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

$A$ block of $200 \text{ g}$ mass moves with a uniform speed in a horizontal circular groove with vertical side walls of radius $20 \text{ cm}$. If the block takes $40 \text{ s}$ to complete one round,the normal force exerted by the side walls of the groove is:

Helium gas undergoes a cycle $ABCDA$ (consisting of two isochoric and two isobaric lines) as shown in the figure. The efficiency of this cycle is nearly ..... $\%$ (Assume the gas to be close to an ideal gas).

Which one is a wrong statement?

In the given potentiometer circuit,the length of the wire $AB$ is $3 \, m$ and its resistance is $R = 4.5 \, \Omega$. The length $AC$ for no deflection in the galvanometer is ................ $m$.

An electron beam travels with a velocity of $1.6 \times 10^7 \ m/s$ perpendicularly to a magnetic field of intensity $0.1 \ T$. Calculate the radius of the path of the electron beam. (Given: $m_e = 9 \times 10^{-31} \ kg$,$e = 1.6 \times 10^{-19} \ C$)