Mathematics Tes...

The equation of line \(\frac{x-1}{1}=\frac{y+2}{-1}=\frac{z-3}{-3}\) and equation of plane is \(4 x+13 y-3 z+1=\) 0. Then find the distance between given point and plane.

Find the sum of the series whose nth term is n (n + 2).

If \(\frac{e^{x}}{1-x}=B_{0}+B_{1} x+B_{2} x^{2}+\ldots+B_{n} x^{n}+\ldots\), then the value of \(B_{n}-B_{n-1}\) is:

What is the modulus of \(\frac{1+7 i }{(2- i )^{2}}\) where \(i =\sqrt{-1} ?\)

If \(\alpha\) and \(\beta\) are the zeros of the quadratic polynomial \(f(x)=x^{2}-5 x+6\), find the value of \(\left(a^{2} \beta+\beta^{2} a\right)\).

\(2\left(\sin ^6 \theta+\cos ^6 \theta\right)-3\left(\sin ^4 \theta+\cos ^4 \theta\right)\) is equal to:

The differential equation of all lines passing through the origin is:

What is the value of the sum \(\sum_{n=2}^{11}\left(i^{n}+i^{n+1}\right)\) where \(i=\sqrt{-1}\)?

For which value(s) of k will the roots of 3x² + 3 = 2kx be real and equal?

If (x) is an odd periodic function with period 2, then f(4) equal to: