Q11. The heat absorbed by a system in going through the given cyclic process is : [Figure]
(1) 19.6 J
(2) 61.6 J
(3) 616 J
(4) 431.2 J

Q11. A galvanometer of resistance $100 \Omega$ when connected in series with $400 \Omega$ measures a voltage of upto 10 V . The value of resistance required to convert the galvanometer into ammeter to read upto 10 A is $x \times 10 ^ { - 2 } \Omega$. The value of $x$ is :
(1) 2
(2) 800
(3) 20
(4) 200

Q11. Ques: $\sigma$ is the uniform surface charge density of a thin spherical shell of radius $R$. The electric field at any point on the surface of the spherical shell is :
(1) $\sigma / \epsilon _ { o } R$
(2) $\sigma / \epsilon _ { o }$
(3) $\sigma / 4 \epsilon _ { o }$
(4) $\sigma / 2 \epsilon _ { o }$

Q11. The number of electrons flowing per second in the filament of a 110 W bulb operating at 220 V is : ( Given $\mathrm { e } = 1.6 \times 10 ^ { - 19 } \mathrm { C }$ )
(1) $6.25 \times 10 ^ { 17 }$
(2) $1.25 \times 10 ^ { 19 }$
(3) $6.25 \times 10 ^ { 18 }$
(4) $31.25 \times 10 ^ { 17 }$
Q12. Match List-I with List-II :
(A) $\mathrm { Y } =$ magnetic susceptibility $\mathrm { X } =$ magnetising field
(B) $\mathrm { Y } =$ magnetic field
(C) $\mathrm { Y } =$ magnetic field $\mathrm { X } =$ distance from centre of a current carrying wire for $x < a$ (where $a =$ radius of wire)

List-1

Y vs X

List-II

Shape of Graph (II) (I) [Figure]
(II) [Figure]
(III) [Figure]
\begin{verbatim} X = distance from centre of a current carrying wire for x>a (where $a =$ radius of wire) \end{verbatim}
(D) $\mathrm { Y } =$ magnetic field inside solenoid
(IV) [Figure]
$\mathrm { X } =$ distance from centre Choose the correct answer from the options given below :
(1) (A)-(IV), (B)-(I), (C)-(III), (D)-(II)
(2) (A)-(I), (B)-(III), (C)-(II), (D)-(IV)
(3) (A)-(III), (B)-(IV), (C)- (I), (D)-(II)
(4) (A)-(III), (B)-(I), (C)-(IV), (D)-(II)

Q11. Two charged conducting spheres of radii $a$ and $b$ are connected to each other by a conducting wire. The ratio of charges of the two spheres respectively is:
(1) $\frac { a } { b } v$
(2) $\sqrt { a b }$
(3) $\frac { b } { a }$
(4) $a b$

Q11. A capacitor has air as dielectric medium and two conducting plates of area $12 \mathrm {~cm} ^ { 2 }$ and they are 0.6 cm apart. When a slab of dielectric having area $12 \mathrm {~cm} ^ { 2 }$ and 0.6 cm thickness is inserted between the plates, one of the conducting plates has to be moved by 0.2 cm to keep the capacitance same as in previous case. The dielectric constant of the slab is : (Given $\epsilon _ { 0 } = 8.834 \times 10 ^ { - 12 } \mathrm {~F} / \mathrm { m }$ )
(1) 1
(2) 1.33
(3) 0.66
(4) 1.50

Q11. A capacitor is made of a flat plate of area A and a second plate having a stair-like structure as shown in figure. If the area of each stair is $\frac { A } { 3 }$ and the height is $d$, the capacitance of the arrangement is : [Figure]
(1) $\frac { 13 \epsilon _ { o } A } { 17 d }$
(2) $\frac { 11 \epsilon _ { 0 } \mathrm {~A} } { 18 \mathrm {~d} }$
(3) $\frac { 18 \epsilon _ { \mathrm { o } } \mathrm { A } } { 11 \mathrm {~d} }$
(4) $\frac { 11 \epsilon _ { \mathrm { o } } \mathrm { A } } { 20 \mathrm {~d} }$

