11-09-2024

6001CJA10102124015 JA

PHYSICS

SECTION-I(i)

1) In the figure shown section CDEF is fixed in the vertical plane made up of conducting rods CD &
EF are smooth and resistanceless. A rod GH of mass ' m ' can move vertically up without losing
contact with the fixed arrangement. There is a uniform magnetic field B in the horizontal direction.
The total heat produced by the time it goes to highest point in the circuit will be:

(A)

(B)
greater than

(C)
less than
(D) zero

2) In the circuit shown switch S is connected to position 2 for a long time and then joined to position

1. The total heat produced in resistance R1 is :

(A)

(B)

(C)

(D)
3) In the given arrangement, the conducting loop is moved with constant velocity v in a uniform
magnetic field B in a restricted region of width a. The time for which the emf is induced in the circuit

is:

(A)

(B)

(C)

(D)

4) A semicircular conducting loop of radius R is rotated about its straight edge which divides the
space into two region one having a uniform magnetic field B and the other having no field. If initially
the plane of loop is perpendicular to (as shown), and if current flowing from O to A be taken as

positive, the correct plot of induced current v/s time for one time period is:

(A)

(B)
(C)

(D)

SECTION-I(ii)

1) A conducting rod of length l is moved at constant velocity 'V0' on two parallel, conducting, smooth,
fixed rails, that are placed in a uniform constant magnetic field B perpendicular to the plane of the
rails as shown in figure. A resistance R is connected between the two ends of the rail. Then which of

the following is/are correct :

The thermal power dissipated in the resistor is equal to rate of work done by external agent
(A)
pulling the rod
(B) If applied external force is doubled then a part of external power increases the velocity of rod
(C) Lenz's law is not satisfied if the rod is accelerated by external force
If resistance R is doubled then power required to maintain the constant velocity V0 becomes
(D)
half

2) In the figure shown, 'A' is a fixed conducting ring of negligible resistance and radius 'a'. PQ is a
uniform rod of resistance r. It is hinged at the centre of the ring and rotated about this point in
clockwise direction with a uniform angular velocity ω. There is a uniform magnetic field of strength
'B' pointing inwards, 'r' is a stationary resistance. Choose correct options.
(A) Current through 'r' is zero

(B)
Current through 'r' is
(C) Direction of current in external 'r' is from centre to circumference
(D) Direction of current in external 'r' is from circumference to centre

3) An infinitely long conducting wire is placed near a conducting square loop as shown in figure,

choose the correct option(s).

(A)
The mutual inductance between the two is

(B)
The mutual inductance between the two is
If a constant current is passed in the straight wire in upward direction and loop is brought close
(C)
to the wire then induced current in the loop is clockwise
(D) In the above condition, induced current in the loop is anticlockwise

4) In the circuit shown in figure, switch is closed at time t = 0. At time t = ln(2) second,

(A) Rate of energy supplied by the battery is 16 J/s

(B) Rate of heat dissipated across resistance is 8 J/s
(C) Rate of heat dissipated across resistance is 16 J/s
(D)

5) Magnetic field in a cylindrical region of radius R in inward direction is as shown in figure. Choose
correct options.

(A) An electron will experience no force kept at (2R, 0, 0) if magnetic field increases with time
(B) In the above situation, electron will experience the force in negative y-direction

(C) If a proton is kept at and magnetic field is decreasing, then it will experience the
force in positive x-direction
If a proton is kept at (-R, 0, 0) and magnetic field is increasing, then it will experience force in
(D)
negative y-direction.

6) An infinite solenoid has radius R and n turns per unit length. The current grows linearly with
time, according to in the solenoid. Here C is some constant. Let the induced electric field at
distance r from axis of solenoid is E. Choose correct alternative(s)

(A)
(B)
In an infinite line charge having uniform linear charge density λ is placed along the axis, then
(C) electrostatic field produced by line charge and induced electric field are perpendicular to each
other
The induced field and electrostatic field produced by line charge placed along axis of solenoid
(D)
can be added vectorically to get net electric field at a point.

7) Consider a metal wire frame falling freely under gravity enters in a uniform magnetic field region
as shown in the figure. Then mark the correct statement as the loop enters the region?

(A) The speed first decreases then increases

(B) The speed continuously increases
(C) The speed may increase or decrease initially but it will definitely increase afterwards
(D) The speed may decrease continuously

8) Initially key was placed on (l) till the capacitor got fully charged. Then key is placed on (2) at t =
0. Then this system will be similar to spring mass system, which of the statements is/are correct.
 Time when the energy in both capacitor and inductor will be same
(A)

Inductance plays the role of mass and Capacitance plays the role of 1/K, where k = spring
(B)
constant.
(C) q is similar to displacement and i is similar to velocity, where q = charge and i = current
(D) The energy stored in the inductor is analogous to mechanical energy of spring mass system.

SECTION-II

1) A uniform magnetic field exists in region given by . A metal rod of length 5 m is

placed along y–axis is moved along x–axis with constant speed 1 m/sec. Then induced e.m.f. in the
rod will be ____ (volt)

2) The magnetic flux through a metal ring varies with time t according
to with and The resistance of the ring is Find the maximum
current (in ampere) induced in the ring during the interval from t = 0 to t = 2.0 s.

3) In the circuit diagram shown, initially there is no energy in the inductor and the capacitor. The

switch is closed at t = 0. If and current I is given as . Find k.

4) A resistance less rod of length 3m is being pulled in a uniform vertical magnetic field of
magnitude 0.8 T with constant speed of 5 m/s. The resistance of circuit is and capacitance is
Initially there is no charge on the capacitor. What is the current (in A) in circuit when charge

on capacitor becomes
5) A loop is formed by two parallel resistance less conductors connected by a solenoid with
inductance L = 103 H and a conducting rod of mass m = 1 gm which can freely slide (without
friction) over a pair of conductors. The conductors are located in a horizontal plane in a uniform
magnetic field B = 4T in the direction perpendicular to the plane of the loop as shown in figure. The
distance between conductors is equal to At the moment t = 0, the rod is imparted an initial
velocity V0 to the right. Determine angular frequency (in rad/s) of oscillation of rod.

6) A ring made of a superconductor is placed into a homogeneous magnetic field whose intensity
grows from zero to B0 = 2T. The plane of the ring is perpendicular to the force lines of the field. The

induced current appearing in the ring is 1/x (amp). The radius of the ring cm and its
inductance L = 1 mH. Find x.

CHEMISTRY

SECTION-I(i)

1)
Product R is:

(A)

(B)

(C)

(D)
2)
(P) decolourise Br2/H2O. Identify the structure of (P).

(A)

(B)

(C)

(D)

3) Which of the following compounds can be prepared in good yield by Gabriel phthalimide
synthesis?

(A)

(B)
(C)

(D)

4) An organic compound [A], of molecular formula was hydrolyzed with dilute sulphuric
acid to give a carboxylic acid [B] and an alcohol [C]. Oxidation of [C] with produced
[B]. Which of the following structures are not possible for [A]?

(A)

(B)

(C)
(D)

SECTION-I(ii)

1)
Which statement(s) is/are correct:

(A) Reduced product of P and Q will be metamers to each other.

(B) By dry distillation of hydrolysed products of P with Ca(OH)2, gives benzophenone.
Hydrolysed product of Q, reacts with NaNO2 + HCl followed by reaction with phenol, gives
(C)
orange red dye.
(D) Electrophile involved in the formation of Q is dichlorocarbene.

2) The correct statement(s) about the following reaction is/are

(A) P on reaction with Zn dust gives Naphthalene
(B) Q is red colour dye
(C) P is Naphthol
(D) Q on reaction with ethyl alcohol can give (P)

3)
Correct compounds for the above reaction is/are:

(A)

(B)

(C)

(D)

4)
Correct statement/s about above reaction is/are:

(A) First step is esterification

(B)

(C) Y is C4H9COOH

(D)

5) Which of them liberate a gas which turns lime water milky.

(A)
(B)

(C)

(D)

6) A positive carbylamine test is given by

(A) N, N-dimethylaniline
(B) 2, 4-dimethylaniline
(C) N-methyl-o-methylaniline
(D) p-methylbenzylamine

7)

Reaction of with a mixture of Br2 and KOH gives R-NH2 as the main product. The
intermediates involved in this reaction are:

(A)

(B) R - NHBr
(C) R - N = C = O

(D)

8) With reference to the scheme given below, which of the given statement(s) about T, U, V and W is
(are) correct?

(A) T is soluble in hot aqueous NaOH

(B) U is optically active
(C) Molecular formula of W is C10H18O4
(D) V gives effervescences on treatment with aqueous NaHCO3.
 SECTION-II

1) How many dicarboxylic acids with molecular formula will liberate CO2 gas on heating

2)
How many total number of products are obtained after the completion of reaction

3)
How many C14 atoms are present in the product.

4) An organic compound (A) consists of C, H and O gives a characteristic colour with ceric
ammonium nitrate. Treatment of (A) with PCl5 gives (B) which reacts with KCN to form (C). The

reduction of (C) with produces (D) which on heating gives piperidine with
the evolution of ammonia. Identify the number of carbon atoms in compound D is x and the number
of carbon atoms in compound A is y, what is the value of x + y?

5) Schemes 1 and 2 describes the conversion of P to Q and R to S, respectively, scheme 3 describes

the synthesis of T from Q and S. The total number of Br atoms in a molecule of T is _______

6) The total number of carboxylic acid groups in the product P is

 MATHEMATICS

SECTION-I(i)

1) If , then A =

(A)

(B)

(C)

(D)

2)

(A)

(B)

(C)

(D)

3) If then a + b =

(A)

(B)

(C)

(D)
4) If , then f (x) =

(A)

(B)

(C)

(D)

SECTION-I(ii)

1) If , then

(A) f (x) is an Even function

(B)

(C)

(D) A + B = 0

2) If then

(A)
(B)
(C)
(D)

3) If and f (0) = 0, then :

(A) f (x) is odd function

(B) f (x) has range R
(C) f (x) = 0 has atleast one real root
(D) f (x) is monotonic function

4) is equal to , then (where a is a constant)

(A) a = -1
(B) f (1) = 0
(C)

(D)

5) The integral can not take the value.

