$A$ $TV$ transmitting antenna is $128 \ m$ tall. If the receiving antenna is at the ground level,the maximum distance between them for satisfactory communication in line-of-sight mode is (radius of the earth $R_e = 6.4 \times 10^6 \ m$):

$A$ horizontal uniform glass tube of $100 \ cm$ length, sealed at both ends, contains a $10 \ cm$ mercury column in the middle. The initial temperature and pressure of air on either side of the mercury column are $31^{\circ} C$ and $76 \ cm$ of mercury, respectively. If the air column at one end is kept at $0^{\circ} C$ and the other end at $273^{\circ} C$, then the pressure of the air at $0^{\circ} C$ is (in $cm$ of $Hg$):

Two identical bodies have temperatures $277^{\circ} C$ and $67^{\circ} C$. If the surroundings temperature is $27^{\circ} C$, the ratio of loss of heats of the two bodies during the same interval of time is (approximately) (in $19 : 1$)

The general solution of $\sin x - \cos x = \sqrt{2}$,for any integer $n$ is

A positive ion $A$ and a negative ion $B$ has charges $6.67 \times 10^{-19}\ {C}$ and $9.6 \times 10^{-10}\ {C}$, and masses $19.2 \times 10^{-27}\ {kg}$ and $9 \times 10^{-27}\ {kg}$ respectively. At an instant, the ions are separated by a certain distance $r$. At that instant the ratio of the magnitudes of electrostatic force to gravitational force is ${P} \times 10^{-13}$, where the value of $P$ is _________ .
(Take $\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9\ {Nm}^2 {C}^{-1}$ and universal gravitational constant as $6.67 \times 10^{-11}\ {Nm}^2 {kg}^{-2}$)

Which of the following is $NOT$ a method of sexual reproduction in fungi?