What is the minimum quantity (in grams) of $methyl$ iodide required for preparing one mole of ethane by Wurtz reaction? (Atomic weight of iodine $= 127$)

Let $PQ$ and $RS$ be tangents at the extremities of the diameter $PR$ of a circle of radius $r$. If $PS$ and $RQ$ intersect at a point $X$ on the circumference of the circle,then $2r$ equals

The angle between the lines whose direction cosines satisfy the equations $l+m+n=0$ and $l^2+m^2-n^2=0$ is

Which one of the following sets correctly represents the increase in the paramagnetic property of the ions?

In a competition, $A, B$, and $C$ are participating. The probability that $A$ wins is twice that of $B$, and the probability that $B$ wins is twice that of $C$. What is the probability that $A$ loses?

Observe the statements given below :
Assertion $(A)$ : $f(x)=x e^{-x}$ has the maximum at $x=1$
Reason $(R)$ : $f^{\prime}(1)=0$ and $f^{\prime \prime}(1) < 0$
Which of the following is correct?