Mathematics Tes...

Find the value of$(\cos 2p\pi +i\sin 2p\pi )(\cos 2q\pi +i\sin 2q\pi )$?

A fair coin is tossed independently four times. The probability of the event "the number of times heads show up is more than the number of times tails show up" is:

The total number of subsets of a finite set A has 56 more elements than the total number of subsets of another finite set B. What is the number of elements in set A?

In a parallelogram \(O A B C\), vectors \(\vec{a}, \vec{b}, \vec{c}\) are, respectively, the position vectors of vertices \(A, B, C\) with reference to \(O\) as origin. A point \(E\) is taken on the side \(BC\) which divides it in the ratio of \(2: 1\). Also, the line segment \(A E\) intersects the line bisecting the angle \(\angle A O C\) internally at point \(P\). If \(C P\) when extended meets \(A B\) in point \(F\), then the position vector of point \(P\) is:

\(\tan \left(2 \tan ^{-1}(\cos x)\right)\) is equal to:

If \(\alpha\) and \(\beta\) are the roots of the equation \(x^{2}-6 x+3=0\), what is the value of \(\frac{\alpha}{\beta}+\frac{\beta}{\alpha} ?\)

Find the middle terms in the expansion of \(\left(1+3 x+3 x^{2}+x^{3}\right)^{2 n}\).

The magnitude of the projection of the vector \(2 \hat{i}+3 \hat{j}+\hat{k}\) on the vector perpendicular to the plane containing the vectors \(\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}\) and \(\hat{i}+2 \hat{j}+3 \hat{k}\), is:

A tea party is arranged for \(16\) people along two sides of a long table with eight chairs on each side. Four particular men wish to sit on one particular side and two particular men on the other side. The number of ways they can be seated is: