For $k=1, 2, 3$, the box $B_k$ contains $k$ red balls and $(k+1)$ white balls. Let $P(B_1)=\frac{1}{2}$, $P(B_2)=\frac{1}{3}$, and $P(B_3)=\frac{1}{6}$. $A$ box is selected at random and a ball is drawn from it. If a red ball is drawn, then the probability that it has come from box $B_2$ is:

$A$ horizontal uniform glass tube of $100 \ cm$ length, sealed at both ends, contains a $10 \ cm$ mercury column in the middle. The initial temperature and pressure of air on either side of the mercury column are $31^{\circ} C$ and $76 \ cm$ of mercury, respectively. If the air column at one end is kept at $0^{\circ} C$ and the other end at $273^{\circ} C$, then the pressure of the air at $0^{\circ} C$ is (in $cm$ of $Hg$):

The angle between the lines whose direction cosines satisfy the equations $l+m+n=0$ and $l^2+m^2-n^2=0$ is

Assertion : Cattle breeds can be improved by super ovulation and embryo transplantation.
Reason : Superovulation in high milk-yielding cows is induced by hormonal injection.

Which of the following oxides cannot act as a reducing agent?

The two thigh bones (femurs),each of cross-sectional area $10 \,cm^2$,support the upper part of a person of mass $50 \,kg$. The average pressure sustained by the femurs is ........... $N/m^2$.