$A$ uniform rod of mass $M$ and length $L$ is placed on a smooth horizontal surface. $A$ horizontal force $F$ is applied at one end of the rod perpendicular to its length. The acceleration of the centre of mass of the rod is:

In Whittaker's classification system,which kingdom acts as the primary producer?

Which of the following statements is/are incorrect?

The coefficient of apparent expansion of mercury in a glass vessel is $153 \times 10^{-6}/^{\circ}C$ and in a steel vessel is $144 \times 10^{-6}/^{\circ}C$. If $\alpha$ for steel is $12 \times 10^{-6}/^{\circ}C$,then $\alpha$ for glass is:

$A$ diode detector is used to detect an amplitude-modulated wave of $60\%$ modulation by using a capacitor of capacity $250 \text{ pF}$ in parallel with a load resistance of $100 \text{ k}\Omega$. Find the maximum modulation frequency which could be detected by it.

Match the compounds in List$-I$ with the appropriate observations in List$-II$ and choose the correct option.

List$-I$	List$-II$
$(P)$ image	$(1)$ Reaction with phenyl diazonium salt gives yellow dye.
$(Q)$ image	$(2)$ Reaction with ninhydrin gives purple color and it also reacts with $FeCl _3$ to give violet color.
$(R)$ image	$(3)$ Reaction with glucose will give corresponding hydrazone.
$(S)$ image	$(4)$ Lassiagne extract of the compound treated with dilute HCl followed by addition of aqueous $FeCl _3$ gives blood red color.
	$(5)$ After complete hydrolysis, it will give ninhydrin test and it $\text{DOES NOT}$ give positive phthalein dye test.