Mathematics Tes...

If \(\alpha\) and \(\beta\) are the roots of the quadratic equation \((5+\sqrt{2}) x^{2}-(4+\sqrt{5}) x+(8+2 \sqrt{5})=0\), then the value of \(\frac{2 \alpha \beta }{(\alpha+\beta)}\) 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 \(P =?\)

What is the diameter of a circle inscribed in a regular polygon of 12 sides, each of length 1 cm?

The distance of line \(3 y-2 z-1=0=3 x-z+4\) from the piont \((2,-1,6)\) is

If the function \(f\) defined as

\(f(x)=\frac{1}{x}-\frac{k-1}{e^{2 x}-1}\)

\(x \neq 0\), is continuous at \(x=0\), then the ordered pair (\(\mathrm{k}, \mathrm{f}(0)\)) is equal to?

If \(\sin ^{-1} x+\cos ^{-1} y=\frac{2 \pi}{5}\), then \(\cos ^{-1} x+\sin ^{-1} y\) is:

\(\int_{1}^{3}|x-2| d x\) equal to?

If \(\alpha, \beta\) are the roots of the equation \(x^{2}+x+2=0\), then \(\frac{\alpha^{10}+\beta^{10}}{\alpha^{-10}+\beta^{-10}}\) is equal to:

If \(6 \sin ^{2} x-2 \cos ^{2} x=4\), then find the value of \(\tan x \).