If one of the lines of the pair $ax^2 + 2hxy + by^2 = 0$ bisects the angle between the positive directions of the axes,then $a, b, h$ satisfy the relation:

$A$ six-faced unbiased die is thrown twice and the sum of the numbers appearing on the upper face is observed to be $7$. The probability that the number $3$ has appeared at least once is:

The atomic numbers of elements $A$,$B$,$C$ and $D$ are $Z-1$,$Z$,$Z+1$ and $Z+2$,respectively. If $B$ is a noble gas,choose the correct statements from the following:
$(1)$ $A$ has high electron affinity
$(2)$ $C$ exists in $+2$ oxidation state
$(3)$ $D$ is an alkaline earth metal

The currents $i_1$ and $i_2$ through the resistors $R_1 = 10\,\Omega$ and $R_2 = 30\,\Omega$ in the circuit diagram with $E_1 = 3\,V$,$E_2 = 3\,V$,and $E_3 = 2\,V$ are respectively:

$A$ player kicks a football of mass $0.5 \ kg$ and the football begins to move with a velocity of $10 \ m/s$. If the contact between the leg and the football lasts for $\frac{1}{50} \ s$,then the force acted on the football should be ........... $N$.

The height of water in a tank is $H$. The range of the liquid emerging out from a hole in the wall of the tank at a depth $\frac{3H}{4}$ from the upper surface of water will be