$A$ bag contains $2n+1$ coins. It is known that $n$ of these coins have a head on both sides,whereas the remaining $n+1$ coins are fair. $A$ coin is picked up at random from the bag and tossed. If the probability that the toss results in a head is $\frac{31}{42}$,then $n$ is equal to

The two surfaces of a biconvex lens have the same radii of curvature. This lens is made of glass with a refractive index of $1.5$ and has a focal length of $10 ~cm$ in air. The lens is cut into two equal halves along a plane perpendicular to its principal axis to yield two plano-convex lenses. The two pieces are glued such that the convex surfaces touch each other. If this combination lens is immersed in water (refractive index $=$ $4/3$),its focal length (in $cm$) is:

Which of the following is incorrect for garden pea?

$\int \frac{3^x dx}{\sqrt{9^x-1}}$ is equal to

Match the following columns:

Column-$I$	Column-$II$
$a$. Bicuspid valve	$p$. Brain
$b$. Nephron	$q$. Liver
$c$. Alveoli	$r$. Heart
$d$. Cerebrum	$s$. Kidney
	$t$. Lungs

$A$ particle of mass $200\,g$ executes a simple harmonic motion. The restoring force is provided by a spring of spring constant $80\,N/m$. The time period is .... $sec$.