Mathematics Tes...

Find the value of \(x\) and \(y\) such that \(\left[\begin{array}{l}x-y \\ x+y\end{array}\right]=\left[\begin{array}{c}2 \\ 16\end{array}\right]\).

General solution of \(\left(x^2+y^2\right) d x-2 x y d y=0\) is:

The derivative of \(\cos ^{-1}\left(\frac{1}{2 x^{2}-1}\right)\) with respect to \(\sqrt{1-x^{2}}\) is:

The area of the region bounded by the curve \(y=\sqrt{16-x^2}\) and \(x\)-axis is:

If \(-2<2 x-1<2\) then the value of \(x\) lies in the interval:

Consider the function \(f: R \rightarrow\{0,1\}\) such that:

\(f(x)=\left\{\begin{array}{c}1 \text { if } x \text { is rational } \\ 0 \text { if } x \text { is irrational }\end{array}\right.\).

Which one of the following is correct?

The maximum value of \(P=x+3 y\) such that \(2 x+y \leq 20, x+2 y \leq\) \(20, x \geq 0, y \geq 0\), is:

The mean and standard deviation of a set of values are 5 and 2 respectively. If 5 is added to each value, then what is the coefficient of variation for the new set of values?

Two dice A and B are rolled. Let numbers obtained on A and B be α and β respectively. If the variance of α−β is $\frac{p}{q}$, where p and q are co-prime, then the sum of the positive divisior of p is equal to:

A passenger wants to travel from Delhi to Mangalore by train. There is no direct train from Delhi to Mangalore, but there are trains from Delhi to Mumbai and from Mumbai to Mangalore. Actually, there are four trains from Delhi to Mumbai and three trains from Mumbai to Bangalore. In how many ways can he travel from Delhi to Mangalore?