(Batches: e-SANKALP-2325 S1, T1 & P1)

I I T – JEE, 2 3 2 5 Paper Code

100848
(CLASS XI)
Time: 2 Hours Maximum Marks: 126
INSTRUCTIONS
A. General
1. Write your Name, Enrolment number in the space provided on this booklet as soon as you get the paper.
2. Blank papers, clipboards, log tables, slide rules, calculators, cameras, cellular phones, pagers, and electronic
gadgets of any kind are NOT allowed in the examination hall.
3. Use a ball point pen do darken the bubbles on OMR sheet as your answer besides Name, Enrolment
number, Phase, Paper sequence, Venue, Date along with your signature on OMR sheet.

B. Question Paper Format

The question paper consists of three parts (Physics, Chemistry and Mathematics). Each part consists of
three sections.
4. Section–1 (01 – 06) contains (06) Multiple Choice Questions which have Only One Correct answer. Each
question will be evaluated according to the following marking scheme.
Full Marks : +3 If only (all) the correct option(s) is (are) chosen;
Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered);
Negative Marks : –1 In all other cases
5 Section–2 (07 – 09) contains (03) Multiple Choice Questions which have one or more than one
correct answer. Each question will be evaluated according to the following marking scheme.
Full Marks : +4 If only (all) the correct option(s) is (are) chosen;
Partial Marks : +3 If all the four options are correct but ONLY three options are chosen;
Partial Marks : +2 If three or more options are correct but ONLY two options are chosen and
both of which are correct;
Partial Marks : +1 If two or more options are correct but ONLY one option is chosen and it is a
correct option;
Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered);
Negative Marks : –2 In all other cases.
6. Section–3 (10 – 12) contains (03) Numerical Value Questions, the answer to each question is a
Numerical Value. For each question, enter the correct numerical value corresponding to the answer
and each question carries +4 marks for correct answer. There is no negative marking.

Enrolment No. :

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e-Sankalp2325 S1, T1 & P1-XI-PCM-(100848)-2

PART I : PHYSICS
SECTION – 1 : (Only One Option Correct Type)

This section contains 6 multiple choice questions. Each question has four choices (A), (B), (C) and (D)
out of which ONLY ONE option is correct.

1. A rod of mass m and length  is lying along the y-axis such that one of its ends is at the origin.
Suddenly an impulse is given to the rod such that immediately after the impulse, the end on the
origin has a velocity v0 î and the other end has a velocity 2v0 î . The magnitude of angular
momentum of the rod about the origin at this instant is
2 3
(A) mv0 (B) mv0
3 2
5 7
(C) mv0 (D) mv0
6 8

2. Three small identical spheres A, B and C each of mass m, are v0

connected to a small ring D of negligible mass by means of three A
C
identical light inextensible strings of length  each, which are equally 120
spaced as shown. The spheres may slide freely on a frictionless D
v0 120 120
horizontal surface. All three spheres have given same speed v0
perpendicular to string, such that, all are moving in a circle about ring D
which is at rest. Suddenly string CD breaks. After the other two string v0
becomes taut again, determine the angular speed of A with respect to D B
is (when string become taut)
3v 0 3v 0
(A) (B)
4 2
3v 0 v0
(C) (D)
8 4

3. In the figure shown a plank of mass m is lying at rest on a smooth m,r

horizontal surface. A disc of same mass m and radius r is rotated to 0
an angular speed 0 and then gently placed on the plank. It is found
that finally slipping cease. Assume that plank is long enough.  is m
coefficient of friction between disc and plank. Time when slipping
ceases
r0 r0
(A) (B)
2g 10g
r0 r0
(C) (D)
4g 2 10g

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 e-Sankalp2325 S1, T1 & P1-XI-PCM-(100848)-3

4. A rod of mass m and length  slides between wall and floor as shown
in the figure. Q is centre of mass of the rod, P is any arbitrary point on R
the rod, R is the instantaneous centre of rotation of rod at that time and P
S is moving on ground with speed v. Choose the correct statement. Q
v
S
(A) Angular velocity of the rod about P will be same as angular velocity of the rod about point Q
at any instant.
(B) At the given instant the angular velocity of rod about point R is not same as angular velocity
of the rod about P.
(C) At the given instant the angular velocity of rod about S is same as angular velocity of the rod
about R.
(D) Angular velocity about a fixed point on the ground and Q will always be same.

