List of top Mathematics Questions

The radius of a sphere (in cm) whose volume is $36\pi \text{ cm}^3$, is :

In the given figure, PA is a tangent from an external point P to a circle with centre O. If $\angle\text{POB} = 125^\circ$, then $\angle\text{APO}$ is equal to :

Shown in the given figure is a circle with centre O. The area of the minor sector is $7 \text{ cm}^2$. Area of circle is :

If the mean and mode of a data are 12 and 21 respectively, then its median is :

Given that $\sin\theta = \frac{a}{b}$, then $\cos\theta$ is equal to :

If TP and TQ are two tangents to a circle with centre O from an external point T so that $\angle\text{POQ} = 120^\circ$, then $\angle\text{PTQ}$ is equal to :

The string of a flying kite is tied to a point on the ground. The length of the string between the kite and the point on the ground is 80 m. The string makes an angle of $30^\circ$ with the ground. The height of the kite above the ground is :

If $\cos A = \frac{1}{2}$, then the value of $\sin^2 A + 2\cos^2 A$ is :

The mid-point of the line segment joining the points $(5, -4)$ and $(6, 4)$ lies on :

The common difference of the AP : $\sqrt{2}, 2\sqrt{2}, 3\sqrt{2}, 4\sqrt{2}, \dots$ is :

If $\Delta$ ABC and $\Delta$ DEF are similar such that $2 \text{ AB} = \text{DE}$ and $\text{BC} = 8 \text{ cm}$, then EF is equal to :

If a pair of linear equations in two variables is represented by two coincident lines, then the pair of equations has :

For any natural number $n$, $6^n$ ends with the digit :

The graph of $y = f(x)$ is given. The number of zeroes of $f(x)$ is :

The general solution of the differential equation \[ \frac{dy}{dx}+\frac{y}{x}=x^2 \] is

Evaluate \[ \int_{1/e}^{e^2} \left| \frac{\log_e x}{x} \right| \,dx \]

If \[ \int \frac{dx}{2\sin^2x+\sin2x} = \frac12\log|f(x)|+C \] and \[ f\!\left(\frac{\pi}{4}\right)=\frac12, \] then \(f(x)\) is

If \[ \int \frac{2\cos x+3\sin x} {3\cos x+4\sin x}\,dx = Ax+B\log|3\cos x+4\sin x|+C, \] then \[ A\cdot B= \]

The closest point on the parabola \[ y=x^2+7x+2 \] to the straight line \[ y=3x-2 \] is

If \[ \int 4^x \cdot 4^{4^x}\cdot 4^{\,4^{4^x}}\,dx = A\,4^{\,4^{4^x}}+C, \] then \(A=\)

Evaluate \[ \lim_{n\to\infty} \frac{1+2^4+3^4+\cdots+n^4}{n^5} - \lim_{n\to\infty} \frac{1+2^3+3^3+\cdots+n^3}{n^5}. \]

If \[ f(x)=\frac1{x^2}\int_{3}^{x}\left(2t-3f'(t)\right)\,dt, \] then \[ f'(3)= \]

If \[ \int \frac{dx}{\sin^3x+\cos^3x} = A\log\left| \frac{\sqrt2+t}{\sqrt2-t} \right| + B\tan^{-1}(t)+C, \] then \[ \left(\frac{B}{A},\,t\right) = \]

Find:

The principal value of \[ \sec^{-1}(\sqrt{2})+2\csc^{-1}(-2) \] is:

The order and degree of the differential equation \[ \left\{1+\left(\frac{dy}{dx}\right)^2\right\}^{3/2} = \frac{d^2y}{dx^2} \] are respectively