$A$ simple pendulum performs simple harmonic motion about $x=0$ with an amplitude '$a$' and time period '$T$'. The speed of the pendulum at $x=\frac{a}{2}$ is

The equation of the circle passing through the point $(1, 2)$ and through the points of intersection of $x^2+y^2-4x-6y-21=0$ and $3x+4y+5=0$ is given by

An eight-digit number divisible by $9$ is to be formed using digits from $0$ to $9$ without repeating the digits. The number of ways in which this can be done is: (in $(7!)$)

Two parallel rails of a railway track, insulated from each other and from the ground, are connected to a millivoltmeter. The distance between the rails is $1 \, m$. $A$ train is travelling with a velocity of $72 \, km/h$ along the track. What is the reading of the millivoltmeter (in $mV$)? (The vertical component of the Earth's magnetic field is $2 \times 10^{-5} \, T$.)

$A$ particle of mass $0.1 \,kg$ is subjected to a force which varies with distance as shown. If it starts its journey from rest at $x=0$,then its velocity at $x=12 \,m$ is .............. $m/s$.

An ovule which becomes curved so that the nucellus and embryo sac lie at a right angle to the funicle is called: