$A$ uniform rope of mass $0.1 ~kg$ and length $2.45 ~m$ hangs from a rigid support. The time taken by the transverse wave formed in the rope to travel through the full length of the rope is (Assume $g=9.8 ~m/s^2$) (in $~s$)

For the reversible reaction $N_{2(g)} + 3H_{2(g)} \rightleftharpoons 2NH_{3(g)}$ at $500 \, ^\circ C$,the value of $K_p$ is $1.44 \times 10^{-5}$. When the partial pressure is measured in atmospheres,the value of $K_c$ in $\text{mol L}^{-1}$ is:

The angle of elevation of an object on a hill is observed from a certain point in the horizontal plane through its base to be $30^{\circ}$. After walking $120 \ m$ towards it on level ground,the angle of elevation is found to be $60^{\circ}$. The height of the object (in metres) is:

The volume in $mL$ of $0.1 M$ solution of $NaOH$ required to completely neutralize $100 \ mL$ of $0.3 M$ solution of $H_3PO_3$ is:

The half-life period of a first-order chemical reaction is $6.93 \ min$. The time required for $99\%$ completion of the reaction is ........ minutes. $(\log 2 = 0.301)$

The angle between the lines whose direction cosines satisfy the equations $l+m+n=0$ and $l^2+m^2-n^2=0$ is