List of top Mathematics Questions

If function $f(x) = \begin{cases} x\, \sin\left(\frac{1}{x} \right) ; & \text{x $\ne$ 0} \\[2ex] a \,;& \text{x = 0} \end{cases}$ is continuous at $x = 0$, then value of $a$ is

The tangents to curve $y=x^{3}-2x^2+x-2$ which are parallel to straight line $y = x$ are

The Solution of the differential equation $\left(x+2y^{3}\right) \frac{dy}{dx}=y$ is

Value of the following expression is $\displaystyle \lim_{n \to \infty}$$\frac{1}{n^{3}}\left(1^{2}+2^{2}+3^{2}+ ..... +n^{2}\right)$

Two vectors $A = 3$ and $B = 4$ are perpendicular. Resultant of both these vectors is $R$. The projection of the vector $B$ on the vector $R$ is

A normal is drawn at a point $(x_1, y_1)$ of the parabola $y^2 = 16x$ and this normal makes equal angle with both $x$ and $y$ axes. Then point $(x_1, y_1)$ is

The Solution of the differential equation $\frac{dy}{dx}=2e^{x-y}+x^{2}e^{-y}$ is

Four men and three women are standing in a line for railway ticket. The probability of standing them in alternate manner is

The value of cos $15^{\circ}\, cos 7 \frac{1^{\circ}}{2}\, sin 7 \frac{1^{\circ}}{2}$ is

If the equation $x^2 + y^2 -10x + 21 = 0$ has real roots $x = a$ and $y=\beta$ then

If $r. v. x :$ waiting time in minutes for bus and $p.d.f.$ of $x$ is given by $f(x) = \begin{cases} \frac{1}{5} , & 0\le x\le5 \\[2ex] 0, & \text{otherwise} \end{cases}$ then probability of waiting time not more than $4$ minutes is = _______

If $ y = sec(tan^{-1}x) $ , then $ \frac{dy}{dx} $ at $ x = 1 $ is

If $ f(x) = \frac{x}{2} -1 $ then on the interval $ [0,\pi] $

A polygon has $44$ diagonals. The number of its sides are

If origin is the centroid of a $ \Delta PQR $ with vertices $ P(2a,2,6),Q(-4,3b,- 10) $ and $ (8,14,2c) $ , then the value of $ a,b $ and $ c $ are respectively.

Given that the points $ P(3,2, - 4) $ , $ Q(5,4, - 6) $ and $ R(9,8,-10) $ are collinear, the ratio in which $ Q $ divides $ PR $ externally is

If $ A $ and $ B $ are two square matrices such that $ AB $ = $ A $ and $ BA $ = $ B $ , then

The function $ f(x) = cos^2x $ is strictly decreasing on

Consider the following propositions : p : I take medicine q : I can sleep Then, the compound statement $ \sim p \rightarrow \sim q $ means

If $ \begin{bmatrix}\alpha&\beta\\ \gamma&-\alpha\end{bmatrix} $ is to be square root of the two rowed unit matrix, then $ \alpha $ , $ \beta $ and $ \gamma $ should statisfy the relation

The sum of two numbers is $10$. Their product will be maximum when they are

The maximum value of $ \frac{log x}{x} $ is

The value of the integral $ \int_{-2}^{0}\frac{dx}{\sqrt{12-x^{2}-4x}} $ is

The integral $ \int \sqrt{16-9x^2} $ $dx$ equals

A line perpendicular to the line segment joining the points $ (1,0) $ and $ (2,3) $ divides it in the ratio $ 1 : n $ . The equation of the line is