$A$ random variate $X$ takes the values $0, 1, 2, 3$ and its mean is $1.3$. If $P(X=3) = 2 P(X=1)$ and $P(X=2) = 0.3$, then $P(X=0)$ is equal to:

The maximum value of $xy$ subject to $x+y=7$ is

The major product of the following reaction is:

Match the items of column $I$ with column $II$. Select the correct option from the following:

Column $I$	Column $II$
$(a)$ $XX$-$XO$ method of sex determination	$(i)$ Turner's syndrome
$(b)$ $XX$-$XY$ method of sex determination	$(ii)$ Female heterogametic
$(c)$ Karyotype-$45$	$(iii)$ Grasshopper
$(d)$ $ZW$-$ZZ$ method of sex determination	$(iv)$ Female homogametic

In the diagram,$I_1$ and $I_2$ are the strengths of the currents in the loop and the infinitely long straight conductor,respectively. Given $OA = AB = R$. The net magnetic field at the centre $O$ is zero. Then the ratio of the currents in the loop and the straight conductor $(I_1/I_2)$ is:

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