The value of $\sqrt{12\sqrt{5} + 2\sqrt{55}}$ is

The moment of inertia of a body about a given axis is $1.2 ~kg \cdot m^2$. Initially,the body is at rest. In order to produce a rotational kinetic energy of $1500 ~J$,an angular acceleration of $25 ~rad/s^2$ must be applied about the axis for a time duration of: (in $~s$)

An ideal gas is subjected to a cyclic process involving four thermodynamic states. The amounts of heat $(Q)$ and work $(W)$ involved in each of these states are:
$\begin{aligned} & Q_1=6000 \text{ J}, \quad Q_2=-5500 \text{ J}, \quad Q_3=-3000 \text{ J}, \quad Q_4=3500 \text{ J} \\ & W_1=2500 \text{ J}, \quad W_2=-1000 \text{ J}, \quad W_3=-1200 \text{ J}, \quad W_4=x \text{ J} \end{aligned}$
The ratio of the net work done by the gas to the total heat absorbed by the gas is $\eta$. The values of $x$ and $\eta$ respectively are:

One mole of alkene $\underline{X}$ on ozonolysis gave one mole of acetaldehyde and one mole of acetone. The $IUPAC$ name of $\underline{X}$ is

In an experiment with $15$ observations of $x$,the results $\sum x^2 = 2830$ and $\sum x = 170$ are obtained. If one observation $20$ is found to be incorrect and is replaced by the correct observation $30$,what is the correct variance?

Which of the following is an endothermic reaction?