Integrated Pest Management $(IPM)$ is based on which of the following?

If $b+c=3a$,then $\cot \frac{B}{2} \cot \frac{C}{2}$ is equal to :

Which statement is false for the balanced equation given below?
$CS_2 + 3O_2 \to 2SO_2 + CO_2$

Three moles of an ideal monoatomic gas undergo a cyclic process as shown in the figure. The temperatures of the gas in different states marked as $1, 2, 3$ and $4$ are $400 \ K, 700 \ K, 2500 \ K$ and $1100 \ K$ respectively. The work done by the gas during the process $1-2-3-4-1$ is (universal gas constant is $R$): (in $R$)

$A$ particle of mass $m$ is located in a one-dimensional potential field where the potential energy is given by: $V(x) = A(1 - \cos px)$,where $A$ and $p$ are constants. The period of small oscillations of the particle is:

$A$ parallel plate capacitor is charged to a potential difference of $100\ V$ and disconnected from the source of emf. $A$ slab of dielectric is then inserted between the plates. Which of the following three quantities change?
$(i)$ The potential difference
$(ii)$ The capacitance
$(iii)$ The charge on the plates