$A$ regular polygon of $n$ sides has $170$ diagonals,then $n$ is equal to

$\int_0^{2 \pi} \sin^6 x \cos^5 x \, dx$ is equal to

$A$ set of defective observation weights is used by a student to find the mass of an object using a physical balance. $A$ large number of readings will reduce:

$A$ car is fitted with a convex side-view mirror of focal length $20\ cm$. $A$ second car $2.8\ m$ behind the first car is overtaking the first car at a relative speed of $15\ m/s$. The speed of the image of the second car as seen in the mirror of the first one is

Which among the following complexes has square pyramidal geometry?

Two particles of mass $m$ each are tied at the ends of a light string of length $2a$. The whole system is kept on a frictionless horizontal surface with the string held tight so that each mass is at a distance $a$ from the centre $P$ (as shown in the figure). Now,the mid-point of the string is pulled vertically upwards with a small but constant force $F$. As a result,the particles move towards each other on the surface. The magnitude of acceleration,when the separation between them becomes $2x$,is