List of top Mathematics Questions

The number of solutions of the trigonometric equation $\sin^2 x - \sin x - 2 = 0$ in the interval $[0, 2\pi]$ is:

The integral $\int \frac{e^x (1 + x)}{\cos^2(x e^x)} \, dx =$

The area (in square units) of the region bounded by the parabola $y^2 = 4x$ and the line $y = 2x$ is:

The value of the definite integral $\int_0^{\pi/2} \frac{\sin^{3/2} x}{\sin^{3/2} x + \cos^{3/2} x} \, dx$ is:

The integral $\int \frac{1}{\cos^2 x (1 - \tan x)^2} \, dx =$

The value of the definite integral $\int_{-\pi/2}^{\pi/2} (x^3 + x\cos x + \tan^5 x + 1) \, dx$ is:

If $y = e^{a \sin^{-1} x}$, then $(1 - x^2) y_2 - x y_1 =$

The slope of the normal to the curve $y = 2x^2 + 3\sin x$ at $x = 0$ is:

The minimum value of the function $f(x) = x^2 + \frac{250}{x}$ for $x > 0$ is:

A balloon, which always remains spherical, has a variable radius. The rate at which its volume is increasing with respect to its radius $r$ when $r = 5$ cm is:

The value of $\lim_{x \to \infty} \left(\frac{x+6}{x+1}\right)^{x+4}$ is:

If $x = a \cos^3 t$ and $y = a \sin^3 t$, then the value of $\frac{dy}{dx}$ at $t = \frac{\pi}{4}$ is:

If $f(x) = \frac{k \cos x}{\pi - 2x}$ for $x \neq \frac{\pi}{2}$ and $f\left(\frac{\pi}{2}\right) = 3$ is continuous at $x = \frac{\pi}{2}$, then the value of $k$ is:

If $y = \tan^{-1}\left(\frac{\sin x + \cos x}{\cos x - \sin x}\right)$, then $\frac{dy}{dx} = $

The ratio in which the $xy$-plane divides the line segment joining the points $(2, 4, 5)$ and $(3, 5, -4)$ is:

The acute angle between the planes $2x - y + z = 6$ and $x + y + 2z = 3$ is:

If a line makes angles $45^\circ$ and $60^\circ$ with the positive $x$ and $y$ axes respectively, then the acute angle it makes with the $z$-axis is:

If the eccentricity of a hyperbola is $\sqrt{3}$, then the eccentricity of its conjugate hyperbola is:

The line $y = mx + c$ touches the ellipse $9x^2 + 16y^2 = 144$ if the value of $c^2$ is:

The equation of the common chord of the circles $x^2 + y^2 - 4x - 4y = 0$ and $x^2 + y^2 - 6x - 8y + 10 = 0$ is:

If the circle $x^2 + y^2 - 4x - 6y + \lambda = 0$ touches the x-axis, then the value of $\lambda$ is:

If the circle $x^2 + y^2 + 2x - 2y + c = 0$ cuts the circle $x^2 + y^2 - 4x - 6y + 11 = 0$ orthogonally, then the value of $c$ is:

The equation of the parabola with focus at $(3, 0)$ and directrix $x + 3 = 0$ is:

If the distance between the foci of an ellipse is 6 and the distance between its directrices is 12, then the length of its latus rectum is:

If the lines joining the origin to the points of intersection of the line $y = mx + 1$ and the circle $x^2 + y^2 = 1$ are perpendicular to each other, then the value of $m^2$ is: