Mathematics Tes...

The set of all real numbers \(\mathrm{x}\) for which \(\mathrm{x}^{2}-|\mathrm{x}+2|+\mathrm{x}>0\) is:

Find the value of \(\mathrm{A}\), if \(\sqrt{3}-3 \sqrt{3 }\tan ^{2} \mathrm{A}=3 \tan \mathrm{A}-\tan ^{3} \mathrm{~A}\)

Evaluate the value of \(\int \tan ^{4} x d x\).

The sum of all odd numbers of two terms will be-

If \(3 \mathrm{~A}+4 \mathrm{~B}^{\prime}=\left[\begin{array}{ccc}7 & -10 & 17 \\ 0 & 6 & 31\end{array}\right]\) and \(2 \mathrm{~B}-3 \mathrm{~A}^{\prime}=\left[\begin{array}{rr}-1 & 18 \\ 4 & 0 \\ -5 & -7\end{array}\right]\) then \(\mathrm{B}=?\)

If \(x y+y^{2}=\tan x+y\), then \(\frac{d y}{d x}\) is equal to:

For all \(x, x^{2}+2 a x+10-3 a>0,\) then the interval in which a lies is:

Three coins are tossed simultaneously. What is the probability that they will fall two heads and one tail?

Let X be a square matrix. Consider the following two statements on X.

I. X is invertible.

II. Determinant of X is non-zero.

Which one of the following is TRUE?