If $x = \sqrt{\frac{2+\sqrt{3}}{2-\sqrt{3}}}$,then $x^2(x-4)^2$ is equal to:

Which of the following is known as the $Christmas$ tree?

An infinitely long thin straight wire has a uniform linear charge density of $\frac{1}{3} ~Cm^{-1}$. The magnitude of the electric field intensity at a point $18 ~cm$ away is (given $\varepsilon_0 = 8.85 \times 10^{-12} ~C^2 N^{-1} m^{-2}$):

Assertion : Replication and transcription occur in the nucleus but translation takes place in the cytoplasm.
Reason : $mRNA$ is transferred from the nucleus into the cytoplasm where ribosomes and amino acids are available for protein synthesis.

Let $O$ be the vertex and $Q$ be any point on the parabola $x^2 = 8y$. If the point $P$ divides the line segment $OQ$ internally in the ratio $1:3$,then the locus of $P$ is:

The time period of a simple pendulum is $T$. When the length is increased by $10 \ cm$,its period is $T_1$. When the length is decreased by $10 \ cm$,its period is $T_2$. Then,the relation between $T, T_1$ and $T_2$ is