List of top Mathematics Questions

For real \(x\), if \(x+\frac{1}{x}=2\cos\theta\), then \(\cos\theta\) is

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

If \(\sin\theta=\frac{3}{5}\), then \(\cos\theta=\)

If \(\cos\theta\cosec\theta=-1\) and \(\theta\) lies in the second quadrant, then \(\cos\theta=\)

The particular integral of \(\displaystyle \frac{d^2y}{dx^2}+3\frac{dy}{dx}+2y=e^{-2x}\) is

The solution of the differential equation \(\displaystyle \frac{dy}{dx}=1+y^2\) is

The solution of the differential equation \(\displaystyle \frac{d^3y}{dx^3}+3\frac{d^2y}{dx^2}+2\frac{dy}{dx}=0\) is

The solution of the differential equation \(\displaystyle \frac{dy}{dx}+\frac{y}{x}=x^2\) under the condition that \(y(1)=1\) is

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

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

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

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

The differential equation \(\displaystyle \frac{dy}{dx}=-\left(\frac{x+y}{1+x^2}\right)\) is

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

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

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

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

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

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

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

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

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

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