An inclined plane makes an angle of $30^{\circ}$ with the horizontal. $A$ solid sphere rolling down this inclined plane from rest without slipping has a linear acceleration equal to:

The transformed equation of $x^2+y^2=r^2$ when the axes are rotated through an angle $36^{\circ}$ is

The number of unpaired electrons in an $O_2$ molecule is

Carbon,Silicon,and Germanium atoms have four valence electrons each. Their valence and conduction bands are separated by energy band gaps represented by $(E_g)_C$,$(E_g)_{Si}$,and $(E_g)_{Ge}$ respectively. Which one of the following relationships is true in their case?

$A$ tower,of $x$ metres high,has a flagstaff at its top. The tower and the flagstaff subtend equal angles at a point distant $y$ metres from the foot of the tower. Then,the length of the flagstaff (in metres) is:

In a meter bridge,the null point is found at a distance of $25\, cm$ from $A$. If now a resistance of $10\,\Omega$ is connected in parallel with $S$,the null point occurs at the midpoint of $AB$. The value of $R$ is .............. $\Omega$. (in $.67$)