Q11. A proton and a deutron ( $q = + \mathrm { e } , m = 2.0 \mathrm { u }$ ) having same kinetic energies enter a region of uniform magnetic field $\vec { B }$, moving perpendicular to $\vec { B }$. The ratio of the radius $r _ { d }$ of deutron path to the radius $r _ { p }$ of the proton path is:
(1) $\sqrt { 2 } : 1$
(2) $1 : 1$
(3) $1 : \sqrt { 2 }$
(4) $1 : 2$

Q12. An infinitely long positively charged straight thread has a linear charge density $\lambda \mathrm { Cm } ^ { - 1 }$. An electron revolves along a circular path having axis along the length of the wire. The graph that correctly represents the variation of the kinetic energy of electron as a function of radius of circular path from the wire is :
(1) [Figure]
(2) [Figure]
(3) [Figure]
(4) [Figure]

Q12. An electric bulb rated $50 \mathrm {~W} - 200 \mathrm {~V}$ is connected across a 100 V supply. The power dissipation of the bulb is:
(1) 25 W
(2) 12.5 W
(3) 50 W
(4) 100 W

Q12. If the collision frequency of hydrogen molecules in a closed chamber at $27 ^ { \circ } \mathrm { C }$ is Z , then the collision frequency of the same system at $127 ^ { \circ } \mathrm { C }$ is :
(1) $\frac { \sqrt { 3 } } { 2 } \mathrm { z }$
(2) $\frac { 2 } { \sqrt { 3 } } \mathrm { Z }$
(3) $\frac { 3 } { 4 } \mathrm { Z }$
(4) $\frac { 4 } { 3 } \mathrm { Z }$

Q12. The ratio of heat dissipated per second through the resistance $5 \Omega$ and $10 \Omega$ in the circuit given below is: [Figure]
(1) $1 : 2$
(2) $2 : 1$
(3) $4 : 1$
(4) $1 : 1$

Q12. The value of unknown resistance ( $x$ ) for which the potential difference between $B$ and $D$ will be zero in the [Figure] arrangement shown, is :
(1) $3 \Omega$
(2) $42 \Omega$
(3) $9 \Omega$
(4) $6 \Omega$

Q12. In the given circuit, the terminal potential difference of the cell is : [Figure]
(1) 2 V
(2) 3 V
(3) 4 V
(4) 1.5 V

Q12. Water boils in an electric kettle in 20 minutes after being switched on. Using the same main supply, the length of the heating element should be $\_\_\_\_$ to $\_\_\_\_$ times of its initial length if the water is to be boiled in 15 minutes.
(1) decreased, $3 / 4$
(2) increased, $4 / 3$
(3) decreased, 4/3
(4) increased, $3 / 4$

Q12. A galvanmeter has a coil of resistance $200 \Omega$ with a full scale deflection at $20 \mu \mathrm {~A}$. The value of resistance to be added to use it as an ammeter of range $( 0 - 20 ) \mathrm { mA }$ is ;
(1) $0.40 \Omega$
(2) $0.20 \Omega$
(3) $0.50 \Omega$
(4) $0.10 \Omega$
Q13. [Figure]
The equivalent resistance between A and B is :
(1) $18 \Omega$
(2) $19 \Omega$
(3) $25 \Omega$
(4) $27 \Omega$

Q12. A square loop of side 15 cm being moved towards right at a constant speed of $2 \mathrm {~cm} / \mathrm { s }$ as shown in figure. The front edge enters the 50 cm wide magnetic field at $t = 0$. The value of induced emf in the loop at $t = 10 \mathrm {~s}$ will [Figure] be :
(1) 0.3 mV
(2) zero
(3) 4.5 mV
(4) 3 mV

