If the lines $3x + 4y - 14 = 0$ and $6x + 8y + 7 = 0$ are both tangents to a circle,then its radius is

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.

$ f: R \rightarrow R $ and $ g:[0, \infty) \rightarrow R $ are defined by $ f(x)=x^{2} $ and $ g(x)=\sqrt{x} $. Which one of the following is not true?

The equation of the $x$-axis is .....

The frequency of vibration in a vibration magnetometer of the combination of two bar magnets of magnetic moments $M_1$ and $M_2$ is $6 ~Hz$ when like poles are tied together and it is $2 ~Hz$ when the unlike poles are tied together,then the ratio $M_1: M_2$ is

Which of the following substances is used in gunpowder?