Mix Test 2...

\(sin[\frac{\pi}{3}-sin^{-1}(-\frac{1}{2})]\) is equal to:

The value of k (k < 0) for which the function f defined as

\(f(x)=\begin{cases}\frac{1-cos\,kx}{xsin\,x},&x\neq0\\\frac{1}{2},&x=0\end{cases}\)

is continuous at x = 0 is:

If \(A=[a_{ij}]\) is a square matrix of order 2 such that \(a_{ij}=\begin{cases}1,&when\,i\neq j\\0,&i=j\end{cases},\) then \(A^2\) is:

The set of values of k, for which \(A=\begin{bmatrix}k&8\\4&2k\end{bmatrix}\) is a singular matrix is:

Given that A is a square matrix of order 3 and |A| = -4, then | adj A | is equal to:

A relation R in set A = {1,2,3} is defined as R = {(1, 1), (1, 2), (2, 2), (3, 3)}. Which of the following ordered pair in R shall be removed to make it an equivalence relation in A?

If \(\begin{bmatrix}2a+b&a-2b\\5c-d&4c+3d\end{bmatrix}=\begin{bmatrix}4&-3\\11&24\end{bmatrix},\) then value of a + b – c + 2d is:

The point at which the normal to the curve \(y=x+\frac{1}{x},\) x > 0 is perpendicular to the line 3x – 4y – 7 = 0 is:

\(sin(tan^{-1}x),\) where |x| < 1, is equal to:

Let the relation R in the set \(A=\{x\in Z:0\leq x\leq12\},\) given by R = {(a, b) : |a – b| is a multiple of 4}. Then [1], the equivalence class containing 1, is:

If \(e^x+e^y=e^{x+y},\) then \(\frac{dy}{dx}\) is:

Given that matrices A and B are of order \(3\times n\,and\,m\times5\) respectively, then the order of matrix C = 5A+3B is:

If y = 5 cos x – 3 sin x, then \(\frac{d^2y}{dx^2}\) is equal to:

For matrix \(A=\begin{bmatrix}2&5\\-11&7\end{bmatrix},(adj\,A)'\) is equal to:

The points on the curve \(\frac{x^2}{9}+\frac{y^2}{16}=1\) at which the tangents are parallel to y axis are:

Given that \(A=[a_{ij}]\) is a square matrix of order \(3\times3\,and\,|A|=-7,\) then the value of \(\sum_{i=1}^3a_{i2}A_{i2},\) where \(A_{ij}\) denotes the cofactor of element \(a_{ij}\) is:

If \(y=log(cos\,e^x),\) then \(\frac{dy}{dx}\) is:

The least value of the function \(f(x)=2cos\,x+x\) in the closed interval \([0,\frac{\pi}{2}]\) is:

The function \(f: R\longrightarrow R\) defined as \(f(x)=x^3\) is:

If \(x=a\,sec\,\theta,y=b\,tan\,\theta,\) then \(\frac{d^2y}{dx^2}\,at\,\theta=\frac{\pi}{6}\) is:

The derivative of \(sin^{-1}\,(2x\sqrt{1-x^2})\) w.r.t \(sin^{-1}x,\frac{1}{\sqrt2}<x<1,\) is:

If \(A=\begin{bmatrix}1&-1&0\\2&3&4\\0&1&2\end{bmatrix}\,and\,B=\begin{bmatrix}2&2&-4\\-4&2&-4\\2&-1&5\end{bmatrix},\) then: