Mathematics Tes...

If \(\alpha\) 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 the equation:

The sum of the first 20 terms of the series \(\sqrt{5}+\sqrt{20}+\sqrt{45}+\sqrt{80}+\ldots\) is

A function y = f(x) has a second order derivative f''(x) = 6(x - 1).  If its graph passes through the point (2, 1) and at that point the tangent to the graph is y = 3x -5.  then the function is :

The complex number \(\frac{1+2i}{1-2i}\) lies in which quadrant of the complex plane.

If (1−p) is a root of quadratic equation x² + px + (1−p) = 0, then the roots are equal to:

If \(\operatorname{cosec} \theta-\cot \theta=m\), then what is \(\operatorname{cosec} \theta\) equal to?

The general solution \(\mathrm{y}(\mathrm{x})\) of the differential equation \(\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{\sqrt{1-\mathrm{y}^2}}{\sqrt{1-\mathrm{x}^2}}\):

Express the given complex number \(\left(\frac{1}{3}+3 i\right)^{3}\) in the form \(a+i b\):

If \(\frac{1}{2}\) is a root of the equation \(x^{2}+k x-(\frac{5}{4})=0\) then the value of \(k\) is:

Consider a binary operation \(^{*}\) on \(\mathrm{N}\) defined as \(a^{*} b=a^{3}+b^{3},\) Choose the correct answer.