Mathematics Tes...

If the vectors \(2 \hat{i}+\hat{j}+\hat{k}\) and \(\hat{i}-4 \hat{j}+\lambda \hat{k}\) are mutually perpendicular, then the value of \(\lambda\) is:

If \(p=\sin \theta+\cos \theta\) and \(q=\sec \theta+\operatorname{cosec} \theta\), then \(q\left(p^{2}-1\right)\) is:

Differentiate the function \(f(t)=\sqrt{t}(a+b t)\).

If \(\cos ^{4} \theta-\sin ^{4} \theta=\frac{1}{3}\), then the value of \(\tan ^{2} \theta\) is:

What is the value of \((-1+i \sqrt{3})^{48}\) ?

Find the value of \(\frac{d}{d x}\left(\frac{x^2+x-2}{x^3+6}\right)\).

Region represented by the in equation system \(x+y \leq 3, y \leq 6\) and \(x \geq 0, y \geq 0\) is:

The conjugate of \(\frac{(2-i)(1+2 i)}{(3+i)(2-3 i)}\) is:

A box contains 5 green pencils and 7 yellow pencils. Two pencils are chosen at random from the box without replacement. What is the probability they are both yellow?

The area (in square units) bounded by the lines x = 0, y = 0, x + y = 1 and 2x + 3y = 6 is: