Which of the following metal carbides is known as a methanide?

One end each of a resistance $r$,a capacitor $C$,and a resistance $2r$ are connected together. The other ends are respectively connected to the positive terminals of batteries $P, Q,$ and $R$ having emf's $E, E,$ and $2E$. The negative terminals of the batteries are then connected together. In this circuit,with steady current,the potential drop across the capacitor is:

The radius of the circle $r = \sqrt{3} \sin \theta + \cos \theta$ is

The magnetic flux near the axis and inside the air-core solenoid of length $60 \ cm$ carrying current $I$ is $1.57 \times 10^{-6} \ Wb$. Its magnetic moment will be (cross-sectional area of a solenoid is very small as compared to its length,$\mu_0 = 4\pi \times 10^{-7} \ SI \ units$). (in $A \ m^2$)

An object is attached to the bottom of a light vertical spring and set vibrating. The maximum speed of the object is $15 \, cm/s$ and the period is $628 \, ms$. The amplitude of the motion in centimeters is

$A$ man moves towards a plane mirror with a velocity $v$ in a direction making an angle $\theta$ with the normal to the mirror. The magnitude of the velocity of the image relative to the man normal to the mirror will be