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

Archaea that live in hot springs belong to which group?

$A$ block of mass $m$ is at rest on another block of the same mass as shown in the figure. The lower block is attached to a spring. What is the maximum amplitude of motion so that both blocks remain in contact?

The value of $\lambda$ such that $\lambda x^2-10 x y+12 y^2+5 x-16 y-3=0$ represents a pair of straight lines is:

$A$ coil of radius '$r$' is placed on another coil (whose radius is '$R$' and current through it is changing) so that their centers coincide. $(R \gg r)$. If both are coplanar,then the mutual inductance between them is proportional to

$A$ car $P$ approaching a crossing at a speed of $10\, m/s$ sounds a horn of frequency $700\, Hz$ when $40\, m$ in front of the crossing. The speed of sound in air is $340\, m/s$. Another car $Q$ is at rest on a road which is perpendicular to the road on which car $P$ is reaching the crossing (see figure). The driver of car $Q$ hears the sound of the horn of car $P$ when he is $30\, m$ in front of the crossing. The apparent frequency heard by the driver of car $Q$ is .... $Hz$.