(A)

(B)

(C)

(D)

6) Which of the following integral value is ?

(A)

(B)

(C)

(D)

7) Which of the following integral value does not vanish.

(A)

(B)

(C)

(D)
8) The value of integral

(A)

(B)

(C)

(D)

SECTION-II

1) then if the value of then a + b is

2) The value of integral , where is a

then is______

3) If , where c is constant of integration and , ,

then the value of is :

4) If then is______.

5) (where [x] is greatest integer function)

6) , where P > 0, P, then P + K = _____

 ANSWER KEYS

PHYSICS

SECTION-I(i)

Q. 1 2 3 4
A. C A B D

SECTION-I(ii)

Q. 5 6 7 8 9 10 11 12
A. A,B,D B,D A,C A,B,D B,C,D A,B,C,D C A,B,C

SECTION-II

Q. 13 14 15 16 17 18
A. 25 6.00 0.00 2.00 4.00 5.00

CHEMISTRY

SECTION-I(i)

Q. 19 20 21 22
A. A B A A

SECTION-I(ii)

Q. 23 24 25 26 27 28 29 30
A. B,C,D A,B,C A,B,C A,B,C,D A,B,C B,D A,C A,C,D

SECTION-II

Q. 31 32 33 34 35 36
A. 3.00 6.00 2.00 8.00 4.00 2.00

MATHEMATICS

SECTION-I(i)

Q. 37 38 39 40
A. D B A C

SECTION-I(ii)

Q. 41 42 43 44 45 46 47 48
A. A,B A,D A,B,C,D A,B,D A,D A,B,C B,C,D A,B,C
 SECTION-II

Q. 49 50 51 52 53 54
A. 10.00 4.00 5.00 32.00 165.00 10.00
 SOLUTIONS

PHYSICS

2)

When the key is at position (2) for a long time ; the energy stored in the inductor is :

This whole energy will be dissipated in the form of heat when the inductor is connected to R1 and no
source is connected.

Hence (A).

3)

The emf will induce when flux changes i.e. when the area changes.
In the given problem, flux changes from situation (i) to (ii) (in figure).

But no flux will change from (ii) to (iii) (as area inside the magnetic field remains unchanged). Again
from (iii) to (iv), flux changes.
The total time taken from (i) to (iv) is :

But during this time, flux does not change from (ii) to (iii) which takes a time:
Hence, the time during which flux changes is :

4)

Emf induced when a loop rotates in a magnetic field is (e = Ns Bω sin ωt), which is a
sinusoidal function.
Therefore, induced current will also be sinusoidal as shown :
The curve will be negative, because initially the flux decreases from t = 0 to T/4 and then increases

from to . But from to , there will be no induced current as there is no field on the
right side. Hence, the current produced will be as shown :

Hence (D).

5)

Rate of work done by external agent is

and thermal power dissipated in the resistor = eI = (BvL) I

6)

Equivalent circuit is

7)

Apply len'z law for direction of induced current.

 8)

9)

For

For
Also apply lenz' law for direction of

10)

The line charge will produce radially electric field which is perpendicular to induced electric field.

11)

As the loop enters the region it will experience a magnetic force in a direction opposite to gravity
but still gravitational force may be greater than or less than the magnetic force hence speed may
increase or decrease. Once it gets completely inside the magnetic field then speed will increase after
that instant.

12)

For given situation

compare this equation with

Solving equation

According to given conditions

 13)

e = 25 volt

14)

Use maxima-minima

15)

16)

17)

Amperes force law opposes velocity

Figure

So, i.e.,

18)

Total magnetic flux through a super conductor is equal to zero.

CHEMISTRY

19)

20)

21)

Gabriel phthalimide synthesis gives 1° amine in good yield.

22)

23)
 24)

25)

26)

28)

NOTE: Only primary amines give carbylamine test.

Hence 2, 4-dimethylaniline and p-methyl-benzylamine both give this test.
 29)

This is an example of Hoffmann degradation of amides.

30)

31)
 32)

34)

x = 5, y = 3

35)
Number of Br atoms in (T) = 4

36)

MATHEMATICS

37)

Let

38)

where tan x = t

39)

Let
Comparing coefficients of sin x and cos x:

,
 40)

Let
Substitute :

41)

Clearly

Where

42)

Put

43)
as
is strictly increasing function.
f (x) is monotonic function.
Range of f (x) is R.
f (x) is polynomial of odd power.
has atleast one real root.

44)

45)

Let

46)

By King's Rule.

47)

(a) is an odd function.

Integral = 0

(b)
(c)

(d)

48)

49)

Put

50)

For interval
 51)

Let

52)

Let

53)

54)
Put