List of top Mathematics Questions

Let \(\vec{a}, \vec{b}, \vec{c}\) be such that \(\vec{a} + \vec{b} + \vec{c} = 0\). If \(|\vec{a}| = 3, |\vec{b}| = 4, |\vec{c}| = 5\) then \(|\vec{a}\cdot\vec{b} + \vec{b}\cdot\vec{c} + \vec{c}\cdot\vec{a}|\) is:

The line $x - 1 = 0$ is the directrix of the parabola $y^2 - kx + 8 = 0$. Then, the values of $k$ are:

The centre and radius of the circle $x^2 + y^2 - 2x + 4y = 8$ respectively are:

If \(\theta\) is the angle between two vectors \(\vec{a}\) and \(\vec{b}\) such that \(|\vec{a}| = 7, |\vec{b}| = 1\) and \(|\vec{a}\times\vec{b}|^2 = k^2 - (\vec{a}\cdot\vec{b})^2\), then the value(s) of \(k\) is/are:

The length of the latus rectum of $x^2 = -9y$ is equal to:

If \(\alpha\) and \(\beta\) are respectively the minimum and maximum values of \(\frac{\pi^2}{8} + 2\left(\sin^{-1}x - \frac{\pi}{4}\right)^2\), then \(\frac{\beta}{\alpha}\) is:

The value of \(\cos^{-1}\left(-\frac{\sqrt{3}}{2}\right) + \sin^{-1}\left(\frac{1}{2}\right)\) is equal to

The distance of the point $P(1,-3)$ from the line $2y - 3x = 4$ is:

If the slope of the line joining the points \((3,4)\) and \((-2,a)\) is equal to \(-\frac{2}{5}\), then the value of \(a\) is:

If the points $(3,-2)$, $(a,2)$, $(8,8)$ are collinear, then the value of $a$ is:

The value of \(2\tan^{-1}\left(\frac{1}{3}\right) + \cot^{-1}\left(\frac{3}{4}\right)\) is

Let $L$ be an arc of a circle which subtends $45^\circ$ at the centre. If the radius of circle is $4$ cm, then the length of $L$ in centimeter is

If $(x-1)(x^2 - 5x + 7) < (x-1)$, then $x$ belongs to

If \(\tan\left(\frac{\pi}{4} + \theta\right) = \frac{1}{2}\) then the value of \(\sin 2\theta\) is

The solution set of \(\left|x + \frac{1}{x}\right| > 2\) is

If \(1 + \cos x = \alpha\), \(0 \leq x \leq \frac{\pi}{2}\), then \(\sin \frac{x}{2}\) is equal to

If \(A=\begin{bmatrix}3 & \lambda-3\\ -1 & 1\end{bmatrix}\) and \(B=\begin{bmatrix}3 & 2\\ 2 & 1\end{bmatrix}\) and \(AB=\begin{bmatrix}7 & 1\\ -1 & -1\end{bmatrix}\), then \(\lambda\) is equal to

If \(A=\begin{bmatrix}1 & 1\\ 0 & i\end{bmatrix}\) and \(A^{42}=\begin{bmatrix}a & b\\ c & d\end{bmatrix}\) then \(a+d\) is equal to

If the 17th and 18th term in the expansion of \((2 + x)^{50}\) are equal, then the value of \(x\) is equal to

Let \(f(x) = \begin{vmatrix} x & 1\\ \sin(2\pi x) & 2x^2 \end{vmatrix}\). If \(f(x)\) is an odd function, \(f(-x)=g(x)\) and \(\lambda f(1)g(1)=4\), then the value of \(\lambda\) is equal to

There are two women participants in a badminton tournament. The number of games the men played between themselves exceeds by 12 the number of games they played with women. If each player played one game with each other, then the number of men in the tournament was

The value of the determinant of the inverse of the matrix \(\begin{bmatrix} -4 & -5\\ 2 & 2 \end{bmatrix}\) is

If three geometric means are inserted between 2 and 32, then the three numbers are

If \(\frac{{}^nP_{r-1}}{a} = \frac{{}^nP_r}{b} = \frac{{}^nP_{r+1}}{c}\), then