Mathematics Tes...

The value of the integral \(\int_{0}^{1.5}\left[x^{2}\right] d x\), where \([x]\) denotes the greatest integer:

Find the sum of series:

0.5+ 0.55 + 0.555+...

If \(A=\left[\begin{array}{lll}2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2\end{array}\right]\), then \(A^5=?\)

The angle between the lines \(\frac{x-2}{2}=\frac{y-1}{7}=\frac{z+3}{-3}\) and \(\frac{x+2}{-1}=\frac{y-4}{2}=\) \(\frac{z-5}{4}\) is:

\(2 x-3 y=0\) and \(2 x+\alpha y=0\)

For what value of \(\alpha\) the system has infinitely many solution.

If \(z_{1}\) and \(z_{2}\) are two distinct complex numbers satisfying the relation \(\left|z_{1}^{2}-z_{2}^{2}\right|=\left|\bar{z}_{1}^{2}+\bar{z}_{2}^{2}-2 \bar{z}_{1} \bar{z}_{2}\right|\) and \(\left(\arg z_{1}-\arg z_{2}\right)=\frac{a \pi}{b},\) then the least possible value of \(|a-b|\) is equal to: (where, \(a \& b\) are integers)

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

A chord subtends an angle \(=120^{\circ}\)at the center of a unit circle. What is the length of the chord?