The energy liberated on complete fission of $1\, kg$ of $_{92}U^{235}$ is (Assume $200\, MeV$ energy is liberated on fission of $1$ nucleus).

If $^nC_r$ denotes the number of combinations of $n$ things taken $r$ at a time,then the expression $^nC_{r+1} + ^nC_{r-1} + 2 \times ^nC_r$ equals

In the reaction $A + 2B \rightleftharpoons 2C + D$,the initial concentration of $B$ was $1.5$ times that of $[A]$. At equilibrium,the concentrations of $A$ and $B$ became equal. The equilibrium constant $K_c$ for the reaction is:

Which among the following is a benzylic halide?

When a tuning fork of frequency $341 \ Hz$ is sounded with another tuning fork,six beats per second are heard. When the second tuning fork is loaded with wax and sounded with the first tuning fork,the number of beats is two per second. The natural frequency of the second tuning fork is (in $Hz$)

If $k > 1$ and the determinant of the matrix $A^2$,where $A = \begin{bmatrix} k & k\alpha & \alpha \\ 0 & \alpha & k\alpha \\ 0 & 0 & k \end{bmatrix}$,is $k^2$,then $|\alpha|$ is equal to