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Two wires of the same material and length but diameters in the ratio $1:2$ are stretched by the same force. The elastic potential energy per unit volume for the wires, when stretched by the same force, will be in the ratio: (in $:1$)

$A$ particle $P$ is moving in a circle of radius $a$ with a uniform speed $v$. $C$ is the centre of the circle and $AB$ is a diameter. When passing through $B$,the angular velocity of $P$ about $A$ and $C$ are in the ratio:

What is the equivalent capacitance of the system of capacitors between $A$ and $B$?

In a $\triangle ABC$,the expression $\frac{(a+b+c)(b+c-a)(c+a-b)(a+b-c)}{4b^2c^2}$ is equal to:

The number of values of $x$ in the interval $[0, 3\pi]$ satisfying $2 \sin^2 x + 5 \sin x - 3 = 0$ is