Mathematics Tes...

Of the members of three athletic teams in a school, 21 are in the cricket team, 26 are in the hockey team and 29 are in the football team. Among them, 14 play hockey and cricket, 15 play hockey and football, 12 play football and cricket and 8 play all three games. The total number of members in the three athletic teams is:

If \(\sin ^{-1} \frac{3}{x}+\sin ^{-1} \frac{9}{x}=\frac{\pi}{2}\) then what is the value of \(x\) ?

For all positive integrals \(10^{\mathrm{n}}+3^{4 \mathrm{n}+2}+8\) is divisible by:

Which of the following functions, \(f: R \rightarrow R\) is one-one?

The coordinates of the foot of the perpendicular drawn from the point A(1,0,3) to the join of the points B(4,7,1) and C(3,5,3) are:

If \(\mathrm{P}, \mathrm{Q}\) and \(\mathrm{R}\) are three sets, then which of the following is correct?

Find the value of $\theta$ if (3+2i sin $\theta$ )/(1-2i sin $\theta$ ) is purely real or purely imaginery.

Find the maximum value of \(4 x+7 y\) with the conditions \(3 x+8 y \leq 24, y \leq 2, x \geq 0\) and \(y \geq 0\).

The factorized form of the following determinant is:

\(\left|\begin{array}{ccc}1 & l & l^{2} \\ 1 & m & m^{2} \\ 1 & n & n^{2}\end{array}\right|\)

The angle between the lines x – 2y = y and y – 2x = 5 is: