The point of intersection of the pair of lines represented by $x^2+xy+2y^2-3x+2y+4=0$ is

The sensitivity of a galvanometer is $60 \text{ div/A}$. When a shunt is used,its sensitivity becomes $10 \text{ div/A}$. If the resistance of the galvanometer is $20 \ \Omega$,then the value of the shunt used is: (in $\Omega$)

When a vibrating tuning fork is placed on a sound box of a sonometer, $8$ beats per second are heard when the length of the sonometer wire is kept at $101 \, cm$ or $100 \, cm$. Then the frequency of the tuning fork is (Consider that the tension in the wire is kept constant). (in $ \, Hz$)

The upper half of an inclined plane of inclination $\theta$ is perfectly smooth while the lower half is rough. $A$ block starting from rest at the top of the plane will again come to rest at the bottom,if the coefficient of friction between the block and the lower half of the plane is given by:

If a change in current of $0.01 ~A$ in one coil produces a change in magnetic flux of $2 \times 10^{-2} ~Wb$ in the other coil,then the mutual inductance of the two coils in henry is (in $~H$)

$A$ metallic frame moves with constant velocity $v$ near an infinitely long current-carrying wire. At any instant,the induced electromotive forces (emf) in sides $AD$ and $BC$ are $5\,V$ and $2\,V$ respectively. If the resistance of the frame is $6\,\Omega$,find the magnitude and direction of the induced current in it.