$A$ radioactive material decays by simultaneous emission of two particles with respective half-lives $1620 \ years$ and $810 \ years$. The time (in years) after which one-fourth of the material remains is

Which of the following statements is true for an $N$-type semiconductor?

Let $P(-1, 0)$,$Q(0, 0)$,and $R(3, 3\sqrt{3})$ be three points. Then the equation of the bisector of the angle $\angle PQR$ is

$A$ body is projected vertically from the surface of the earth of radius $R$ with a velocity equal to half of the escape velocity. The maximum height reached by the body is

What is the period of small oscillations of the block of mass $m$ if the springs are ideal and pulleys are massless?

Select the correct option on the basis of the following sentences regarding a gland's function:
$(I)$ Hormones increase alertness.
$(II)$ Hormones increase the heart beat.
$(III)$ Stimulate the breakdown of glycogen.
$(IV)$ Stimulate the breakdown of lipids and proteins.