If the pair of straight lines $xy-x-y+1=0$ and the line $ax+2y-3a=0$ are concurrent,then $a$ is equal to

If $\frac{\cos x}{\cos (x-2y)} = \lambda$,then $\tan (x-y) \tan y$ is equal to

Which of the following is paramagnetic?

Which relation is incorrect?

If $x = \frac{1}{2} \left( \sqrt{3} + \frac{1}{\sqrt{3}} \right)$,then the value of $\frac{\sqrt{x^2 - 1}}{x - \sqrt{x^2 - 1}}$ is equal to

$50 \, g$ of copper is heated to increase its temperature by $10 \, ^\circ C$. If the same quantity of heat is given to $10 \, g$ of water,the rise in its temperature is ........ $^\circ C$. (Specific heat of copper $= 420 \, J \, kg^{-1} \, ^\circ C^{-1}$,Specific heat of water $= 4200 \, J \, kg^{-1} \, ^\circ C^{-1}$)