Mathematics Tes...

In a room, there are eight couples. Out of them if 4 people are selected at random, the probability that they may be couples is?

If the angles of a triangle ABC are in AP and b : c =$\sqrt{3}:\sqrt{2}$,then what is the measure of angle A?

Find the value of\(\left|\begin{array}{ccc}a+x & y & z \\ x & a+y & z \\ x & y & a+z\end{array}\right|\).

The expected value of the number of heads obtained when three fair coins are tossed simultaneously is:

What is the minimum value of \(\frac{a^{2}}{\cos ^{2} x}+\frac{b^{2}}{\sin ^{2} x}\) where \(a>0\) and \(b>0\)

What is the general solution of the differential equation \(x^{2} d y+y^{2} d x=0\)?

Consider a binary operation \(^{*}\) on \(\mathrm{N}\) defined as \(a^{*} b=a^{3}+b^{3},\) Choose the correct answer.

\(|\overrightarrow{\mathrm{a}}+\overrightarrow{\mathrm{b}}|=|\overrightarrow{\mathrm{a}}-\overrightarrow{\mathrm{b}}|,\) then which one of the following is correct?

If \(A=\left[\begin{array}{cc}2 & 3 \\ -1 & 2\end{array}\right]=\frac{1}{2}(P+Q)\) where \(P\) is symmetric and \(Q\) is skew symmetric matrix then \(P\) and \(Q\) are:

Find the differentiation of the following function \(\sec ^{-1} \tan x .\)