15-06-2025

1721CJA101029250011 JA

PART - 1 (PHYSICS)

SECTION-I (i)

1) A long cylinder has radius R and charge is distributed symmetrically in its volume such that
electric field at distance r(r < R) from the axis is E. What is charge density at distance r(r < R)?

(A)

(B)

(C)

(D)

2) Block 'A' of mass m is placed over a wedge of the same mass. Assuming all surface to be smooth,
calculate the displacement of the block A in 1 second.

(A)

(B)

(C)

(D)

3) A perfectly straight portion of a uniform rope has mass M and length L. At end A of the segment,
the tension in the rope is at end B it is . The tension in the rope at a distance L/5 from
end A is

(A)

(B)
(C)

(D)

4) A conducting ball of radius r is charged to a potential V0. It is surrounded by a thin-walled

conducting sphere of radius R (where R>r), and the two spheres are connected by a conducting
wire. Determine the potential of the outer sphere.

(A)

(B)

(C)

(D)

5) A square surface of side L meter in the plane of the paper is placed in a uniform electric field E
(volt/m) acting along the same plane at a angle with the horizontal side of the square as shown in
figure

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

SECTION-I (ii)

1) An isolated metallic spherical thin shell has given a charged Q as shown. The parameter r is the
distance to be measured from center of sphere. Which of the following statements(s) is/are
CORRECT.

The energy stored in space R < r < 2R is

(A)

The energy stored in space R < r < 2R is

(B)

Energy stored in space is

(C)

(D)
If switch S is closed the heat generated in wire is

2) A small charged particle 'q' lies at the centre of two concentric conducting hollow spheres of
inner radii R and 5R and outer radii 3R and 7R respectively. Then which of the following is/are
correct.

(A)
The energy stored in the space between 3R to 5 R (cavity) is .

(B)
The energy stored in the space between 3R to 5R (cavity) is
 The amount of work has to be performed to slowly transfer the charge 'q' from centre through
(C)
the orifice to infinity is
The amount of work has to be performed to slowly transfer the charge 'q' from centre through
(D)
the orifice to infinity is

3) Two point charges each of charge 'q' are moving towards the centre 'O' of an earthed spherical
conducting shell of radius R with the constant velocities v and 2v as shown in the figure. Then
choose the correct option(s)

(A)
When and , the charge on the spherical conducting shell is

(B)
When and , the charge on the spherical conducting shell is
When and , the current flowing from the spherical conducting shell to the earth
(C)
is
When and , the current flowing from the spherical conducting shell to the earth
(D)
is

4) A positive point charge q is located inside a neutral hollow spherical conducting shell. The shell
has inner radius a and outer radius b; b - a is not negligible. The shell is centred on the origin. Which
of the following is correct graph of electric field vs radial distance x or electric potential vs radial
distance x? The point charge can be located anywhere inside shell on x-axis
(A)

(B)

(C)

(D)

5) In the figure shown, both the shells are conducting. The outer shell is thick & has a total charge
of Q, inner shell is thin & is earthed.

(A) Charge on inner shell is (-2Q/5)

(B) Charge on inner shell is (-3Q/5)
(C) Total charge on outer shell remain Q
(D) Charge on outer surface of outer shell is (3Q/5)

6) Assuming pulleys and string massless. When system is released from rest. Which of the following
are correct:
(A)
Tension on 1 kg block is

(B)
Tension on 2 kg block is
(C) Force on pulley connected by 1 kg block is

(D) Force on pulley connected by 2 kg block is

SECTION-I (iii)

Common Content for Question No. 1 to 2

There is a hollow prism with hexagonal base of side L0 and height H0 as shown. There are identical
non conducting uniformly charged solid spheres are placed at each corner and two identical spheres
at the centre of flat hexagonal faces. The charges spheres have uniform density of d0 and radius of
R0. What will be the flux passing through the shaded region and average charge density ( )
hexagonal prism. It is given that the flux passing through the hexagonal flat surface is k times the
total flux passing through the prism.

Take SI units & SI units

1) The value of is .........

(A) 0.35
(B) 0.45
(C) 0.55
(D) 0.65

2) The value of d is ..........

(A) 5.83
(B) 4.83
(C) 3.83
(D) 2.83

Common Content for Question No. 3 to 4

A metal sphere with its centre at origin has radius R = 1m. It has three spherical cavities each of

radius R/4 and their centres are at and respectively. Initially

cavity A and B have some non zero charges and cavity C is empty. The electric field at point P is
zero.

3) When charge from cavity A is removed, electric field at point P(2R,2R,0) is found to be 1 . The
magnitude of charge present in the cavity A (in ) was .......

(A) 0.89
(B) 0.99
(C) 0.79
(D) 0.69

4) By keeping the charges same in the cavities A and B and the charges of is placed at the

centre of cavity C. The electric field at point P (in ) is .......

