List of top Mathematics Questions

The order of the differential equation whose general solution is \(y = a \sin x + b \cos x\) is (where a and b are arbitrary constants)

The degree of the differential equation \(y' + y = \frac{5}{y'}\) is

The RMS value of \(x^2\) in [0, 1] is

The area bounded by the curve \(y = 4x^2\), the x-axis, the line x=0 and the line x = 1 is

\(\int_{0}^{\pi/2} \frac{\cos 2x}{\sin x + \cos x} \,dx =\)

\(\int_{-a}^{a} |x| \,dx =\)

The value of \(\int_0^1 x(1-x)^9 \,dx\) is

\(\int \frac{dx}{25 - x^2} =\)

\(\int \sin^2 x \,dx =\)

The value of \(\int (\log \sec x) \tan x \,dx\) is

If \(u = e^{xy}\), then the value of \(\frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2}\) at (1, 1) is

If \(z = x^2 - y^2\) then \( \frac{1}{x} \frac{\partial z}{\partial x} + \frac{1}{y} \frac{\partial z}{\partial y} = \)

For what value of x, the function \(f(x) = 2x^3 + 3x^2 - 36x + 10\) has minimum

The equation of the tangent to the curve \(y = x^3\) at (1, 1) is

Slope of the normal to the curve \(x^{2/3} + y^{2/3} = 2\) at the point (1, 1) is

If \(y = \sqrt{\sin x + \sqrt{\sin x + \sqrt{\sin x + \dots \infty}}}\) then \( \frac{dy}{dx} = \)

\(\frac{d}{dx} \left( \tan^{-1} \frac{x}{a} \right) =\)

The derivative of \(x^x\) with respective to x is

The value of \( \lim_{x\to 1} \frac{x^3 - 1}{x - 1} \) is

The value of \( \lim_{x\to\infty} \frac{4x^3 - x + 1}{x^2 - 4x(1-x^2)} \) is

The eccentricity of the ellipse \(16x^2 + 7y^2 = 112\) is

If (2,0) is the vertex and y-axis is the directrix of a parabola then its focus is

The equation of the parabola with focus (2, 0) and vertex (1, 0) is

If length of the tangent is 8 cm and the distance between the center of the circle and the external point is 11 cm, then the area of the circle is

The length of the tangent from the point (5, 1) to the circle \(x^2 + y^2 + 6x - 4y - 3 = 0\) is