MCA Entrance Previous Year Question Bank

With the usual notation, $\frac{d^{2}x}{d{y}^2}$ is:

If $f(a+b)=f(a)\times f(b)$ for all $a$ and $b$ and $f(5)=2,f^{\prime }(0)=3$, then $f^{\prime }(5)$ is equal to

Find $\frac{d}{dx}\left(\sqrt{x}-\frac{5}{\sqrt{x}}\right)$

Derivative of $\sin x^2$ with respect to $2x^2$ is:

If $x=a\cos t$, $y=b\sin t$, then $\frac{d^{2}y}{d{x}^2}$ is:

If $f(x)={\tan }^{-1}\left[\frac{\sin x}{1+\cos x}\right]$, then what is the first derivative of $f(x)$?

The number of points in $(-\infty ,\infty )$ for which $x^2-x\sin x-\cos x=0$ is

If the radius of the circle changes at the rate of $-\frac{2}{\pi }$ m/sec, at what rate does the circle's area change when the radius is 10 m?

The interval(s) on which the graph $y=2x^3{e}^x$ is increasing are:

If $x^m{y}^n=(x+y{)}^{m+n}$, then $\frac{dy}{dx}$ is