Mathematics Tes...

Find the angle between two vectors \((\vec{a}=2 \hat{i}+\hat{j}-3 \hat{k})\) and \((\vec{b}=3 \hat{i}-2 \hat{j}-\hat{k})\).

Maximise,

\(Z=x+y\), subject to \(x-y \leq-1,-x+y \leq 0\), and \(x, y \leq 0\)

Find the value of \(\frac{(\sin x+\cos x+1)(\sin x+\cos x-1)}{(\tan x+\cot x)\left(\sin ^{2} x \cos ^{2} x\right)}\):

The equation of sphere is \(x^2+y^2+z^2-x+z-2=0\), its radius is:

If \(\sin ^{4} x+2 \cos ^{4} x=\frac{2}{3}\), then what is the value of \(\sec ^{2} x ?\)

The curve represented by the equations

\(x=3(\cos t+\sin t)\)

\(y=4(\cos t-\sin t)\) is:

What is the number of outcomes when a coin is tossed and then a die is rolled only in case a head is shown on the coin?

For any positive integer \(n,(-1 \sqrt{-1})^{4 n+5}\) is:

\(\int_{0}^{\frac{\pi}{2}} \frac{\sin x}{\sin x+\cos x} d x\) is equal to?

Find the value of \(i^{1325}\) where \(i=\sqrt{-1}\).