FIITJEE – INTERNAL Phase Test

PHYSICS, CHEMISTRY & MATHEMATICS

QP CODE: 100608 Advanced

Time Allotted: 3 Hours Maximum Marks: 180

▪ Please read the instructions carefully. You are allotted 5 minutes specifically for
this purpose.
▪ You are not allowed to leave the Examination Hall before the end of the test.

INSTRUCTIONS
BATCHES – Two Year CRP325_PT2

Caution: Question Paper CODE as given above MUST be correctly marked in the answer
OMR sheet before attempting the paper. Wrong CODE or no CODE will give wrong results.

A. General Instructions
1. Attempt ALL the questions. Answers have to be marked on the OMR sheets.
2. This question paper contains Three Sections.
3. Section-I is Physics, Section-II is Chemistry and Section-III is Mathematics.
4. All the section can be filled in PART-A & B of OMR.
5. Rough spaces are provided for rough work inside the question paper. No additional sheets will be
provided for rough work.
6. Blank Papers, clip boards, log tables, slide rule, calculator, cellular phones, pagers and electronic
devices, in any form, are not allowed.

B. Filling of OMR Sheet

1. Ensure matching of OMR sheet with the Question paper before you start marking your answers on
OMR sheet.
2. On the OMR sheet, darken the appropriate bubble with Blue/Black Ball Point Pen for each
character of your Enrolment No. and write in ink your Name, Test Centre and other details at the
designated places.
3. OMR sheet contains alphabets, numerals & special characters for marking answers.

C. Marking Scheme For All Two Parts.

(i) Part-A (01-04) – Contains Four (04) multiple choice questions which have ONLY ONE CORRECT answer
Each question carries +3 marks for correct answer and -1 marks for wrong answer.

(ii) PART–A (05–07) contains (3) Multiple Choice Questions which have One or More Than One Correct
answer.
Full Marks: +4 If only the bubble(s) corresponding to all the correct options(s) is (are) darkened.
Partial Marks: +1 For darkening a bubble corresponding to each correct option, provided NO incorrect
option is darkened.
Zero Marks: 0 If none of the bubbles is darkened.
Negative Marks: −1 In all other cases.
For example, if (A), (C) and (D) are all the correct options for a question, darkening all these three will
result in +4 marks; darkening only (A) and (D) will result in +2 marks; and darkening (A) and (B) will result
in −1 marks, as a wrong option is also darkened.
(iii) Part-B (01-04) This section contains Two paragraphs. Each paragraph having TWO questions Numerical
answer type with answer XXXX.XX. For each question, enter the correct numerical value. If the numerical
value has more than two decimal places, truncate/round-off the value to TWO decimal places. Each
question carries +3 marks for the correct answer. There is no negative marking.

(iv) Part-B (05-10) This section contains SIX (06) questions. The answer to each question is a NON-
NEGATIVE INTEGER. For each question, enter the correct integer corresponding to the answer. Each
question carries +4 marks for correct answer. There is no negative marking.

Name of the Candidate: ____________________________________________

Batch: ____________________ Date of Examination: ___________________

Enrolment Number: _______________________________________________

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 2 Two Year CRP325 _PT2_Advanced

S
SEEC
CTTIIO
ONN –– II :: P
PHHY
YSSIIC
CSS
(PART – A)
(Single Correct Answer Type)
This section contains 4 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out
of which ONLY ONE is correct.

1. As bomb at rest explodes into 3 parts of the same mass. The momentum of the 2 parts is
−2p ˆi and pjˆ . The momentum of the third part will have a magnitude of
(A) p (B) 3p (C) p 5 (D) zero

2. A uniform ring of radius R and mass m is fitted with a massless A

rod AB along its diameter. An ideal horizontal string (whose
one end is attached with the rod at a height r) passes over a R
smooth pulley and other end of the string is attached with a r
block of mass 2 m, as shown. The co-efficient of friction B
between the ring and the surface is . When the system is
released from rest, the ring moves such that rod AB remains 2m
vertical. The value of r is
 3    
(A) R  1 −  (B) R  1 − 
 2(1 +  )   2(1 +  ) 
 3   3 
(C) R  2 −  (D) R  1 − 
 2(1 + )   (1 + ) 

3. A uniform ring of mass m and radius r is placed directly above a uniform sphere of mass M
and of equal radius . The centre of the ring is at a distance 3r from the centre of the
sphere . the gravitational force exerted by the sphere on the ring will be :
3GMm GMm GMm GMm
(A) (B) 2
(C) 2
(D)
8r 2
6r 8r 4r 2

4. Two small balls A and B, each of mass m, are joined rigidly m

at the ends of a light rod of length L. They are placed on a
frictionless horizontal surface. Another ball of mass 2 m moving
L
with speed u towards one of the ball and perpendicular to the
length of the rod on the horizontal frictionless surface as shown 2m
in the figure. If the coefficient of restitution is 1/2 then the u m
angular speed of the rod after the collision will be
4 u u 2 u
(A) (B) (C) (D) None of these
3 3
Space For Rough Work

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 3 Two Year CRP325 _PT2_Advanced

(One or More Than One Options Correct Type)

This section contains 3 multiple choice questions. Each question has 4 choices (A), (B), (C)
and (D), out of which ONE or MORE THAN ONE is correct.

5. The magnitude of gravitational field at distance r1 and r2 from the centre of a uniform sphere
of radius R and mass M are I1 and I2 respectively. Then
I1 r1 I1 r22
(A) if r1 R and r2 R (B) if r1 R and r2 R
I2 r2 I2 r12
I1 r1 I1 r12
(C) if r1 R and r2 R (D) if r1 R and r2 R
I2 r2 I2 r22

6. A constant force F is applied at the top of a ring as shown in figure. F

Mass of the ring is M and radius is R. The angular momentum of
particle about point of contact at time t
(A) is constant (B) increases linearly with time
(C) is 2F Rt (D) decreases linearly with time

7. A particle of mass m is projected with a velocity v making an angle of 45 0 with the horizontal.
The magnitude of the angular momentum of the projectile about the point of projection when
the particle is at its maximum height h is
(A) zero (B) mv 3 / ( 4 2 ) g (C) mv 3 ( 2 ) g (D) m 2gh3

(PART – B)
This section contains Two paragraphs. Each paragraph having TWO questions Numerical answer type with
answer XXXX.XX. For each question, enter the correct numerical value. If the numerical value has more than
two decimal places, truncate/round-off the value to TWO decimal places.

Paragraph for Question no. 1 to 2

A ball of mass 2 kg is dropped from a height H = 10 m m

above a level floor as shown in figure. After striking the
ground it bounces off back and reaches up to height
h = 5 m. H h
Based on above information, answer the following
questions:

1. The speed of the ball just after striking is ________ (in m/s).

2. Loss in energy just before and after striking is

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Paragraph for Question no. 3 to 4

Two blocks A and B of mass m = 1kg each are connected with

each other by an inextensible light string and friction less pulley.
At t = 0 an inelastic ball of mass m = 1 kg collides from bottom
with block A with velocity 16 m/s vertically upwards. On the basis B A
m m
of above information answer the following questions M M
V0 = 16 m/s

3. Let velocities of blocks are just after collision (in m/sec) are VA and VB then find VA + VB

4. Time after which string becomes tight is (in sec)

(PART – B)
(Non – Negative Integer)

5. A gun weighing 15 kg fires a bullet of 150 gm with a velocity of 500 m/s. With what velocity
does the gun recoil (in m/s)?

6. A satellite is moving in a circular orbit around earth at a height R above earth surface
(R being radius of earth) It’s velocity should be increased to k times its initial orbital speed
value, so as to make it escape from earth gravitational pull and reach infinity. Find k

7. Three particles, each of mass m, are situated at the vertices of an equilateral triangle of side
length a. The only forces acting on the particles are their mutual gravitational forces. It is
desired that each particle moves in a circle while maintaining the original mutual separation
a. Find the initial velocity that should be given to each particle.  take a =
GM 
 16 

8. A solid sphere of radius 10 cm and mass 5 kg is gently placed on a rough horizontal ground
with no linear velocity, but initial angular velocity 14 rad/sec. If  = 0.9, find the angular
velocity in rad/sec at the end of slipping

Space For Rough Work

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 5 Two Year CRP325 _PT2_Advanced

9. ( )
Gravitational filed in a region is given by E = 3iˆ − 4ˆj N/kg. Find out the work done (in J) in
displacing a particle by 1m along the line 4y = 3x + 9?

10. Four massless springs whose force constants are 2k, 2k , k and 2k respectively are attached
to a mass M kept on a frictionless plane ( as shown in figure) . If the mass M is displaced in
the horizontal direction, then the frequency of the system is  Take K = 2Nm−1, M = 1kg 
k
2k 2k
M 2k

Space For Rough Work

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 6 Two Year CRP325 _PT2_Advanced

S
SEEC
CTTIIO
ONN –– IIII :: C
CHHE
EMMIIS
STTR
RYY
(PART – A)
(Single Correct Answer Type)
This section contains 4 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out
of which ONLY ONE is correct.

1. In which reversible reaction the formation of O2 is favoured by increasing the volume of

reaction vessel?
(A) N2 ( g) + O2 ( g) 2NO ( g) (B) H2 ( g) + Cl2 ( g) 2HCl ( g)
(C) 2KClO3 ( s ) 2KCl ( s ) + 3 O2 ( g) (D) C ( s ) + O2 ( g) CO2 ( g)

2. Which of the following solutions on mixing produces maximum heat?

(A) NaCl + KOH (B) HCl + NaOH
(C) Ca(NO3)2 + KCl (D) NH4OH + NaOH

3. The tendency of group-13 elements to form compounds in +1 oxidation state

(A) decreases on moving down the group
(B) increases on moving down the group
(C) increases upto indium and then decreases
(D) increases upto aluminium and then decreases

4. Which of the following property is different between graphite and boron nitride?
(A) Presence of hexagonal ring (B) Layer structure
(C) Conductivity (D) As a lubricant

(One or More Than One Options Correct Type)

This section contains 3 multiple choice questions. Each question has 4 choices (A), (B), (C)
and (D), out of which ONE or MORE THAN ONE is correct.

5. Which of the following statement(s) is/are correct for the following reaction?
H2 ( g) + Cl2 ( g) ⎯⎯
h
→ 2HCl ( g) + 64Kcal mol−1
(A) It is an exothermic reaction
(B) It is called a synthesis reaction
(C) The heat of formation of HCl is -64 Kcal mol–1
(D) For this reaction, H = E

6. The concentration of the saturated solution of a salt AX2 is 0.01 mol L–1. Choose correct
statement(s) regarding the solution?
(A) The solubility product of the salt is 4  10–6
(B) The concentration of X– ions is twice that of A2+ ion
(C) More solute can be dissolved in the solution by heating
(D) The pH of the solution must be seven
Space For Rough Work

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 7 Two Year CRP325 _PT2_Advanced

7. The correct statement(s) regarding B2H6 is/are

(A) it contain 3c – 2e as well as 2c – 2e covalent bonds
(B) H2 gas is produced when it reacts with water
(C) it is a Lewis acid
(D) it contains no B – B bond
(PART – B)
This section contains Two paragraphs. Each paragraph having TWO questions Numerical answer type with
answer XXXX.XX. For each question, enter the correct numerical value. If the numerical value has more than
two decimal places, truncate/round-off the value to TWO decimal places.

Paragraph for Question no. 1 to 2

The experimental data for the reaction, 2X ( g) + 3Y ( g) ⎯⎯

→ X2 Y3 ( g) is given as follows:
Expt. [X0] in M [Y0] in M Rate in M s–1
1. 0.01 0.01 4  10–10
2. 0.02 0.02 32  10–10
3. 0.02 0.04 128  10–10
Answer the following questions on the basis of above write up.

1. What is overall order of the reaction?

2. If the rate constant of the reaction is expressed as (y  10–4 mol2 L–2 s–1). What is y?

Paragraph for Question no. 3 to 4

Hydrolysis of salts in water change the pH of the resulting solution, but hydrolysis of some salts of
weak acid and weak base cannot change the pH which remains at 7. Also the salts of strong acid
and strong base does not change the pH. Consider a salt [CH3NH3]+[COOCH3]– which is obtained
from the base CH3NH2 and acid CH3COOH. Kb of CH3NH2 is 10–4 and Ka of CH3COOH is 10–5.
Answer the following questions on the basis of above write up.

3. What is the pK a of the conjugate acid CH3NH3+ ?

4. What is the pH of the aqueous solution of 10–3 M CH3NH3+ ?

(PART – B)
(Non – Negative Integer)

t 99.99%
5. What is the value of of a first order reaction?
2  t1 2
t99.99% = Time needed for 99.99% completion of the reaction
t1 2 = Half-life period of the reaction

Space For Rough Work

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6. A buffer solution contains CH3COOH and CH3COONa in the molar ratio of 10 : 1. What is
the pH of the buffer? [Ka of CH3COOH = 10–5]

7.
N (0.02 atm, 200 L)

M (0.01 atm, 400 L)

V
The irreversible work done along the path M → N on a system containing 1 mol of an ideal
gas in L atm unit in the above figure is:

8. What is the pH of 10–3 M aqueous solution of CH3COONa?

[Ka of CH3COOH = 10–5]

9. The entropy change, by increasing the volume of a certain amount of an ideal gas by 100
times in an isothermal reversible process, is 191.47142 J K–1 mol–1. How many moles of gas
is present in the system?

10. 
T 2O3 ⎯⎯ → ( X) + O2
If the oxidation number of thalium ( T ) in compound(X) is +y, the value of ‘y’ is

Space For Rough Work

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 9 Two Year CRP325 _PT2_Advanced

S
SEEC
CTTIIO
ONN –– IIIIII :: M
MAAT
THHE
EMMA
ATTIIC
CSS
(PART – A)
(Single Correct Answer Type)
This section contains 4 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out
of which ONLY ONE is correct.

1. The number of solution (s) of the equation, sin−1 x + cos−1 (1 − x ) = sin−1 ( −x ), is/are
(A) 0 (B) 1
(C) 2 (D) more than 2

2. If the roots of the equation x2 + bx + c = 0 and x2 − cx + b = 0 differ by the same quantity,

then the value of (b + c), is:
(A) 4 (B) 1
(C) 0 (D) –4

3. In an experiment with 15 observations on x, the following results were available.

 x2 = 2830,  x = 170 . One observation that was 20 found to be wrong and was replaced
by the correct value 30. Then the corrected variance is
(A) 78.00 (B) 188.66
(C) 177.33 (D) 8.33

 1 − sin x + 1 + sin x  
4. The value of cot −1   ,  x  , is
 1 − sin x − 1 + sin x  2
x  x
(A)  − (B) +
2 2 2
x x
(C) (D) 2 −
2 2

(One or More Than One Options Correct Type)

This section contains 3 multiple choice questions. Each question has 4 choices (A), (B), (C)
and (D), out of which ONE or MORE THAN ONE is correct.

5. Which of the following, when simplified, reduces to unity?

(A) log3 log27 log4 64 (B) 2log18 ( 2+ 8 )
(C) log2 10 + log2 
 2 
 5
 (D) − log 2 −1 ( 2 + 1)
Space For Rough Work

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 10 Two Year CRP325 _PT2_Advanced

6. The adjoining figure shows the graph of y = ax2 + bx + c , then

y

x
O

(A) a  0 (B) b2  4ac

(C) c  0 (D) a and b are of opposite sign

7. f ( x ) = sin x − cos2 x − 1, attains the minimum value for the set of values of ‘x’ given by:
  n  
(A) x = n + ( −1) (B) x = n + ( −1)   , n  I
n+1
 6 , n I
  6
n   n  
(C) x = n + ( −1)   , n  I (D) x = n − ( −1)   , n  I
3 6

(PART – B)
This section contains Two paragraphs. Each paragraph having TWO questions Numerical answer type with
answer XXXX.XX. For each question, enter the correct numerical value. If the numerical value has more than
two decimal places, truncate/round-off the value to TWO decimal places.

Paragraph for Question no. 1 to 2

Sum of certain consecutive odd positive integers is 572 − 132 .

1. Number of integers is:

2. The least value of an integer is:

Space For Rough Work

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Paragraph for Question no. 3 to 4

A parabola which is symmetric about x-axis and passes through (3,-6) has its vertex at the
origin and length of latus rectum as 12, is translated with its axis parallel to original axis and
vertex now at (2, 4)

3. If the equation of new axis is y =  then value of  is

4. If the equation of new directrix is x +  = 0 then value of  is

(PART – B)
(Non – Negative Integer)

5. If 9x2 + 4y2 + 2kxy + 4x − 2y + 3 = 0 represents parabola then k is __________

5
Find the sum of all the integral roots of (log5 x ) + log5x   = 1
2
6.
x

7. If x 2 + bx + c = 0 has two distinct roots and after subtracting 2 from each of the roots; the
resultant roots are reciprocal of the original roots. Find the value of b2 + c 2

8. If eleven A.M.’s are inserted between 28 and 10, then the number of integral A.M.’s is
______

9. The number of integral values of k for which the equation sin−1 x + sin−1 ( sin x ) + tan−1 x
= 2k − 1 has a real solution is

10. Total number of solutions of sin x.tan 4x = cos x belonging to ( 0, ) is:

Space For Rough Work

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12 Two Year CRP325 _PT2_Advanced

FIITJEE INTERNAL TEST

BATCHES: Two Year CRP325
PHASE TEST–2: Advanced
Code: 100608
JEE ADVANCED LEVEL
ANSWER KEY
ANSWER KEYS
Physics
PART – A
1. C 2. A 3. A 4. C
5. AB 6. BC 7. BD
PART – B
1. 10 2. 100 3. 8 4. 0.8
5. 5 6. 2 7. 4 8. 4
9. 0 10. 1

Chemistry
PART – A
1. C 2. B 3. B 4. C
5. ABD 6. ABC 7. ABCD
PART – B
1. 3 2. 4 3. 10 4. 6.5
5. 5 6. 4 7. 4 8. 8
9. 5 10. 1

Mathematics
PART – A
1. B 2. D 3. A 4. B
5. BD 6. ACD 7. AD
PART – B
1. 44 2. 27 3. 4 4. 1
5. 6 6. 6 7. 5 8. 5
9. 4 10. 5

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