5. A particle of mass m is doing horizontal circular motion with the Z(vertical)

help of a string (conical pendulum) as shown in the figure. If
speed of the particle is constant then, choose the INCORRECT O
option. y
(A) the angular momentum of the particle about O is constant 
x
(B) magnitude of angular momentum about O remains constant g
(C) z component of the angular momentum remains conserved
(D) z component of torque is always zero.

6. Consider a disc rotating in the horizontal plane with a constant y 

angular speed  about its centre O. The disc has a shaded region R
on one side of the diameter and an unshaded region on the other Q
side as shown in the figure. When the disc is in the orientation as x
shown, two pebbles P and Q are simultaneously projected at an
P
angle towards R. The velocity of projection is in the y-z plane an
same for both pebbles with respect to the disc. Assume that (i) they land back on the disc before
1
the disc has completed rotation, (ii) their range is less than half the disc radius, and (iii) 
8
remains constant throughout. Then
(A) P lands in the shaded region and Q in the unshaded region.
(B) P lands in the unshaded region and Q in the shaded region.
(C) Both P and Q land in the unshaded region.
(D) Both P and Q land in the shaded region.

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e-Sankalp2325 S1, T1 & P1-XI-PCM-(100848)-4

SECTION – 2 : (One or More Than One Options Correct Type)

This section contains 3 multiple choice type questions. Each question has four choices (A), (B), (C)
and (D) out of which ONE or MORE THAN ONE are correct.

7. A rod CD of length L and mass M is placed horizontally on a D

frictionless horizontal surface as shown. A second identical rod AB
which is also placed horizontally (perpendicular to CD) on the same
horizontal surface is moving along the surface with a velocity v in a L
direction perpendicular to rod CD and its end B strikes the rod CD
at end C and sticks to it rigidly. Then, v
A L B C
v
(A) velocity of centre of mass of the system just after impact is .
4

3v
(B) the (angular speed) of system just after collision is .
5L
v
(C) velocity of centre of mass of the system just after impact is .
2
5v
(D) the (angular speed) of system just after collision is .
3L

Space for Rough work

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 e-Sankalp2325 S1, T1 & P1-XI-PCM-(100848)-5

8. A rod of mass m and length  is placed vertically on a smooth floor

as shown in the figure. The lower end of the rod is given a negligible
slight push towards left due to which the lower end of the rod moves 
towards left and collides perfectly inelastically with the fixed point P
and then the rod rotates about the point P.
P
[ = (2  3)m]
/4

24
(A) The angular velocity of the rod just before its lowest point collide with P is g
7
21
(B) The angular velocity of the rod just after its lowest point collides with P is g
32
21
(C) The velocity of the top most point of the rod immediately after collision is g 2  3 
32
21
(D) The velocity of the top most point of the rod immediately after collision is g 2  3 
32

9. Two identical particles of each of mass ‘m’ P Q

are connected by a mass less rod (PQ). This d
rod is hinged about it’s centre (A) and is A R S
rotating on a smooth horizontal plane with an B
angular velocity of 5 rad/sec. Another
identical arrangement (RS), hinged at B but
having particles of each of mass “4m” is placed very near to the first arrangement at “ t = 0” as
shown in the figure. The coefficient of restitution between any two particles is 0.5. Then (assume
‘d’ distance between R and Q tends to zero)
(A) angular velocity of (PQ) after it’s first collision with (RS) is  rad/sec

(B) Angular velocity of (RS) after its first collision with (PQ) is rad/sec
2
(C) The time gap between first and second collision between PQ and RS is 4 sec
(D) The time gap between first and second collision between PQ and RS is 2 sec

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e-Sankalp2325 S1, T1 & P1-XI-PCM-(100848)-6

SECTION – 3: (Numerical Answer Type)

This section contains THREE questions. The answer to each question is a NUMERICAL VALUE. For
each question, enter the correct numerical value (in decimal notation, truncated/rounded‐off to the
second decimal place; e.g. xxxxx.xx).

