The enthalpy change $(\Delta H)$ for the reaction,$N_{2(g)} + 3H_{2(g)} \longrightarrow 2NH_{3(g)}$ is $-92.38 \ kJ$ at $298 \ K$. The internal energy change $\Delta U$ at $298 \ K$ is ...... $kJ$.

$A$ bullet of mass $10 \ g$ pierces through a plate $A$ of mass $500 \ g$ and then gets embedded into a second plate $B$ of mass $1.49 \ kg$ as shown in the figure. Initially,the two plates $A$ and $B$ are at rest and move with the same velocity after the collision. The percentage loss in the initial kinetic energy of the bullet,when it is between the plates $A$ and $B$,is . . . . . .
(Neglect any loss of material of the plates during the collision)

Which one of the following statements is $WRONG$ in the context of $X-$rays generated from an $X-$ray tube?

If the circle $x^2+y^2+8x-4y+c=0$ touches the circle $x^2+y^2+2x+4y-11=0$ externally and cuts the circle $x^2+y^2-6x+8y+k=0$ orthogonally,then $k$ is equal to

If $x$ and $y$ are acute angles such that $\cos x + \cos y = \frac{3}{2}$ and $\sin x + \sin y = \frac{3}{4}$,then $\sin(x+y)$ is equal to

Chemical $A$ is used for water softening to remove temporary hardness. $A$ reacts with sodium carbonate to produce caustic soda. When $CO_2$ is passed through a solution of $A$,it turns milky. What is the chemical formula of $A$?