Mix Test 3...

Simplest form of \(tan^{-1}\left(\frac{\sqrt{1+cos\,x}+\sqrt{1-cos\,x}}{\sqrt{1+cos\,x}-\sqrt{1-cos\,x}}\right),\) \(\pi<x<\frac{3\pi}{2}\) is:

Given that A is a non-singular matrix of order 3 such that \(A^2\) = 2A, then value of |2A| is:

The value of b for which the function f(x) = x+cos x+b is strictly decreasing over R is:

Let R be the relation in the set N given by R = {(a, b) : a = b – 2, b > 6}, then:

The point(s), at which the function f given by \(f(x)=\begin{cases}\frac{x}{|x|},&x<0\\-1,&x\geq0\end{cases}\) is continuous, is/are:

If \(A=\begin{bmatrix}0&2\\3&-4\end{bmatrix}\,and\,kA=\begin{bmatrix}0&3a\\2b&24\end{bmatrix},\) then the values of k, a and b respectively are:

The area of a trapezium is defined by function f and given by f(x) = (10+x) \(\sqrt{100-x^2},\) then the area when it is maximised is:

If A is square matrix such that \(A^2=A,\) then \((I+A)^3-7\,A\) is equal to:

If \(tan^{-1}\,x=y,\) then:

Let A = {1, 2, 3}, B = {4, 5, 6, 7} and let f = {(1, 4), (2, 5), (3, 6)} be a function from A to B. Based on the given information, f is best defined as:

For \(A=\begin{bmatrix}3&1\\-1&2\end{bmatrix},\) then \(14A^{-1}\) is given by:

The point(s) on the curve \(y=x^3-11x+5\) at which the tangent is y = x - 11 is/are:

Given that \(A=\begin{bmatrix}\alpha&\beta\\\gamma&-\alpha\end{bmatrix}\,and\,A^2=3I,\) then:

For an objective function Z = ax + by, where a, b > 0; the corner points of the feasible region determined by a set of constraints (linear inequalities) are (0, 20), (10, 10), (30, 30) and (0, 40). The condition on a and b such that the maximum Z occurs at both the points (30, 30) and (0, 40) is:

For which value of m is the line y = mx + 1 a tangent to the curve \(y^2=4x?\)

The maximum value of \([x(x-1)+1]^{\frac{1}{3}},\) \(0\leq x\leq1\) is:

Let \(A=\begin{bmatrix}1&sin\alpha&1\\-sin\alpha&1&sin\alpha\\-1&-sin\alpha&1\end{bmatrix},\) where \(0\leq\alpha\leq2\pi,\) then:

Given that the fuel cost per hour is k times the square of the speed the train generates in km/h, the value of k is:

If the train has travelled a distance of 500 km, then the total cost of running the train is given by function:

If the train has travelled a distance of 500 km, then the most economical speed to run the train is:

The fuel cost for the train to travel 500 km at the most economical speed is:

The total cost of the train to travel 500 km at the most economical speed is: