List of top Mathematics Questions

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

The sum to the infinity of the series $1+\frac{2}{3}+\frac{6}{3^{2}}+\frac{10}{3^{3}}+\frac{10}{3^{3}}+\frac{14}{3^{4}}+......$ is

The number of $3 \times 3$ non-singular matrices with four entries as $1$ and all other entries as $0$ is

The area of the region bounded by the parabola $(y-2)^2=x-1$ , the tangent to the parabola at the point $(2, 3)$ and the $x$-axis is

: The variance of first $n$ even natural numbers is $\frac{n^{2}-1}{4}$ : The sum of first $n$ natural numbers is $\frac{n\left(n+1\right)}{2}$ and the sum of squares of first $n$ natural numbers is $\frac{n\left(n+1\right)\left(2n+1\right)}{6}$

$ \sin \,\,{{47}^{o}}+\sin {{61}^{o}}-\sin {{11}^{o}}-\sin {{25}^{o}} $ is equal to

One ticket is selected at random from $50$ tickets numbered $00, 01, 02, ??, 49$. Then the probability that the sum of the digits on the selected ticket is $8$, given that the product of these digits is zero, equals

Let $A$ and $B$ denote the statements $A: cos\,\alpha + cos\,\beta + cos \,\gamma = 0$ $B: sin \alpha + sin\, \beta + sin\,\gamma = 0$ If $cos\left(\beta-\gamma\right)+cos\left(\gamma-\alpha\right)+cos\left(\alpha-\beta\right)=-\frac{3}{2}$, then

If $m_1, m_2, m_3$ and $m_4$ are respectively the magnitudes of the vectors $a_1 = 2i - j + k, a_2 = 3i - 4j - 4 k $ $a_3 = i + j - k$ and $a_4 = - i + 3j + k , $ then the correct order of $m_1, m_2, m_3 $ and $m_4$ is

Given $P(x) = x^4 + ax^3 + bx^2 + cx + d$ such that $x = 0$ is the only real root of $P'(x) = 0$ . If $P(-1) < P(1)$ , then in the interval $[-1, 1]$

Three distinct points $A, B$ and $C$ are given in the $2$ - dimensional coordinate plane such that the ratio of the distance of any one of them from the point $(1, 0)$ to the distance from the point $( - 1, 0)$ is equal to $\frac{1}{3}$. Then the circumcentre of the triangle $ABC$ is at the point

If $\left|Z-\frac{4}{z}\right|=2$, then the maximum value of $\left|Z\right|$ is equal to

If P and Q are the points of intersection of the circles $x^2 + y^2 + 3x + 7y + 2p - 5 = 0$ and $x^2 + y^2 + 2x + 2y - p^2 = 0$ , then there is a circle passing through $P, Q$ and $(1, 1)$ for

The projections of a vector on the three coordinate axis are $6, - 3, 2$ respectively. The direction cosines of the vector are