(A) 1.25
(B) 3.25
(C) 2.25
(D) 4.25

SECTION-III

1) In the diagram there are four conducting plates A,B, C and D placed parallel to each other at
equal separation L. If plate C starts moving towards plate B with velocity v, then the current flowing

in the wire connecting A and D is . (Assume all other plates to be fixed) where n is an
integer. Find n
2) In a cubical volume of side 1m, the electric field is and a
= 1 m. Cube has one vertex at origin and sides parallel to coordinates axes. The flux eminating from

the front face parallel to YOZY - plane shaded will be (SI units). Find n = ?

3) Two particles having positive charges +Q and +2Q are fixed at equal distance x from centre of a
conducting sphere having zero net charge and radius r as shown. Initially the switch S is open. After

the switch S is closed, the net charge flowing out of sphere is , find P

4) A system consist of a uniformly charged sphere of radius R and surrounding medium filled by a

charge with the volume charge density where is positive constant and r is the distance
from the centre of sphere. The value of charge on sphere is found to be for which the
electric field intensity E outside the sphere is independent of r. Then find the value of n.

PART - 2 (CHEMISTRY)
 SECTION-I (i)

1)

In which of the following pairs, the bromination of first member is easier than the second member ?

(A) Isobutane, n-butane

(B) n-Butane, isobutane
(C) Methane, ethane
(D) None of these

2) Which alcohol produce turbidity with Lucas reagent immediately ?

(A)

(B)

(C)

(D)

3) In which of the following reaction, 2º alcohol is obtained as major product.

(A)

(B)

(C)

(D)

4) Which of the following ester form 2º alcohol with excess of MeMgBr :

(A)

(B)
(C)

(D)

5)
Which of the following statement is correct.
(i) If A & B are same gases then T2 > T1
(ii) If T1 = T2 then A(g) may be SO2(g) & B(g) may be CH4(g)
(iii) If B & C are same gases then T3 > T2
(iv) If T1 = T2 = T3 then A(g) may be CH4, B(g) may be SO2 & C(g) may be SO3(g)

(A) i, ii & iii only

(B) i, ii, & iv only
(C) All are correct
(D) ii & iii only

SECTION-I (ii)

1) CH2 = CHCH2CH = CH2 A, A can be

(A)

(B) CH2 = CHCH = CH – CH2Br

(C) CH2 = CHCH2CH = CHBr

(D)

2) Which of the following reagent used for following transformations

(A) PCl5
(B) HCl + ZnCl2
(C) SOCl2
(D) PCl3

3) Ph—CH = CH2 + BrCCl3 Product is :

(A)

(B)

(C)

(D)

4) उन अिभियाओं का चयन कीिजए जो अपने उपाद से सही सु मेिलत है -

(A)
CH3–COOH

(B)

(C)

(D)
Me–CHO

5) Consider the given reaction

which of following statements is/are correct for the above reaction.

(A) Product formation takes place due to the breaking of O–Ts

(B) The reaction is SN2
(C) The reaction is SN1
(D) Configuration of product is (R)
6) An open-ended mercury manometer is used to measure the pressure exerted by a trapped gas as
shown in the figure. Initially manometer shows no difference in mercury level in both columns as
shown in diagram.

After sparking 'A' dissociates according to following reaction 2A(g) → 3B(g) + 2C(g)
If pressure of Gas "A" decreases to 0.8 atm. Then
(Assume temperature to be constant and is 300 K)

(A) total pressure increased by 1.3 atm

(B) total pressure increased by 0.3 atm
(C) total pressure increased by 22.3 cm of Hg
(D) difference in mercury level is 228 mm

SECTION-I (iii)

Common Content for Question No. 1 to 2

Dehydration of alcohol is an elimination reaction, which may proceed via formation of carbocation
intermediate & carbocation rearrangement is also considered if required. Alkene is the product of
the reaction where usually more stable alkene is major product.

1) Which of the following represent correct energy profile diagram for the reaction given in
paragraph :-

(A)
(B)

(C)

(D)

2) Which of the following represent product P1

(A)

(B)

(C)

(D)

Common Content for Question No. 3 to 4

Andrews isotherm for CO2 may be plotted as shown
3) At point ‘A’ , which of the following is true ?
(P) compressibility factor becomes 0.375
(Q) the given gas is called vander Waals’ gas
(R) below ‘A’ only one variable is required for liquefaction

(A) Only P, Q
(B) Only Q, R
(C) P, Q and R
(D) Only P, R

4) Which of the following is a correct statement?

(P) With in the area BAC, state of matter is called “vapour”
(Q) At Tb, PV remains a constant
(R) At point “A”, liquid state of matter loses its meniscus

(A) Only P, Q
(B) Only Q, R
(C) P, Q and R
(D) Only P, R

SECTION-III

1) Calculate the change in pressure (in atm) when 2 mol of NO and 16 gm O2 in a 6.25 litre originally
at 27°C react to produce the maximum quantity of NO2 possible according to the equation, 2NO(g) +

O2(g) → 2NO2(g) (Take R = litre atm / mol K)

2) From the graph of vs P at a constant temperature of 300K, calculate molar mass of gas.
3) Degree of unsaturation in the major product is
X then (X–2)

4)

Which Cl is most reactive toward AgNO3(aq)?

PART - 3 (MATHS)

SECTION-I (i)

1) A semicircle with diameter PQ sits on an isosceles triangle PQR to form a region shaped like an
ice-cream cone, as shown in the figure, where . If is the area of the semicircle and

is the area of the triangle, then is

(A)

(B)

(C) 0

(D)
2) If is continuous at , then k is

(A)

(B)

(C)

(D)

3) Consider
Where represents integral and fractional part functions, respectively, then-

(A) f is derivable at x = 0
(B) f is continuous but not derivable at x = 0
(C) f is not continuous at x = 0
(D) f is neither cont. nor derivable at x = 0

4) If f(x) = [x]{x} + {x}[x] + sin , where [.] and {.} represent the greatest integer function and the

fractional part function respectively, then is equal to

(A)

(B)

(C)

(D)

5) Let h (x) = f3(x) where f is a differentiable function. If f (0) = and then the equation
of line tangent to the graph of h (x) at x = 0 is

(A) 8x – 16y + 1 = 0
(B) 16x + 8y – 1 = 0
(C) 16x – 8y + 1 = 0
(D) 16x – 8y – 1 = 0
 SECTION-I (ii)

1) If the quadratic equation , where , does not have two real & distinct
roots, then

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

2) Let then which of the following is/are

correct?

(A)

(B) Largest possible value of a is

(C) Number of possible integral values of a is 3
(D) Sum of all possible integral value of a is '0'

3) Find all the positive integral solutions of, = .

(A) (1,2)
(B) (2, 3)
(C) (2, 7)
(D) (1, 4)

4) If is a function defined by and f is

surjective then

(A)

(B)

(C)

(D)

5) If LT, LN, LST and LSN denotes the lengths of tangent, normal, subtangent and subnormal
respectively of a curve y = ƒ(x) at a point P(2009, 2010) on it then

(A)
(B)
= constant

(C)
1 – LST . LSN =
(D) 1 – LST . LSN = –(2009)(2011)

6) If = 1 is a tangent to the curve x = Kt, y = , K > 0 then :

(A) a > 0, b > 0

(B) a > 0, b < 0
(C) a < 0, b > 0
(D) a < 0, b < 0

SECTION-I (iii)

Common Content for Question No. 1 to 2

Consider the quadratic equation and where

1) Number of values of a for which the two equations will have exactly one common real root is

(A) 0
(B) 1
(C) 2
(D) 3

2) Value of a for which both the roots of first equation are negative and those of second equation are
of opposite sign is:

(A)

(B)

(C)

(D)

Common Content for Question No. 3 to 4

If
3) Which is correct?

(A)
(B)

(C)

(D)

4) If then the value of x is

(A) 3
(B) 10
(C) 13
(D) 15

SECTION-III

1) If & are the roots of the equation .

Then is equal to

2) Let . If ƒ'(0) exist and is equal to non-zero value b, then value

of is

3) If x = cos(tan–1((secθ + 1) cotθ)), y = sin(cot–1((secθ – 1) cotθ)) where , then

is equal to

4) At the point P(a, an) on the graph of y = xn (n ∈ N) in the first quadrant a normal is drawn. The

normal intersects the y-axis at the point (0, b). If .Then value of n is
 ANSWER KEYS

PART - 1 (PHYSICS)

SECTION-I (i)

Q. 1 2 3 4 5
A. D B C A D

SECTION-I (ii)

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

SECTION-I (iii)

Q. 12 13 14 15
A. A B A C

SECTION-III

Q. 16 17 18 19
A. 3 3 2 2

PART - 2 (CHEMISTRY)

SECTION-I (i)

Q. 20 21 22 23 24
A. A D C B A

SECTION-I (ii)

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

SECTION-I (iii)

Q. 31 32 33 34
A. C B C B

SECTION-III

Q. 35 36 37 38
A. 2 4 9 4

PART - 3 (MATHS)
 SECTION-I (i)

Q. 39 40 41 42 43
A. C C B D D

SECTION-I (ii)

Q. 44 45 46 47 48 49
A. C,D C,D A,C A,B,C A,B,D A,D

SECTION-I (iii)

Q. 50 51 52 53
A. B C B C

SECTION-III

Q. 54 55 56 57
A. 6 7 1 2
 SOLUTIONS

PART - 1 (PHYSICS)

1)

2)

3)

4)

5) Ans. Zero

6) The energy stored in space R < r < 2R is

If switch S is closed the heat generated in wire is

7) The energy stored in the space between 3R to 5 R (cavity) is .

