In a fission reaction ${}_{92}^{236}U \to {}^{117}X + {}^{117}Y + n + n,$ the binding energy per nucleon of $X$ and $Y$ is $8.5\, MeV$ whereas that of ${}^{236}U$ is $7.6\, MeV$. The total energy liberated will be about:

$A$ straight line which makes equal intercepts on positive $X$ and $Y$ axes and which is at a distance of $1$ unit from the origin intersects the straight line $y = 2x + 3 + \sqrt{2}$ at $(x_0, y_0)$. Then $2x_0 + y_0$ is equal to

Which of the following aqueous solutions will have the highest boiling point?

The period of $f(x)=\cos \left(\frac{x}{3}\right)+\sin \left(\frac{x}{2}\right)$ is (in $\pi$)

Let $I$ be the moment of inertia of a uniform square plate about an axis $AB$ passing through its center and parallel to two of its sides. $CD$ is an axis in the plane of the square and passing through the center,making an angle $\theta$ with $AB$. The moment of inertia of the plate about the axis $CD$ is:

Two equal resistances when connected in series to a battery,consume electric power of $60 \ W$. If these resistances are now connected in parallel combination to the same battery,the electric power consumed will be............. $W$