List of top Mathematics Questions

If the lines \(\frac{2x-1}{2} = \frac{3-y}{1} = \frac{z-1}{3}\) and \(\frac{x+3}{2} = \frac{y+2}{5} = \frac{z+1}{a}\) are perpendicular to each other, then the value of \(a\) is:

The vector equation of the straight line \(\frac{x-2}{3} = \frac{y+1}{2} = \frac{z-3}{2}\) is:

The equation of a line passing through the point $(1,-2,3)$ and equally inclined to the axes are:

The equation of straight line passing through $(a,b,c)$ and parallel to x-axis is:

If \(\vec{a} = \hat{i} + \hat{j} + \hat{k}\) and \(\vec{b} = \hat{i} - \hat{j} + \hat{k}\), then the projection of \(\vec{a}\) on \(\vec{b}\) is:

If the length of the major axis of an ellipse is thrice the length of the minor axis, then its eccentricity is equal to:

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:

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:

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:

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

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

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

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 \(\tan\left(\frac{\pi}{4} + \theta\right) = \frac{1}{2}\) then the value of \(\sin 2\theta\) 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 \(A=\begin{bmatrix}3 & \lambda-3\\ -1 & 1\end{bmatrix}\) 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