The amount of work has to be performed to slowly transfer the charge 'q' from centre through

the orifice to infinity is

8) When and , the charge on the spherical conducting shell is

When and , the current flowing from the spherical conducting shell to the earth

is
 9)

10) Charge on inner shell is (-2Q/5)

Total charge on outer shell remain Q
Charge on outer surface of outer shell is (3Q/5)

11) All Option is correct

12) Ans. 0.35

13) Ans. 4.83

14) Ans. 0.89

15) Ans. 2.25

16) Ans. 3

17) 3

18) 2

19) 2

PART - 2 (CHEMISTRY)

20)

3°H > 2°H > 1°H.

21) 3°- alcohols gives turbidity most readily

22) Explain Question :

Asking about the reaction in which 2° alcohol is the major product among the following.
Concept :
1. Electrophilic addition of alkene
2. Nucleophilic substitution followed by nucleophilic addition in reaction of acid halide with
Grignard reagent.
Solution :

Conclusion → 2° Alcohol is obtained as a major product in hydroboration oxidation reaction of

alkene in option 3.
Final Answer : (3)

23)

24)

If T1 = T2 = T3 then molecular mass of gas 'A' > molecular mass of gas 'B' > molecular mass of
gas 'C'.

25)

Selective Bromination at allylic carbon.

26)
HCl and ZnCl2 goes through SN1 mechanism.
SOCl2 goes through SNi mechanism.

27)

28) (A) Hell volhard Zelinskii

(B) SN2

(C) ( followed by SNi)

(D)

29)

30) Pext = 1 atm (Ptotal)

So length of Hg = 76 cm of Hg.
Pressure of Gas(A) = 1atm

Now, After sparking 'A' PT becomes

PT = 0.8 + 0.3 + 0.2
= 1.3 atm
Total Pressure increased by 0.3 atm
1.3 atm = 98.8 cm of Hg
Difference in mercury level
= 98.8 – 76
= 22.8 cm of Hg
= 228 mm of Hg

31)

Explain Question :
Asking about the energy diagrams of dehydration reaction of alcohol.

Concept :
Mechanism is E1 elimination.
Number of transition states (T.S.) or activated complexes is equal to number of total steps of
reaction.

Solution :

*Total steps = 5. Total T.S. = 5

*Step-2 is the slowest step [highest energy state]
*Energy diagram-3 is the most appropriate for the dehydration of given compound.

Final Answer : (3)

32)

33) For T < TC, 3 zones exist for substance.

* Pure liquid only
* Liquid + Vapour zone (Like ΔBAC region)
* only vapour zone.
‘A’ location is point of inflection where all variable are at criticality.
Below TC, just by increasing pressure, a real gas can be liquefied.

34)

(Q) At Tb, PV remains a constant

(R) At point “A”, liquid state of matter loses its meniscus

35) 2NO(g) + O2(g) → 2NO2(g)

t = 0 moles 2 0.5 0
t = t moles 2 – 2 × 0.5 0.5–0.5 2 × 0.5
=1 =0 =1
nf = 1 + 1 = 2
Δn = 2.5 – 2 = 0.5 moles
∴ change in pressure

36)

Refer theory notes.

37)

38)

Rate of SN1 reaction µ Stability of carbocation

Stability of carbocation
PART - 3 (MATHS)

39)
40)

41)

42)

43) h ' (x) = 3 f 2 (x) f ' (x)

h ' (0) = 3 f 2 (0) f ' (0) = 3 =+2

also h (0) = [f(0)]3 = –

y+ = 2 (x – 0)

⇒ y = 2x –
⇒ 16x – 8y – 1 = 0
44)

45)

46)

Clearly (A) and (C) satisfies above equation

47)
For 'f ' to be surjective, tan α – 2 = –1 ⇒ α = tan 1
–1

Now, verify the options.

48)

LST . LSN = y12 = (2010)2

(A is correct)

=1 (B is also correct)

1 – LST . LSN =
= 1 – y12 1 – (2010)2 (C is incorrect)
(1 – 2010) (1 + 2010)
– 2009 (2011) (D is correct)

49)

xy = k2

b & a have same sign

50)

51)
52)

Now

Now,

53)

54)
55)

b is finite if a – 2 = 0 ⇒ a=2

& ⇒

56)

⇒ ⇒

57)
equation of normal at P.xr

⇒ at x = 0,

⇒ if x = 2