$2 \tanh^{-1} \frac{1}{2}$ is equal to

$A$ bimetallic strip is formed out of two identical strips,one of copper and the other of brass. The coefficients of linear expansion of the two metals are $\alpha_C$ and $\alpha_B$. On heating,the temperature of the strip increases by $\Delta T$ and the strip bends to form an arc of radius $R$. Then $R$ is proportional to

$A$ series combination of $n_1$ capacitors,each of value $C_1$,is charged by a source of potential difference $4V$. When another parallel combination of $n_2$ capacitors,each of value $C_2$,is charged by a source of potential difference $V$,it has the same (total) energy stored in it as the first combination has. The value of $C_2$,in terms of $C_1$,is then

$A$ thin converging lens of focal length $f=25 \ cm$ forms the image of an object on a screen placed at a distance of $75 \ cm$ from the lens. The screen is moved closer to the lens by a distance of $25 \ cm$. The distance through which the object has to be shifted,so that its image on the screen is sharp again,is (in $cm$)

The number of arrangements of the letters of the word $PALANHAR$ in which no two vowels are together and exactly two vowels are at odd places,is

Match the columns.

Column-$I$	Column-$II$
$(a)$ Parturition	$(p)$ Attachment of embryo to endometrium
$(b)$ Gestation	$(q)$ Release of egg from Graafian follicle
$(c)$ Ovulation	$(r)$ Delivery of Foetus from uterus
$(d)$ Implantation	$(s)$ Duration between pregnancy and birth
	$(t)$ Formation of zygote by fusion of egg and sperm