Mathematics Tes...

In the given figure, O is the centre of the circle. The length of chord BC is:

In a quadrilateral \(PQRS , \overrightarrow{ PQ }=\overrightarrow{ a }, \overrightarrow{ QR }=\overrightarrow{ b }, \overrightarrow{ SP }=\overrightarrow{ a }-\overrightarrow{ b }\). \(M\) is the mid-point of \(QR\) and \(X\) is a point on \(SM\) such that \(SX =\frac{4}{5} SM\), then \(\overrightarrow{ PX }\) is:

\(\left[\begin{array}{ll}1 & 6 \\ 7 & 2\end{array}\right]= P + Q\), where \(P\) is a symmetric & \(Q\) is a skew-symmetric, then \(P =?\)

The least value of \(n\) for which \(\left \{\frac{(1+i)}{(1-i)}\right\}^{n}\) is real, is:

The sum of the series 5 + 9 + 13 + … + 49 is:

What is \(\int \frac{d x}{\sec ^{2}\left(\tan ^{-1} x\right)}\) equal to?

In the given figure, O is the center of the circle, \(\mathrm{AM}=\mathrm{PQ}\) and \(\angle \mathrm{POQ}=45^{\circ}\). The measure of \(\angle \mathrm{AOM}\) is:

There is a quadratic equation $5x^2–10x+p=0$. The product of roots of this equation is 4 times of sum of the roots. What is the value of p?

If \(\sec \theta-\tan \theta=k\), then the value of \(\sec \theta+\tan \theta\) is:

Out of 6 teachers and 8 students a committee of 11 is to be formed. In how many ways can this be done such that the committee has exactly 4 teachers?