiped formed by planes drawn through the points $ (2,3,5) $ and $ (5,9,7), $ parallel to the co-ordinate planes?

Let $n\ge2$ be an integer, $A=\begin{pmatrix}\cos\left(2\pi/ n\right)&\sin \left(2\pi / n\right)&0\\ -\sin\left(2\pi / n\right)&\cos\left(2\pi / n\right)&0\\ 0&0&1\end{pmatrix}$ and $?$ is the identity matrix of order $3$. Then

Suppose $M=\int\limits_{0}^{\pi / 2} \frac{\cos x}{x+2} d x$, $N=\int\limits_{0}^{\pi / 4} \frac{\sin x \cos x}{(x+1)^{2}} d x$ Then, the value of $(M-N)$ equals

Out of $7$ consonants and $4 $ vowels, the number of words (not necessarily meaningful) that can be made, each consisting of $3$ consonants and $2 $ vowels, is

The angle of intersection between the curves $y=\left[\left|\sin\,x\right|+\left|\cos\,x\right|\right]$ and $x^{2}+y^{2}=10, $ where $[x]$ denotes the greatest integer $= x,$ is

The minimum value of $2^{\sin\, x} + 2^{\cos\, x}$ is

The coefficient of $x^3$ in the infinite series expansion of $\frac{2}{\left(1-x\right)\left(2-x\right)},$ for $\left|x\right|< 1,$ is

Let \(R\) be the set of all real numbers and \(f : R \rightarrow R\) be given by \(f(x) = 3x^2 + 1\).Then the set \(f ^{-1}\left(\left[1, 6\right]\right)\) is

The equation of the common tangent with positive slope to the parabola $y^{2}=8\sqrt{3x}$ and the hyperbola $4x^2 - y^2 = 4$ is

The point on the parabola $y^2 = 64x$ which is nearest to the line $4x + 3y + 35 = 0$ has coordinates

The remainder obtained when \(1!+2!+3!+.....+11!\) is divided by 12 is