The sum of the last eight coefficients in the expansion of $(1 + x)^{15}$ is:

$A$ reversible engine converts one-sixth of the heat supplied into work. When the temperature of the sink is reduced by $62^{\circ} C$,the efficiency of the engine is doubled. The temperatures of the source and sink are

The time period of a second's pendulum is $2\, s$. The spherical bob,which is empty from inside,has a mass of $50\, g$. This is now replaced by another solid bob of the same radius but having a mass of $100\, g$. The new time period will be .... $s$.

The increasing order of magnetic moments of the following complexes is:-
$I. [Fe(CN)_6]^{4-}$
$II. [Fe(CN)_6]^{3-}$
$III. [Cr(NH_3)_6]^{3+}$
$IV. [Ni(H_2O)_4]^{2+}$

Which of the following have $3C-2e^-$ bond?
$I.$ $Al_2Cl_6$
$II.$ $B_2H_6$
$III.$ $Fe_2Cl_6$
$IV.$ $Si_2H_6$

If two events $A$ and $B$ are such that $P(A^c) = 0.3$,$P(B) = 0.4$,and $P(A \cap B^c) = 0.5$,then $P\left[ \frac{B}{A \cup B^c} \right]$ is equal to