List of top Mathematics Questions

An ice ball melts at the rate which is proportional to the amount of ice at that instant. Half the quantity of ice melts in 20 minutes, $x_0$ is the initial quantity of ice. If after 40 minutes the amount of ice left is $Kx_0$, then K =

If $\int_0^{\frac{\pi}{2}} \frac{dx}{5+4\sin x} = A \tan^{-1} B$, then A + B =

If $X \sim B(4, p)$ and $P(X = 0) = \frac{16}{81}$, then $P(X = 4) =$

If the lines $3x - 4y + 4 = 0$ and $6x - 8y - 7 = 0$ are tangents to a circle, then the radius of the circle is

If $x = a \cos \theta$, $y = b \sin \theta$, then $\left[\frac{d^2 y}{d x^2}\right] = $

If $h(x)=\sqrt{4 f(x)+3 g(x)}$, $f(1)=4$, $g(1)=3$, $f^{\prime}(1)=3$, $g^{\prime}(1)=4$, then $h^{\prime}(1)=$

If the line $\frac{x+1}{2}=\frac{y-m}{3}=\frac{z-4}{6}$ lies in the plane $3x-14y+6z+49=0$, then the value of $m$ is

If $4 \sin ^{-1} x+6 \cos ^{-1} x=3 \pi$, where $-1 \leq x \leq 1$, then $x =$

If $x \in \left(0, \frac{\pi}{2}\right)$ and $x$ satisfies the equation $\sin x \cos x = \frac{1}{4}$, then the values of $x$ are

$\int \frac{x+\sin x}{1+\cos x} d x=$

The value of $\sin 18^{\circ}$ is

The equation of the tangent to the curve $y = 4x e^x$ at $\left(-1, -\frac{4}{e}\right)$ is

All the letters of the word 'ABRACADABRA' are arranged in different possible ways. Then the number of such arrangements in which the vowels are together is

The domain of the function $f(x) = \frac{1}{\sqrt{x + |x|}}$ is

If $\int \frac{1+x^2}{1+x^4} d x=\frac{1}{\sqrt{2}} \tan ^{-1}\left[\frac{f(x)}{\sqrt{2}}\right]+c$, then $f(x)=$

The slope of the line through the origin which makes an angle of $30^\circ$ with the positive direction of Y-axis measured anticlockwise is :

With usual notations if the angles of a triangle are in the ratio 1 : 2 : 3, then their corresponding sides are in the ratio

The angle between a line with direction ratios 2, 2, 1 and a line joining $(3, 1, 4)$ and $(7, 2, 12)$ is

The differential equation of all circles which pass through the origin and whose centre lie on Y-axis is

$(2\hat{\mathrm{i}} + 6\hat{\mathrm{j}} + 27\hat{\mathrm{k}}) \times (\hat{\mathrm{i}} + \lambda\hat{\mathrm{j}} + \mu\hat{\mathrm{k}}) = \vec{0}$, then $\lambda$ and $\mu$ are respectively

If $f(x) = [x]$, for $x \in (-1, 2)$, then $f$ is discontinuous at (where $[x]$ represents floor function)

If $A = \begin{bmatrix} 3 & 2 & 4 \\ 1 & 2 & 1 \\ 3 & 2 & 6 \end{bmatrix}$ and $A_{ij}$ are cofactors of the elements $a_{ij}$ of $A$, then $a_{11}A_{11} + a_{12}A_{12} + a_{13}A_{13}$ is equal to

The general solution of the differential equation $x + y \frac{d y}{d x} = \sec(x^2 + y^2)$ is

The value of $(1 + i)^5 (1 - i)^7$ is

$\lim_{x \to \infty} \left( \sqrt{x^2 + 5x - 7} - x \right) =$