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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

Derivative of $\cos^{-1}(\frac{\sin x+\cos x}{\sqrt{2}})$, $-\frac{\pi}{4}<x<\frac{\pi}{4}$ 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 $B=0$

If A and B are skew-symmetric matrices of same order, then $AB^{\prime}+BA^{\prime}$ is a/an:

If the area of $\Delta$ ABC with vertices $A(3,1)$, $B(-2,1)$ and $C(0,k)$ is 5 sq. units, then values of k are:

If A is a square matrix such that $A^{2}=A$ then $(A-I)^{3}-A$ is equal to :

If A is a non-singular matrix, then which of the following is not true?

If $\begin{bmatrix}4\\1\\3\end{bmatrix}A=\begin{bmatrix}-4&8&4\\-1&2&1\\-3&6&3\end{bmatrix}$, then order of A must be:

If matrix $A=\begin{bmatrix}-p&q\\r&p\end{bmatrix}$ is such that $A^{2}=I$ then :

For a square matrix A, $(3A)^{-1}=$

If $A=\begin{bmatrix}\cos x&-\sin x\\\sin x&\cos x\end{bmatrix}$ and $A+A^{\prime}=I$, then the value of $x \in [0,\frac{\pi}{2}]$ is

Let $A=\begin{bmatrix}0&-3&4\\1&0&2\end{bmatrix}$ and $B=\begin{bmatrix}-3&0&1\\2&4&0\end{bmatrix}$. If $A + B + C = O$, then matrix C is:

If $A=[a_{ij}]$ is a $2\times 2$ matrix whose elements are given by $a_{ij}=\frac{|i-3j|}{2}$, then $A^{\prime}$ is:

If $adj(B)=\begin{bmatrix}\frac{1}{3}&0&0\\0&\frac{1}{3}&0\\0&0&\frac{1}{3}\end{bmatrix}$, then the value of det $(B^{-1})=$

If $\begin{vmatrix}-1&-2&5\\-2&a&-1\\0&4&2a\end{vmatrix}=-86$, then the sum of all possible values of a is