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The value of $\int_{-5}^{-1}\frac{1}{x}dx$ is equal to:

If $\int_{0}^{2a}\frac{1}{1+4x^{2}}dx=\frac{\pi}{6}$, then the value of a is

$\int_{-1}^{1}(1-|x|)dx$ is equal to:

If $\int_{0}^{1}\frac{dx}{e^{x}+e^{-x}}=\tan^{-1}e+k$, then the value of k is:

$\int\frac{1}{\sqrt{1+\cos 2x}}dx$ is equal to:

$\int\frac{dx}{\sqrt{25-16x^{2}}}$ is equal to:

$\int\frac{dx}{2^{x}+2^{-x}}$ is equal to:

For $f(x)=x+\frac{1}{x} (x \ne 0)$

The rate of change of volume of a sphere with respect to its diameter, when its radius is 5 cm, is:

The surface area of a sphere when its volume changes at the same rate as its radius is :

Absolute minimum value of $f(x)=(x-2)^{2}+5$ in the interval [-3, 2] is :

If $e^{-x}+e^{-y}=2$, then $\frac{dy}{dx}$ is

If $\sin^{-1}x=y$ then $\frac{dy}{dx}$ is:

Derivative of $\cos^{-1}(\frac{\sin x+\cos x}{\sqrt{2}})$, $-\frac{\pi}{4}<x<\frac{\pi}{4}$ with respect to x is :

Differential of $e^{e^{x}}$ with respect to x is:

The greatest integer function, $f(x)=[x]$ for $0<x<3$ is not differentiable at how many points?

If $f(x)=\begin{cases}\frac{\sin x}{x}+\cos x, & x\ne0 \\ k, & x=0\end{cases}$ is continuous at $x=0$, then the value of k is:

The value of k for which the function $f(x)=\begin{cases} x^{2}\sin\frac{1}{x}, & x\ne0 \\ k(x+1), & x=0 \end{cases}$ is a continuous function, is:

If $f(x)=\begin{cases}\frac{x^{2}-4x-5}{x+1},&x\ne-1\\k,&x=-1\end{cases}$ is continuous at $x=-1$ then the value of k is:

If A and B are square matrices of same order, then which of the following statements is/are always true? (i) $(A+B)(A-B)=A^{2}-B^{2}$ (ii) $AB=BA$ (iii) $(A+B)^{2}=A^{2}+AB+BA+B^{2}$ (iv) $AB=0 \Rightarrow A=0$ or $B=0$