List of top Mathematics Questions

Let $P(2, 1, -3)$ be a given point. If the point $Q$ is such that $\vec{PQ} = 3\hat{i} - \hat{j} + 5\hat{k}$, then the distance of $Q$ from the origin $O$ is

If $\vec{a} = 4\hat{i} + \lambda \hat{j} - 6\hat{k}$ and $\vec{b} = -6\hat{i} + 12\hat{j} + 9\hat{k}$ are collinear, then the value of $\lambda$ is equal to

Let $\theta$ be the angle between the unit vectors $\hat{a}$ and $\hat{b}$. If $|\hat{a} - \hat{b}| = \frac{\sqrt{3}}{2}$, then the value of $\cos \theta$ is

The position vectors of the points $A$ and $B$ are $\vec{a} = 2\hat{i} - \lambda \hat{j} + 5\hat{k}$ and $\vec{b} = \mu \hat{i} + 7\hat{j} + 3\hat{k}$ respectively. If the position vector of the mid-point of the line segment $AB$ is $\vec{c} = 3\hat{i} + 2\hat{j} + 4\hat{k}$, then the value of $\lambda + \mu$ is equal to

If the distance between the foci of an ellipse is 4 and its eccentricity is $\frac{1}{2}$, then the length of its latus rectum is

The vertex of the parabola $2y = -3x^2 + 48x - 200$, is

If the foci of the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ coincide with the foci of the ellipse $\frac{x^2}{49} + \frac{y^2}{36} = 1$, then the value of $a^2 + b^2$ is equal to

The area of the circle $x^2 + y^2 + 8x - 6y + c = 0$ is $75\pi$. Then the value of $c$ is equal to

The straight line passing through the points $(1, 5)$ and $(3, -5)$ meets the coordinate axes at the points $A$ and $B$. Then the area of the triangle $\triangle OAB$, where $O$ is the origin, is

If the equation of the straight line passing through the points $(3, -4)$ and $(4, a)$ is $x - y = 7$, then the value of $a$ is equal to

Let $O$ be the origin and $P$ be a point on a line such that $OP$ is perpendicular to that line. If $OP$ makes an obtuse angle $\alpha$ with the $x$-axis, $OP = 5$ and $\sin \alpha = \frac{3}{5}$, then the equation of the line is

The point $P(\frac{1}{6}, \alpha)$, where $\alpha$ is a constant, lies on the curve with equation $\sin^{-1}(3x) + 2\sin^{-1}(y) = \frac{\pi}{2}, |x| \leq \frac{1}{3}, |y| \leq 1$, then the value of $\alpha$ is equal to

If $2\cot^{-1}(\frac{4}{3}) = \cos^{-1}(\frac{x}{5})$, then the value of $x$ is equal to

If $\cos^{-1}(x - 2) = \sin^{-1}(y + 1)$, then the variables $x$ and $y$ satisfy the equation}

If $\alpha$ and $\beta$ are real constants such that $\alpha - \beta = \frac{\pi}{4}$, then the value of $(\sin \alpha + \sin \beta)^2 + (\cos \alpha + \cos \beta)^2$ is equal to

If $(3 \cos x - 2 \sec x)^2 = 9 \cos^2 x + 4 \tan^2 x + k$, where $k$ is a constant, then the value of $k$ is equal to

If $\tan \alpha = \frac{1}{2}$, then the value of $\tan^2(2\alpha) \sec^2(2\alpha)$ is equal to

The value of the product $\cot 10^\circ \cot 20^\circ \cot 30^\circ \cot 45^\circ \cot 60^\circ \cot 70^\circ \cot 80^\circ$ is equal to

In a right-angled trapezium $ABCD$, $\angle A = 90^\circ$, $\angle D = 90^\circ$, $AB = 7a + 1$, $CD = 3a + 1$ and $AD = 3a$. If the perimeter of the trapezium is greater than 56 but less than 92, then the range of possible values of $a$ is

The solution set of the inequality $6(2x + 3) + x > 53 - 2x$ is

Let $A$ be a non-singular square matrix of order 3. If $A^2 - A = 20I$, where $I$ is the unit matrix of order 3, then $A^{-1} =$}

If the coefficient of $x^3$ in the binomial expansion of $(2 + x)^n$ is 160, then the coefficient of $x^6$ in the binomial expansion of $(2 - x^2)^n$ is

The number of arrangements of the letters of the word BANANA so that the arrangement starts and ends with the same letter, is

Let $(2 - x)^9 = a_0 + a_1x + a_2x^2 + \dots + a_9x^9$. Then the value of $a_1 + a_2 + a_3 + \dots + a_8$ is equal to

There are 3 boys and 4 girls in a group. The number of ways they can sit in a row so that between any two boys there is a girl and between any two girls there is a boy, is