A potentiometer PQ is set up to compare two resistances as shown in the figure. The ammeter A in the circuit reads 1.0 A when two way key K₃ is open. The balance point is at a length $$\ell $$₁ cm from P when two way key K₃ is plugged in between 2 and 1, while the balance point is at a length $$\ell $$₂ cm from P when key K₃ is plugged in between 3 and 1. The ratio of two resistances $${{{R_1}} \over {{R_2}}}$$, is found to be :

A uniform disc of radius R and mass M is free to rotate only about its axis. A string is wrapped over its rim and a body of mass m is tied to the free end of the string as shown in the figure. The body is released from rest. Then the acceleration of the body is :

A small circular loop of wire of radius a is located at the centre of a much larger circular wire loop of radius b. The two loops are in the same plane. The outer loop of radius b carries an alternating current I = I_o cos ($$\omega $$t). The emf induced in the smaller inner loop is nearly :

What is the conductivity of a semiconductor sale having electron concentration of $$5 \times {10^{18}}\,\,{m^{ - 3}},$$ hole concentration of $$5 \times {10^{19}}\,\,{m^{ - 3}},$$ electron mobility of 2.0 m² V^$$-$$1 s^-1 and hole mobility of 0.01 m² V^$$-$$1 s^$$-$$1 ?

(Take charge of electronas 1.6 $$ \times $$ 10 ^$$-$$19 c)