Out of $13$ cricket players,$4$ are bowlers. In how many ways can a cricket team of $11$ players be formed such that at least $2$ bowlers are included?

If $10000\, V$ is applied across an $X$-ray tube, what will be the ratio of the de-Broglie wavelength of the incident electrons to the shortest wavelength of the $X$-rays produced? (Given: $\frac{e}{m}$ for an electron is $1.8 \times 10^{11}\, C\, kg^{-1}$)

If $A(1,2,3), B(3,7,-2), C(6,7,7)$ and $D(-1,0,-1)$ are points in a plane, then the vector equation of the line passing through the centroids of $\triangle ABD$ and $\triangle ACD$ is

If the lines $x^2+2xy-35y^2-4x+44y-12=0$ and $5x+\lambda y-8=0$ are concurrent,then the value of $\lambda$ is

The separation of a racemic mixture into pure enantiomers is termed as

An ideal gas of mass $m$ in a state $A$ goes to another state $B$ via three different processes as shown in the figure. If ${Q_1}, {Q_2}$ and ${Q_3}$ denote the heat absorbed by the gas along the three paths,then