List of top Mathematics Questions

\[ \int_{-a}^{a}|x|\,dx= \]

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

\[ \int \frac{dx}{25-x^2}= \]

\[ \int \sin^2x\,dx= \]

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

If \(u=e^{xy}\), then the value of \[ \frac{\partial^2u}{\partial x^2}+\frac{\partial^2u}{\partial y^2} \] 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 \[ 2x^3+3x^2-36x+10 \] 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 \[ y=\sqrt{\sin x+\sqrt{\sin x+\sqrt{\sin x+\cdots}}}, \] then \(\frac{dy}{dx}=\)

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

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

The value of \[ \lim_{x\to 1}\left(\frac{x^3-1}{x-1}\right) \] 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

In a circle with center \(O\), a \(6\) cm long chord is at a distance \(4\) cm from the center. Then the length of diameter is

Modulus of the complex number \[ \frac{(1+i)^{10}}{(2i-4)^4} \] is equal to

The real part of \[ \frac{1+2i}{(2-i)^2} \] is

If \(\sin\theta-\cos\theta=\frac{4}{5}\), then the value of \(\sin\theta+\cos\theta\) is

The value of \[ \cos\frac{5\pi}{17}+\cos\frac{7\pi}{17}+2\cos\frac{11\pi}{17}\cos\frac{\pi}{17} \] is