Mathematics Tes...

Let \(\alpha\) and \(\beta\) are the lengths of the perpendiculars from the points \((2,3,-5)\) and \((3,1,1)\) respectively from the plane \(x+2 y-2 z-9=0\), then \(\alpha\) and \(\beta\) are the roots of which equation?

The total number of symmetric relation that can be defined on the set \(1,2,3,4,5,6,7\) is:

\(A=\left[\begin{array}{cc}x & -7 \\ 7 & y\end{array}\right]\) is a skew-symmetric matrix, then \((x, y)=?\)

If \(\omega\) is a complex cube root of unit, then \(1+\omega+\omega^{2}+\ldots+\omega^{100}\) is equal to:

A bag contains \(5\) red balls and some blue balls .If the probability of drawing a blue ball is double that of a red ball, then the number of blue balls in a bag is:

Find the value of \(a, b, c\) and d if: \(\left[\begin{array}{cc}a-b & 2 a+c \\ 2 a-b & 3 c+d\end{array}\right]=\left[\begin{array}{cc}-1 & 5 \\ 0 & 13\end{array}\right]\)

If \(\theta\) is an acute angle such that \(\tan ^2 \theta=\frac{8}{7}\), then the value of \(\frac{(1+\sin \theta)(1-\sin \theta)}{(1+\cos \theta)(1-\cos \theta)}\) is:

Coefficient of \(x^{48}\) in \(\sum_{r=0}^{50}\left({ }^{50} C_{r}\right)(x-2)^{r} 3^{50-r}\):