10. A ring and a disc are initially at rest, side by side, at the top of an inclined plane which makes an
angle 60° with the horizontal. They start to roll without slipping at the same instant of time along
the shortest path. If the time difference between their reaching the ground is (2 – 3 ) / 10 s ,
then the height of the top of the inclined plane, in metres, is __________. Take g = 10 ms–2.

11. A uniform circular disc of mass 50 kg and radius 0.4 m is rotating with an angular velocity of 10
rad s-1 about its own axis, which is vertical. Two uniform circular rings, each of mass 6.25 kg and
radius 0.2 m, are gently placed symmetrically on the disc in such a manner that they are touching
each other along the axis of the disc and are horizontal. Assume that the friction is large enough
such that the rings are at rest relative to the disc and the system rotates about the original axis.
The new angular velocity (in rad s-1) of the system is

12. A boy is pushing a ring of mass 2 kg and radius 0.5 m with a Stick
stick as shown in the figure. The stick applies a force of 2N
on the ring and rolls it without slipping with an acceleration
of 0.3 m/s2. The coefficient of friction between the ground
and the ring is large enough that rolling always occurs and
the coefficeint of friction between the stick and the ring is
(P/10). The value of P is
Ground

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 e-Sankalp2325 S1, T1 & P1-XI-PCM-(100848)-7

PART II : CHEMISTRY
SECTION – 1 : (Only One Option Correct Type)

This section contains 6 multiple choice questions. Each question has four choices (A), (B), (C) and (D)
out of which ONLY ONE option is correct.

1. The solubility of Ag2CO3 in water at 25° C is 1.42 x 10–5 mole/litre. What is its solubility in 0.01 M
Na2CO3 solution? Assume no hydrolysis of CO 32 ion.

(A) 1.6 x 10–6 mole/litre (B) 4.2 x 10–5 mole/litre

(C) 1.7 x 10–5 mole/litre (D) 2.4 x 10–5 mole/litre

2. A solution is prepared by dissolving 2.8 g of lime (CaO) in enough water to make 1.00 L of lime water
(Ca(OH)2(aq)). If solubility of Ca(OH)2 in water is 1.48 gm/lt. The pH of the solution obtained will be:
[log 2 = 0.3, Ca = 40, O = 16, H = 1]
(A) 12.3 (B) 12.6
(C) 1.3 (D) 13

3. The pH at which a 0.01 M Al+3 solution is 99.99% precipitated is : (Ksp Al(OH)3 = 1 × 10-18 at 25oC)
(A) 6.67 (B) 7.67
(C) 8.67 (D) 10

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4. An acid type indicator, HIn differs in colour from its conjugate base (In ). The human eye is
sensitive to colour difference only when the ratio [In ] / [HIn] is greater than 10 or smaller than
0.1. What should be the minimum change in pH of the solution to observe a complete colour
change? (K In  1.0  10 5 ).
(A) 1 (B) 5
(C) 2 (D) 3

5. The solubility product of Ag2C2O4 at 25o C is 1.29  10 11 mol3 L3 . A solution of
o
K 2C2O 4 containing 0.1520 mol in 500 mL water is shaken at 25 C with excess of Ag2CO3 till
the equilibrium is reached :
Ag2CO3  K 2C2O 4    Ag2C2O 4  K 2CO3
At equilibrium, the solution contains 0.0358 mol of K 2CO3 . Assuming the degree of dissociation
of K 2C2O4 and K 2CO3 to be equal, calculate the solubility product of Ag2CO3 .
(A) 3.97  10 12 (B) 3.00  10 12
(C) 3.97  10 11 (D) 3.00  10 11

6. A solution has 0.05 M Mg2+ and 0.05 M NH3. What is the concentration of NH 4Cl required to
prevent the formation of Mg(OH)2 in solution. Ksp of Mg  OH2  9.0  10 12 and ionization
constant of NH3 is 1.8  10 5 . [log1.8 = 0.26, log1.34 = 0.13]
(A) 0.0134 (B) 0.05
(C) 0.067 (D) 0.037
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 e-Sankalp2325 S1, T1 & P1-XI-PCM-(100848)-9

SECTION – 2 : (One or More Than One Options Correct Type)

This section contains 3 multiple choice type questions. Each question has four choices (A), (B), (C)
and (D) out of which ONE or MORE THAN ONE are correct.

7. A solution contains 0.1 M NaCl, 0.01 M NaBr and 0.001 M NaI. Solid AgNO 3 is gradually added to
the solution and its addition does not change the volume of solution:
Ksp (AgCl) = 10 – 10 , Ksp (AgBr) = 10 – 13 , Ksp (AgI) = 10 – 17
Choose the correct statement
(A) AgI precipitates first
(B) The maximum [Ag+] which can be maintained in the solution so that only AgI is precipitated is
10 – 11 M
(C) When the precipitation of AgCl just starts, [I–] in the solution is 10 – 8 M
(D) If sufficient NaI is added to a saturated solution of AgCl, precipitate of AgI is obtained

8. Which of the following would dissolve Pb(OH)2 more than pure water?
[Given Ksp of Pb(OH)2 = 1.35 × 10-20]
(A) Buffer solution having pH = 6 (B) 0.01 M PbCl2 solution
(C) 0.01 M NH4OH solution (D) A buffer solution of pH = 9

9. Experiment # 1: A mixture of water and AgCl(s) is shaken until a saturated solution is obtained.
Now, the solution is filtered and to 100 ml of the clear filterate, 100 ml of 0.003 M NaBr is added.
Experiment # 2: A mixture of water and AgBr (s) is shaken until a saturated solution is obtained.
Now, the solution is filtered and to 100 ml of the clear filterate, 100 ml of 0.003 M NaCl is added.
Experiment # 3: 0.1 mole NH3 is passed through solution obtained in Experiment # 2.
Experiment # 4: 0.01 mole Na2S2O3 is mixed to solution obtained in Experiment # 1.
Given Ksp (AgCl) = 10 – 10 and Ksp(AgBr) = 10 – 14 at 25oC; Kf of [Ag(S2O3)2]3- = 10+13. Kf of
[Ag(NH3)2]+ = 10+8.
(A) In experiment no. 1, resultant [Ag+] = 6. 675 × 10-12 M
(B) In experiment no. 2, resultant [Ag+] = 5 × 10-8 M
(C) After experiment no. 3, final [Ag+] = 5 × 10-15 M
(D) After experiment no. 4, final [Ag+] = 6.675 × 10-13 M

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e-Sankalp2325 S1, T1 & P1-XI-PCM-(100848)-10

SECTION – 3: (Numerical Answer Type)

This section contains THREE questions. The answer to each question is a NUMERICAL VALUE. For
each question, enter the correct numerical value (in decimal notation, truncated/rounded‐off to the
second decimal place; e.g. xxxxx.xx).

10. x × 10-1 moles of NH3 is added to a 25 × 10-3 (M) Ag+ solution to just prevent the precipitation of
AgCl when [Cl-] reaches to 10-3(M) ? What is the value of x ? Assume total volume of solution is 1
lit. (Give Ksp (AgCl) = 10-10) and Kinstability of [(Ag(NH3)2]+ = 10-8

11. A particular water sample has 131 ppm CaSO4. What % of the water must be evaporated in a
container before solid CaSO4 begins to deposit Ksp of CaSO 4  9.0  10 6 ?

12. At 25oC at a minimum pH (= x), 1.0  10 3 mol of Al(OH)3 will go into solution (1 dm3) as
Al  OH 4 ; while at 25oC at a maximum pH (= y), 1.0  10 3 mol of Al(OH)3 will go into solution


(1 dm3) as Al3  . What is the value of (x + y) (Given :

K sp  Al  OH3   5.0  10 33 M4 K inst of Al  OH 4  1.3  10 34 M4 )


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 e-Sankalp2325 S1, T1 & P1-XI-PCM-(100848)-11

PART III : MATHEMATICS

SECTION – 1: (Only One Options Correct Type)

This section contains 6 multiple choice type questions. Each question has four choices (A), (B), (C)
and (D) out of which ONE is correct.

1. Let a and b be positive real numbers such that a + b = 1, then the maximum value of a abb + abba
is equal to
(A) 1 (B) 2
(C) 3 (D) 3/4


r 3  (r 2  1)2
2.  (r
r 1
4
 r 2  1)(r 2  r)
is equal to

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

n n2

  n  1  r 
4
3. The value of r4  is equal to
r 1 r 1
(A) – [1 + n4 + (n + 1)4] (B) – [1 + (n + 1)4 + (n + 2)4]
(C) – [1 + (n – 1)4 + n4] (D) none of these

In a function f(x) = 2x – 1 – x 2 x 1 , x  N, if g(x) =  f  x  

1/ 2n
4. , (n  N) then range of g(x) is [k, ),
x  N where ‘k + 1’ is
(A) 1 (B) 2
(C) 3 (D) none of these

5. For the series 21, 22, 23, ....,k –1, k; the A.M. and G.M. of the first and last numbers exist in the
given series. If ‘k’ is a three digit number, then ‘k’ can attain
(A) 5 values (B) 6 values
(C) 2 values (D) 4 values

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6. If f(x) = 0 is a cubic equation with positive and distinct roots , ,  such that  is the H.M of the
roots of f(x) = 0. Then , ,  are in
(A) A.P. (B) G.P.
(C) H.P. (D) none of these

SECTION – 2: (Multi Correct Choice Type)

This section contains 3 multiple choice questions. Each question has four choices (A), (B), (C) and (D)
out of which ONE OR MORE may be correct.

4
7. Let <an> be a sequence of positive numbers such that a1 = 4 and an = an  1 + , n > 1, then
an 1
the value of [a100] may be (Where [x] represents the integral part of x)
(A) 28 (B) 29
(C) 30 (D) 31

8. If a, b, c be three unequal positive quantities in H.P. then

(A) a100 + c100 > 2b100 (B) a3+c3 > 2b3
(C) a + c > 2b
5 5 5 (D) a2 + c2 > 2b2

9. If the roots of the equation x2 – px – 1 = 0 and x2 – qx – 1 = 0 form (in a suitable order) an

arithmetic progression with four members then
2 2 4 4
(A) p  ,q (B) p  ,q
3 3 3 3
4 4 2 2
(C) p  ,q (D) p  ,q
3 3 3 3

SECTION – 3: (Numerical Answer Type)

This section contains THREE questions. The answer to each question is a NUMERICAL VALUE. For
each question, enter the correct numerical value (in decimal notation, truncated/rounded‐off to the
second decimal place; e.g. xxxxx.xx).

1
10. If the equations x2  3x  ai = 0 has integral roots  ai  N and ai  300 then
800
 ai =
_________

11. Let dn be the distance travelled by a fighter plane in nth hour. (e.g. d1 is the distance travelled
during first hours, d2 is the distance travelled during second hours, and so on … ), d1, d2, d3 … dn
are related by dn+1 = 2dn + n.(1 + 2n), d1 = 1 and n  10. If dn = (n2  2n + 13)2n2  n  1, then the
value of n is __________.


k2 p
12. If  3k 
q
, (where p and q are relatively co-prime the integers), then the value of p + q is
k 1
_______

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