If $\vec{a} + \vec{b} + \vec{c} = 0$,$|\vec{a}| = 3$,$|\vec{b}| = 5$,and $|\vec{c}| = 7$,then the angle between $\vec{a}$ and $\vec{b}$ is

Two cylinders $A$ and $B$ fitted with pistons contain equal number of moles of an ideal monoatomic gas at $400 ~K$. The piston of $A$ is free to move while that of $B$ is held fixed. Same amount of heat energy is given to the gas in each cylinder. If the rise in temperature of the gas in $A$ is $42 ~K$,the rise in temperature of the gas in $B$ is (in $~K$)

Modern farmers have been able to increase rice production by $50\%$ using which of the following?

The half-life of a radioactive element is $10 \ h$. The fraction of initial radioactivity of the element that will remain after $40 \ h$ is

When bauxite powder is mixed with coke and reacted with nitrogen at $2075 \ K$,carbon monoxide and $X$ are formed. What is the gas formed when $X$ is reacted with water?

The major product of the following reaction is