List of top Mathematics Questions

The number of subgroups of the group $(Z_5, +_5)$is

Angle between $y^{2}=x$ and $x^{2}=y$ at the origin is

If $A=\begin{bmatrix} {2}&{1} &{0}\\ {0}&{2}& {1} \\ {1}&{0}&{2}\\ \end{bmatrix}$ then $| adj A|$ =

Triangle $ABC$ has vertices $(0, 0), (11, 60)$ and $(91, 0)$. If the line $ y=kx $ cuts the triangle into $2$ two triangles of equal area, then $k$ is equal to

If $\alpha$ and $\beta$ are the roots of $x^2 + x + 1 = 0$ then $\alpha^{16}+\beta^{16}$=

If one side of a triangle is double the other and the angles opposite to these sides differ by $60^\circ$, then the triangle is

In the group $G= \{0, 1,2, 3,4, 5\}$ under addition modulo $6,(2 +_6 3^{-1} +_6 4)^{-1}$=

The smallest positive integral value of $'n'$ such that $\left[\frac {1+\sin \frac {\pi}{8}+\,i\,\cos \frac {\pi}{8}}{1+\sin \frac {\pi}{8}-\,i\,\cos \frac {\pi}{8}} \right]^n$ is purely imaginary is, $n$ =

If $\begin{vmatrix} {1+\sin^2}&{\cos^2 \theta } &{4\sin 2\theta}\\ {\sin^2}&{1+\cos^2}& {4\sin2\theta} \\ {\sin^2\theta}&{\cos^2\theta}&{4\sin2\theta-1}\\ \end{vmatrix} =0 $ and $ 0< \theta

If$\vec{a}.\vec{b}\, = \,- |\vec{a}| \, |\vec{b}|$ then the angle between $\vec{a}$ and $ \vec{b}$ is

If the volume of the parallelopiped with $ \vec{a},\vec{b} $ and $ \vec{c}$ as coterminous edges is $40 \,cubic$ units, then the volume of the parallelopiped having $ \vec{b}+\vec{c} , \vec{c}+ \vec{a} $ and $ \vec{a}+ \vec{b}$ as coterminous edges in cubic units is

The foot of the perpendicular from the point $(2, 4)$ upon $x + y = 4$ is

For any complex number $z$, the minimum value of $\left|z\right|+\left|z-1\right|$ is

The number of ways in which $5$ boys and $5$ girls can be seated for a photograph so that no two girls sit next to each other is

Let a relation $ R $ in the set $N $ of natural numbers be defined by $(x, y)\Leftrightarrow x^2 - 4xy + 3y^2 = 0\,\forall\,x, y \in\,N.$The relation $ R$ is

Let $z = \cos \theta + i \sin \theta$. Then, the value of $\displaystyle \sum _{m=0}^{15} Im (z^{2m-1})$ at $\theta = 2^\circ$ is

For real $x,$ let $f (x) = x^3 + 5x + 1,$ then

Let $A$ be a $2 \times 2$ matrix Statement-1 : adj (adj A) $= A$ Statement-2 : $|adj \,A| = |A|$

Given $ P(A \cup B ) = 0.6,P(A\cap B) = 0.2 $ , the probability of exactly one of the event occurs is

The shortest distance between the line $y-x=1$ and the curve $x = y^2$ is

The set representing the correct order of ionic radius is :

The ellipse $x^2 + 4y^2 = 4$ is inscribed in a rectangle aligned with the coordinate axes, which in turn in inscribed in another ellipse that passes through the point $(4, 0)$. Then the equation of the ellipse is

On the set of all natural numbers $N$, which one of the following $*$ is a binary operation ?

From a group of $ 8 $ boys and $ 3 $ girls, a commitee of $ 5 $ members to be formed. Find the probability that $ 2 $ particular girls are included in the committe is