$A$ body of mass $m$ moving with velocity $v$ collides head-on with another body of mass $2m$ which is initially at rest. The ratio of the kinetic energy of the colliding body before and after the collision will be: (in $:1$)

$A$ radioactive sample of $U^{238}$ decays to $Pb$ through a process for which the half-life is $4.5 \times 10^9 \text{ years}$. What is the ratio of the number of nuclei of $Pb$ to $U^{238}$ after a time of $1.5 \times 10^9 \text{ years}$? (Given $2^{1/3} = 1.26$)

Pressure versus temperature graphs of an ideal gas are as shown in the figure. Choose the wrong statement.

Pulses are a rich source of which of the following?

The condition that $f(x)=a x^3+b x^2+c x+d$ has no extreme value,is

Match the following columns:

Column-$I$	Column-$II$
$(a)$ $Oscillatoria$	$(p)$ $Prothallus$
$(b)$ $Cycas$	$(q)$ $Cell$ $wall$ $contains$ $chitin$ $mixed$ $with$ $cellulose$
$(c)$ $Dryopteris$	$(r)$ $Primitive$ $flowers$
$(d)$ $Yeast$	$(s)$ $Food$ $stored$ $as$ $starch$