FIITJEE INTERNAL TEST IIT – JEE 2023
PHASE – V
IIT-2017 (P1)
DATE: 25.07.2022
SET–A
Time: 3 hours Maximum Marks: 183
INSTRUCTIONS:
A. General
1. This booklet is your Question Paper containing 54 questions.
2. Blank papers, clipboards, log tables, slide rules, calculators, cellular phones, pagers and electronic
gadgets in any form are not allowed to be carried inside the examination hall.
3. Fill in the boxes provided for Name and Enrolment No.
4. The answer sheet, a machine-readable Objective Response (ORS), is provided separately.
5. DO NOT TAMPER WITH / MULTILATE THE ORS OR THE BOOKLET.
B. Filling in the OMR:
6. The instructions for the OMR sheet are given on the OMR itself.
C. Question paper format & Marking Scheme
7. Each part has three sections as detailed in the following table:
Section Question Number of Category wise Marks Each Question Maximum
Type Questions Full Marks Partial Marks Zero Marks Negative marks of
Marks the
section
One or +4 +1 0 –2 28
1 more 7 If only the For darkening a If none of the In all
correct bubble(s) bubble bubbles is other
option (s) corresponding corresponding darkened cases
to all the to each correct
correct option, provided
option(s) is(are) NO incorrect
darkened option is
darkened
Single +3 ––– 0 ––– 15
2 digit 5 If only the In all other
integer bubble cases
(0–9) corresponding
to the correct
answer is
darkened.
Single +3 ––– 0 –1 18
3 correct 6 If only the If none of the In all
option bubble bubbles is other
corresponding darkened cases
to the correct
option is
darkened
Don’t write / mark your answers in this question booklet.
If you mark the answers in question booklet, you will not be allowed to continue the exam.
NAME:
ENROLLMENT NO.:
FIITJEE (Hyderabad Classes) Limited., 5-9-14/B, Saifabad, (Opp. Secretariat) Hyderabad–500 063. Phone: 040-66777000-03 Fax: 040-66777004
PAPER–I
PART I: PHYSICS
SECTION 1 (Maximum Marks: 28)
This section contains SEVEN questions.
Each question has FOUR options (A), (B), (C) and (D). ONE OR MORE THAN ONE of these four options is(are)
correct.
For each question, darken the bubble(s) corresponding to all the correct option(s) in the ORS
For example, if (A), (C) and (D) are all the correct options for a question, darkening all these three will get +4
marks; darkening only (A) and (D) will get +2 marks; and darkening (A) and (B) will get –2 marks, as a wrong
option is also darkened.
1. In the circuit shown in the adjacent figure
(A) the potential at P is –7.5 V (B) the potential at Q is –1 V
(C) the potential at R is zero (D) the potential at S is zero
2. Each of the following figures shows electric field vectors at two points A and B in an electric field. In which
figure or figures can the illustrated field be created by a single point charge ?
(A) (B)
(C) (D)
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3. A particle of charge q and mass m moves rectilinearly under the action of an electric field E = - x. Here,
and are positive constants and x is the distance from the point where the particle was initially at rest.
Then:
(A) the motion of the particle is oscillatory
(B) the amplitude of the particle is
(C) the mean position of the particle is at x =
q
(D) the maximum acceleration of the particle is
m
4. A thin disk of radius R is held closing the opening of a thin hemispherical shell of the same radius. Both the
bodies are made of insulating materials and have uniform charges of surface charge density each. The
plate is released keeping the shell fixed. How much maximum kinetic energy will the plate acquire after it is
released ?
R3 2 R3 2 R3 2
(A) (B) (C) (D) Insufficient information
8 0 4 0 20
5. Two identical point charges are moving in free space, when they are 60 cm apart; their velocity vectors are
equal in modulus and make angles of 45 from the line joining them as shown in the figure. If at this
instant, their total kinetic energy is equal to their potential energy, what will be the distance of closest
approach between them ?
(A) 20 cm (B) 30 cm (C) 40 cm (D) 45 cm
6. A parallel plate air capacitor is connected to a battery. The quantities charge, voltage, electric field and
energy associated with this capacitor are given by Q0, V0, E0 and U0 respectively. A dielectric slab is now
introduced to fill the space between the plates with the battery still in connection. The corresponding
quantities now given by Q, V, E and U are related to the previous one as:
(A) Q > Q0 (B) V > V0
(C) E > E0 (D) U > U0
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7. Figure shows some of the electric field lines corresponding to an
electric field. The figure suggests that (E = electric field, V =
potential):
(A) EA > EB (B) EA < EB
(C) VA > VB (D) VA < VB
SECTION 2 (Maximum Marks: 15)
This section contains FIVE questions.
The answer to each question is a SINGLE DIGIT INTEGER ranging from 0 to 9, both inclusive.
For each question, darken the bubble corresponding to the correct integer the ORS.
8. A thin rod of mass m carrying uniform negative charge –q is placed symmetrically along the axis of a thin
ring of radius R carrying uniformly distributed charge Q. The ring is held fixed in free space and length of
the rod is 2R. If period of the small amplitude oscillations of the rod along the axis of the ring comes out to
N2 2 0 mR
be N1R then find the value of N1 N2 .
Qq
9. Two hemispherical thin shells made of insulating materials are concentrically arranged in a free space as
shown. The radii of the larger and the smaller hemispheres are R and r and they carry net positive charges
Q and q respectively. The charges are uniformly distributed over the surfaces of the shells. If the force of
Qq
electrostatic interaction between the shells is equal to , then N is ..
N 0 R2
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10. A grounded metallic ball of radius r is placed on the centre of a uniformly charged thin insulating disc of
radius R(R >> r). Total charge on the disc is Q. If force of electrostatic interaction between the ball and the
NQ2r
disc is then the value of N is ……..
2 0 R3
11. Five identical metal plates are placed at equal gap ‘d’ has a
cross section area A shown in figure. If the equivalent
n 0 A
capacitance between a and b is ; find the value of n
2d b
12. Twelve infinite long wire of uniform linear charge density () are
passing along the twelve edges of a cube of side length . If
electric flux through any face of cube is . The value of n
n 0
is
SECTION 3 (Maximum Marks: 18)
This section contains SIX questions of matching type.
This section contains TWO tables (each having 3 columns and 4 rows)
Based on the table, there are THREE questions
Each question has FOUR options (A), (B), (C) and (D). ONLY ONE of these four options is correct.
For each question, darken the bubble corresponding to the correct option in the ORS.
I
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Figure shows total charge given to a conductor
Here, Column 1 represents arrangement of conductors.
Column 2 represents charge on surface –1
Column 3 represents charge on surface –2
Column 1 Column 2 Column 3
(I) (i) +Q (P) +Q
(II) (ii) –Q (Q) –Q
(III) (iii) +Q/2 (R) +Q/2
(IV) (iv) –Q/2 (S) –Q/2
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13. For part (I) the correct combination is
(A) I, i, P (B) I, ii, P (C) I, iii, R (D) I, iii, S
14. For part (II) the correct combination is
(A) II, i, Q (B) II, iii, R (C) II, iii, S (D) II, i, R
15. For part (III) and (IV) the correct combination is
(A) IV, iv, S (B) IV, iii, S (C) III, iv, R (D) III, iv, S
Column–I shows four different resistor networks connected to a battery of emf . Each resistor shown is same
and has a resistance R. Column – II and column – III respectively list the value of equivalent resistance
(across terminals ‘a’ and ‘b;) and the value of current I (shown in figure).
Column 1 Column 2 Column 3
(I) (i) R/2 (P) Zero
(II) (ii) R/3 (Q) E/2R
(III) (iii) 2R/3 (R) 3E/R
(IV) (iv) 3R/2 (S) E/3R
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16. Pick the correct option.
(A) I, iii, P (B) II, ii, Q (C) III, iv, S (D) IV, ii, R
17. Pick correct option for maximum value of equivalent resistance.
(A) IV, ii, R (B) III, iv, S (C) II, ii, Q (D) I, iv, S
18. Pick correct option for minimum value of current I .
(A) I, iii, P (B) II, i, P (C) III, iv, S (D) IV, iii, R
PART II: CHEMISTRY
SECTION 1 (Maximum Marks: 28)
This section contains SEVEN questions.
Each question has FOUR options (A), (B), (C) and (D). ONE OR MORE THAN ONE of these four options is(are)
correct.
For each question, darken the bubble(s) corresponding to all the correct option(s) in the ORS
For example, if (A), (C) and (D) are all the correct options for a question, darkening all these three will get +4
marks; darkening only (A) and (D) will get +2 marks; and darkening (A) and (B) will get –2 marks, as a wrong
option is also darkened.
19. Which of the following salts produces N2 on heating
(A) (NH4)Cr2O7 (B) NH4NO3 (C) NH4NO2 (D) NH4Cl
20. Which of the following compounds will give acid base reaction with RMg X?
O
(A) HCOOH (B) (C) CH3–COCH3 (D) H2O
21. Which of the following statement is correct?
(A) XeF4 and SbF5 combine to form salt
(B) He and Ne do not form clathrates
(C) He cannot be adsorbed by coconut charcoal
(D) In XeO 64 , Xe undergoes sp3d2 hybridisation
22. Which of the following occurs during the formation of CHCl3 from C 2 H 5OH and bleaching powder?
(A) Oxidation (B) Reduction (C) Hydrolysis (D) Chlorination
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23. Which reacts with AgNO3 aqueous solution to give precipitate?
Ph - Br Ph - CH = CH - CH 2 - Br Br Br
(A) (B) (C) (D)
24. Consider the following statements and pick up the correct statements:
(A) p-methoxy benzyl bromide will react more readily than p-nitro benzyl bromide for SN1 reaction
Br Br
(B) will react more readily than for SN1 reaction
Cl
Cl
(C) will react more readily than for SN1 reaction
N
H N
(D) SN1 reaction takes place in polar protic solvent
25. Which of the following combination of reagents can give 3-methyl-3-hexanol?
(A) CH 3 MgBr + 3-hexanone followed by hydrolysis
(B) C 2 H 5 MgBr + 2-pentanone followed by hydrolysis
(C) C 3 H7 MgBr + butanone followed by hydrolysis
(D) C 4 H 9 MgBr + propanone followed by hydrolysis
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SECTION 2 (Maximum Marks: 15)
This section contains FIVE questions.
The answer to each question is a SINGLE DIGIT INTEGER ranging from 0 to 9, both inclusive.
For each question, darken the bubble corresponding to the correct integer the ORS.
26. Find the number of CORRECT statements about NH3
(i) basic nature gas
(ii) turns red litmus to blue litmus
(iii) gives white dense fumes with HCl
(iv) gives brown ppt. with nessler’s reagent
(v) gives deep blue colour with CuSO4 solution when passed in excess
27. How many of the following statements are correct about SN 2 mechanism.
a) Tertiary alkyl halides reacts faster than primary alkyl halides.
b) The reaction shows first order kinetics.
c) The rate of reaction depends on the nucleophilicity of the attacking reagent.
d) It has a mechanism with two steps.
e) Carbocation is the intermediate.
f) Rate= K [ alkyl halide] [Nucleophile]
g) The rate of reaction depends on the nature of the leaving group.
h) Slowest step of this mechanism is formation of carbocation.
i) It is a stereo specific reaction
28. Alcoholic group of which position reacts fastest with Lucas reagent.(mention the nuber)
CH3 OH
CH3
HO OH
3
1 2 4
OH
29. ‘X’ is a smallest optically active alkanol. On dehydration it can form Y number of alkenes (including
stereoisomers). On reaction with Lucas reagent it forms Z number of alkyl halides (including
stereoisomers). Then Y + Z is?
CH MgBr
30. Ethyl propanoate ester
3
P. The final organic product P, will have “x” methyl substituent(s) and a
excess
total of “y” carbons. Value of “x+y” will be ?
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SECTION 3 (Maximum Marks: 18)
This section contains SIX questions of matching type.
This section contains TWO tables (each having 3 columns and 4 rows)
Based on the table, there are THREE questions
Each question has FOUR options (A), (B), (C) and (D). ONLY ONE of these four options is correct.
For each question, darken the bubble corresponding to the correct option in the ORS.
I.
Column 1 Column 2 Column 3
Name of oxyacid Formula Basicity
(I) Metaphosphoric acid (i) H3PO3 (P) 1
(II) Phosphorus acid (ii) H4P2 O7 (Q) 2
(III) Hypophosphoric acid (iii) H4P2 O6 (R) 4
(IV) Pyrophosphoric acid (iv) HPO3 (S) 4
31. Which of the following combination is correct ?
(A) I, iv, P (B) II, ii, R (C) III, ii, Q (D) IV, i, S
32. Which of the following combination is incorrect ?
(A) IV, ii, R (B) III, iii, S (C) II, i, Q (D) II, iii, P
33. Which of the following combination is correct ?
(A) IV, i, R (B) III, ii, Q (C) III, iii, S (D) IV, iv, P
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Column–1 Column–2 Column–3
Tri angular planar gas at room
(I) O3 (i) (P) Used in ostwald process
temperature with 2p–d bonds
Acts as oxidizing agent &
(II) SO3 (ii) Diamagnetic (Q)
reducing agent
(III) O2 (iii) Para magnetic (R) Cyclic trimer in solid state
34. Identify the correct pair
(A) I, i, Q (B) I, ii, Q (C) II, i, Q (D) II, ii, Q
35. Identify the correct pair
(A) III, i, P (B) III, iii, P (C) II, iii, R (D) I, i, R
36. Identify the correct pair
(A) II, i, Q (B) II, i, R (C) I, iii, Q (D) iii, ii, P
PART III: MATHEMATICS
SECTION 1 (Maximum Marks: 28)
This section contains SEVEN questions.
Each question has FOUR options (A), (B), (C) and (D). ONE OR MORE THAN ONE of these four options is(are)
correct.
For each question, darken the bubble(s) corresponding to all the correct option(s) in the ORS
For example, if (A), (C) and (D) are all the correct options for a question, darkening all these three will get +4
marks; darkening only (A) and (D) will get +2 marks; and darkening (A) and (B) will get –2 marks, as a wrong
option is also darkened.
37. The equation a8 x 8 a7 x 7 a6 x 6 ..... a0 0 has all its root positive and real (where
a8 1,a7 4,a0 1/ 2 , then 8
1 1 7 1
(A) a1 (B) a1 (C) a2 (D) a3
28 24 24 22
If ac > b2 then the sum of the coefficients in the expansion of a 2 x 2 2bx c ; a,b,c, R, n N is
n
38.
(A) positive if a > 0 (B) positive if c > 0
(C) negative if a < 0, n is odd (D) positive if c < 0, n is even.
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39. The exhaustive range of values of ‘a’ such that the angle between the pair of tangents drawn from (a, a) to
the circle x 2 y 2 2x 2y 6 0 lies in the range , , is
3
(A) 1, (B) 5, 3 3,5
(C) , 2 2 2 2, (D) 3, 1 3,5
40. ABCD is a square side 1, P and Q lie on the side AB and R lies on the side CD. The possible values for the
circumradius of triangle PQR is ?
(A) 0.5 (B) 0.6 (C) 0.7 (D) 0.8
41. If ax 2 bx c 0 and cx 2 bx a 0 a,b,c R have a common non–real root, then
(A) 2 a b 2 a (B) 2 c b 2 c
(C) a c (D) a = c
If 1 x
2n
42. a0 a1x a2 x 2 .... a2n x 2n , then
1
(A) a0 a2 a 4 .... a0 a1 a2 a3 .... (B) an 1 an
2
(C) an 3 an 3 (D) an 3 an 3
The interval in which x must lie so that the numerically greatest term in the expansion of 1 x
21
43. has the
greatest coefficient is, x 0
5 6 5 6 6 7 6 7
(A) , (B) , (C) , (D) ,
6 5 6 5 7 6 7 6
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SECTION 2 (Maximum Marks: 15)
This section contains FIVE questions.
The answer to each question is a SINGLE DIGIT INTEGER ranging from 0 to 9, both inclusive.
For each question, darken the bubble corresponding to the correct integer the ORS.
44. Two circles whose equations are x 2 y 2 9 and x 2 y 2 8x 6y m2 0 , m I having exactly two
common tangents. Find the number of values of n.
45. Consider the circles with radii 4 5 and which are tangent to the line x 2y 20 at the point 6, 7 the
difference of the x–coordinates of the centers of the circle is __
46. Consider a circles S with centre at the origin and radius 4. Four circles A, B, C and D each with radius unity
and centres (–3, 0), (–1, 0), (1, 0) and (3, 0) respectively are drawn. A chord PQ of the circle S touches the
circle B and passes through the centre of the circle C. If the length of this chord can be expressed as ,
then the value of is
9
47. A circle x 2 y 2 4x 2 2y c 0 is the director circle of the circle C1 and C1 is the director circle of circle
C2 and so on. If the sum of radii of all these circles is 2 and if c 2 , then the value of is
48. If the area bounded by the circles x 2 y 2 r 2 , r 1,2 and the rays given by 2x 2 3xy 2y 2 0, y 0 is
sq units, then the value of is
4
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SECTION 3 (Maximum Marks: 18)
This section contains SIX questions of matching type.
This section contains TWO tables (each having 3 columns and 4 rows)
Based on the table, there are THREE questions
Each question has FOUR options (A), (B), (C) and (D). ONLY ONE of these four options is correct.
For each question, darken the bubble corresponding to the correct option in the ORS.
I.
Column – I : contains some quadratic equation with variable ‘k’, Column – II : contains value of ‘k’ for which
‘I’ lies between roots of p(x) = 0 and Column – III: contains value of ‘k’ for which exactly one root of p(x) = 0
lies on (0, 1).
Column 1 Column 2 Column 3
(I) p x x 2 2kx 1 (i) k 1 (P) 1
k
2
(II) p x x 2 k 1 x 2 (ii) k>0 (Q) k 1
(III) p x x 2k 1 x 1
2
(iii) k<2 (R) k0
(IV) p x x kx 2
2
(iv) 1 (S) k>2
k
2
49. Which of the following combination is CORRECT ?
(A) I, ii, Q (B) II, i, S (C) III, ii, R (D) I, ii, R
50. Which of the following combination is CORRECT ?
(A) III, ii, Q (B) II, iii, S (C) II, iii, R (D) I, ii, Q
51. Which of the following combination is INCORRECT ?
(A) III, iv, P (B) IV, i, P (C) IV, i, R (D) III, iv, Q
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Two fixed point A and B are 4 units apart and are on the same side of a moving line L. If perpendicular distances of
A and B say P1 and P2 from the line L are such that P1 + 3P2 = K, K being a constant, then line L always touches a
fixed circle C.
Column 1 Column 2 Column 3
(I) The centre of the (i) If K = 4 radius of circle (P) If A(0, 0) and B(4, 0) then the centre
circle C lies on the is r = 2 of circle is (3, 0)
line segment
joining AB
(II) The centre of (ii) If K = 4 radius of circle (Q) If A(0, 0) and B(4, 0) and K =4 is of
circle C lies on is r = 1 circle is x 2 y 2 6x 9 0
one of A or B
(III) If A and B are (–2, (iii) If K = 8 radius of circle (R) If A 2,0 and B 2,0 and K = 8,
0) and (2, 0) is r = 4 then origin lies inside the circle
respectively, then
the centre of the
circle C is (1, 0)
(IV) If A and B are (–2, (iv) If K = 8 radius of circle (S) If A 2,0 and B(2,0) and K = 4,
0) and (2, 0) is r = 1 then origin lies inside the circle
respectively, K = 4
equation circle is
x 2 y 2 2x 1 0
52. Which of the following combination is CORRECT ?
(A) I, ii, R (B) III, ii, R (C) I, ii, P (D) I, i, Q
53. Which of the following combination is CORRECT ?
(A) II, iii, S (B) III, i, P (C) II, iii, R (D) III, iii, Q
54. Which of the following combination is INCORRECT ?
(A) I, i, S (B) IV, i, S (C) II, ii, S (D) II, ii, P
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