Four charges are placed at the circumference of a dial clock as shown in the figure. If the clock has only an hour hand, then the resultant force on a charge $q_0$ placed at the center points in the direction which shows the time as: (in $.30$)

$A$ body executes simple harmonic motion under the action of a force $F_1$ with a time period $T_1 = \frac{4}{5} \ s$. If the force is changed to $F_2$,it executes $SHM$ with a time period $T_2 = \frac{3}{5} \ s$. If both the forces $F_1$ and $F_2$ act simultaneously in the same direction on the body,what is its new time period in seconds?

An atomic power nuclear reactor can deliver $300 \, MW$. The energy released due to fission of each nucleus of uranium atom $U^{238}$ is $170 \, MeV$. The number of uranium atoms fissioned per hour will be

Evaluate the sum: $\sum\limits_{k = 1}^n {\frac{1}{{{{\log }_{{2^k}}}(a)}}}$

If $\overrightarrow{a} \cdot \hat{i} = \overrightarrow{a} \cdot (2 \hat{i} + \hat{j}) = \overrightarrow{a} \cdot (\hat{i} + \hat{j} + 3 \hat{k}) = 1$,then $\overrightarrow{a}$ is equal to :

During which phase of meiosis does crossing over occur?