$A$ disc of mass $M$ and radius $R$ rolls on a horizontal surface and then rolls up an inclined plane as shown in the figure. If the velocity of the disc is $v$,the height to which the disc will rise will be

In angiosperms,the functional megaspore develops into which of the following?

The sum of the distinct real values of $\mu$,for which the vectors $\mu \hat{i}+\hat{j}+\hat{k}$,$\hat{i}+\mu \hat{j}+\hat{k}$,and $\hat{i}+\hat{j}+\mu \hat{k}$ are coplanar is

If the angle $2 \theta$ is acute,then the acute angle between the pair of straight lines $x^2(\cos \theta - \sin \theta) + 2xy \cos \theta + y^2(\cos \theta + \sin \theta) = 0$ is:

$A$ diode detector is used to detect an amplitude-modulated wave of $60\%$ modulation by using a capacitor of capacity $250 \text{ pF}$ in parallel with a load resistance of $100 \text{ k}\Omega$. Find the maximum modulation frequency which could be detected by it.

Two adjacent sides of a parallelogram $ABCD$ are given by $\overline{AB}=2 \hat{i}+10 \hat{j}+11 \hat{k}$ and $\overline{AD}=-\hat{i}+2 \hat{j}+2 \hat{k}$. The side $AD$ is rotated by an acute angle $\alpha$ in the plane of the parallelogram so that $AD$ becomes $AD^{\prime}$. If $AD^{\prime}$ makes a right angle with side $AB$,then the cosine of the angle $\alpha$ is given by