Q13. To measure the internal resistance of a battery, potentiometer is used. For $\mathrm { R } = 10 \Omega$, the balance point is observed at $l = 500 \mathrm {~cm}$ and for $\mathrm { R } = 1 \Omega$ the balance point is observed at $l = 400 \mathrm {~cm}$. The internal resistance of the battery is approximately :
(1) $0.2 \Omega$
(2) $0.3 \Omega$
(3) $0.4 \Omega$
(4) $0.1 \Omega$

Q13. The magnetic moment of a bar magnet is $0.5 \mathrm { Am } ^ { 2 }$. It is suspended in a uniform magnetic field of $8 \times 10 ^ { - 2 } \mathrm {~T}$. The work done in rotating it from its most stable to most unstable position is:
(1) $8 \times 10 ^ { - 2 } \mathrm {~J}$
(2) $4 \times 10 ^ { - 2 } \mathrm {~J}$
(3) Zero
(4) $16 \times 10 ^ { - 2 } \mathrm {~J}$
Q14. [Figure]

Match List I with List II

Choose the correct answer from the options given below:
(1) A-I. B-IV, C-II, D-III
(2) A-IV. B-I. C-II. D-III
(3) A-IV. B-I, C-III, D-II
(4) A-I. B-IV, C-III, D-II

Q13. In the given figure $\mathrm { R } _ { 1 } = 10 \Omega , \mathrm { R } _ { 2 } = 8 \Omega , \mathrm { R } _ { 3 } = 4 \Omega$ and $\mathrm { R } _ { 4 } = 8 \Omega$. Battery is ideal with emf 12 V . Equivalent resistant of the circuit and current supplied by battery are respectively: [Figure]
(1) $10.5 \Omega$ and 1.14 A
(2) $12 \Omega$ and 1 A
(3) $10.5 \Omega$ and 1 A
(4) $12 \Omega$ and 11.4 A

Q13. The electrostatic force $\left( \overrightarrow { F _ { 1 } } \right)$ and magnetic force $\left( \vec { F } _ { 2 } \right)$ acting on a charge $q$ moving with velocity $v$ can be written :
(1) $\vec { F } _ { 1 } = q \vec { E } , \vec { F } _ { 2 } = q ( \vec { V } \times \vec { B } )$
(2) $\vec { F } _ { 1 } = q \vec { B } , \vec { F } _ { 2 } = q ( \vec { B } \times \vec { V } )$
(3) $\vec { F } _ { 1 } = q \vec { E } , \vec { F } _ { 2 } = q ( \vec { B } \times \vec { V } )$
(4) $\vec { F } _ { 1 } = q \vec { V } \cdot \vec { E } , \vec { F } _ { 2 } = q ( \vec { B } \cdot \vec { V } )$

Q13. An element $\Delta l = \Delta x \hat { i }$ is placed at the origin and carries a large current $I = 10 \mathrm {~A}$. The magnetic field on the $y$ axis at a distance of 0.5 m from the elements $\Delta x$ of 1 cm length is: [Figure]
(1) $4 \times 10 ^ { - 8 } \mathrm {~T}$
(2) $10 \times 10 ^ { - 8 } \mathrm {~T}$
(3) $8 \times 10 ^ { - 8 } \mathrm {~T}$
(4) $12 \times 10 ^ { - 8 } \mathrm {~T}$

Q13. In a coil, the current changes from - 2 A to + 2 A in 0.2 s and induces an emf of 0.1 V . The self inductance of the coil is :
(1) 4 mH
(2) 1 mH
(3) 5 mH
(4) 2.5 mH

Q13. Paramagnetic substances: A. align themselves along the directions of external magnetic field. B. attract strongly towards external magnetic field. C. has susceptibility little more than zero. D. move from a region of strong magnetic field to weak magnetic field. Choose the most appropriate answer from the options given below:
(1) A, B, C Only
(2) A, B, C, D
(3) A, C Only
(4) B, D Only

Q13. A long straight wire of radius a carries a steady current I. The current is uniformly distributed across its cross section. The ratio of the magnetic field at $\frac { a } { 2 }$ and $2 a$ from axis of the wire is :
(1) $1 : 4$
(2) $1 : 1$
(3) $3 : 4$
(4) $4 : 1$