$A$ coin and a six-faced die,both unbiased,are thrown simultaneously. The probability of getting a head on the coin and an odd number on the die is:

$A$ mass $M$ hangs on a massless rod of length $l$ which rotates at a constant angular frequency. The mass $M$ moves with steady speed in a circular path of constant radius. Assume that the system is in steady circular motion with constant angular velocity $\omega$. The angular momentum of $M$ about point $A$ is $L_A$ which lies in the positive $z$ direction and the angular momentum of $M$ about $B$ is $L_B$. The correct statement for this system is

Given the circle $C$ with the equation $x^2+y^2-2x+10y-38=0$. Match the List-$I$ with the List-$II$ given below concerning $C$.

$A$. The equation of the polar of $(4, 3)$ with respect to $C$	$I$. $y + 5 = 0$
$B$. The equation of the tangent at $(9, -5)$ on $C$	$II$. $x = 1$
$C$. The equation of the normal at $(-7, -5)$ on $C$	$III$. $3x + 8y = 27$
$D$. The equation of the diameter passing through $(1, -5)$ and $(1, 3)$	$IV$. $x = 9$

Dry distillation of calcium acetate and calcium formate forms:

Pollen grains of a plant,whose $2n = 28$,are cultured to get callus by tissue culture method. What would be the number of chromosomes in the cells of the callus?

The values of a function $f(x)$ at different values of $x$ are given in the table below:

$x$	$0$	$1$	$2$	$3$	$4$	$5$
$f(x)$	$2$	$3$	$6$	$11$	$18$	$27$

Then,the approximate area (in square units) bounded by the curve $y=f(x)$ and the $x$-axis between $x=0$ and $x=5$,using the Trapezoidal rule,is