If $y = (\cos x^2)^2$,then $\frac{dy}{dx}$ is equal to:

Three point charges $1 \ C$,$-2 \ C$,and $-2 \ C$ are placed at the vertices of an equilateral triangle of side $1 \ m$. The work done by an external force to increase the separation of the charges to $2 \ m$ in joules is $(\varepsilon_0 = \text{permittivity of air})$

If $a$ and $b$ are odd integers,then the roots of the equation $2ax^2 + (2a + b)x + b = 0, a \ne 0,$ will be

Half-life of a radioactive substance is $20 \, min$. The difference between the points of time when it is $33 \%$ disintegrated and $67 \%$ disintegrated is approximately .......... $min$.

$A$ thermally insulated vessel contains an ideal gas of molecular mass $M$ and ratio of specific heats $\gamma$. It is moving with speed $v$ and is suddenly brought to rest. Assuming no heat is lost to the surroundings,its temperature increases by:

The component of vector $\vec{A} = 2\hat{i} + 3\hat{j}$ along the vector $\vec{B} = \hat{i} + \hat{j}$ is: