Mathematics Tes...

Three persons \({P}, {Q}\) and \({R}\) independently try to hit a target. If the probabilities of their hitting the target are \(\frac{3}{4}, \frac{1}{2}\) and \(\frac{5}{8}\) respectively, then the probability that the target is hit by \({P}\) or \({Q}\) but not by \({R}\) is:

If two vectors \(\vec{a}\) and \(\vec{b}\) are such that \(|\vec{a}|= 2, |\vec{b}|=3\) and \(\vec{a}\cdot\vec{b} = 4\) then find \(|\vec{a}-\vec{b}|\).

The equation of circle which passes through the origin and cuts off intercepts 5 and 6 from the positive parts of the \(x\) axis and \(y\) -axis respectively is \(\left(x-\frac{5}{2}\right)^{2}+(y-3)^{2}=\lambda\), where \(\lambda\) is:

The solution of the matrix equation \(\left[\begin{array}{ccc}2 & -1 & 3 \\ 1 & 1 & 1 \\ 1 & -1 & 1\end{array}\right]\left[\begin{array}{l}x \\ y \\ z\end{array}\right]=\left[\begin{array}{l}9 \\ 6 \\ 2\end{array}\right]\) is:

What is \(C(n, r)+2 C(n, r+1)+C(n, r+2)\) equal to?

The mean and variance of a binomial distribution are 8 and 4 respectively, then \(p(x = 1)\) is equal to?

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