If $3p^2 = 5p + 2$ and $3q^2 = 5q + 2$ where $p \neq q$,then the equation whose roots are $3p - 2q$ and $3q - 2p$ is:

The standard deviation of the numbers $22, 26, 28, 20, 24, 30$ is

If $A$ and $B$ are mutually exclusive events with $P(B) \neq 1$,then $P(A \mid \bar{B})$ is equal to (Here $\bar{B}$ is the complement of the event $B$)

Let $R_1$ be a relation defined by $R_1 = \{(a, b) | a \geq b, a, b \in \mathbb{R}\}$. Then $R_1$ is

Assertion $(A)$: $A$ particle of mass $m$ dropped into a hole made along the diameter of the Earth from one end to the other executes simple harmonic motion.
Reason $(R)$: Gravitational force between any two particles is inversely proportional to the square of the distance between them.

Observe the following statements:
$I. f(x) = a x^{41} + b x^{-40} \Rightarrow \frac{f^{\prime \prime}(x)}{f(x)} = 1640 x^{-2}$
$II. \frac{d}{d x} \tan ^{-1}\left(\frac{2 x}{1-x^2}\right) = \frac{1}{1+x^2}$
Which of the following is correct?