Fiitjee: Internal Test
Fiitjee: Internal Test
Fiitjee: Internal Test
Instructions
Note:
1. The question paper contains 3 sections (Sec-1, Physics, Sec-II, Chemistry & Sec-III, Mathematics.)
2. Each section is divided into one part, Part-A.
3. Part – A contains 18 questions which are further divided as follows:
❖ Q. 1 – 6 are multiple choice questions. Each question has four choices (A), (B), (C) and (D), out of
which only one is correct.
❖ Q. 7 – 14 are multiple correct answer type questions. Each question has four choices (A), (B), (C) and
(D), out of which one or more answer(s) is/are correct.
❖ Q. 15 – 18) contains 2 Paragraphs. Based upon each paragraph, 2 Multiple Choice Questions have to
be answered. Each question has Only One Correct answer.
Marking Scheme
1. For each question in the group Q. 1 – 6 to Part – A you will be awarded 3 marks if you have darkened only
the bubble corresponding to the answer and zero marks if no bubble is darkened. In all other cases, minus
one (–1) mark will be awarded.
2. For each question in the group Q. 7 – 14 of Part – A contains 8 Multiple Choice Questions which have One
or More Correct answer. Each question carries +4 marks for correct answer and – 1 marks for wrong
answer.
For each question in the group Q. 7 – 14 of PART – A you will be awarded
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.
3. For each question in the group Q. 15 – 18 of Part – A you will be awarded 3 marks if you have darkened all
the bubble(s) corresponding to the correct answer and zero marks if no bubble is darkened. No negative
marks will be awarded in this section.
Enrolment Number :
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Section – I (Physics)
PART – A
(Single Correct Choice 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 be correct.
1. A light emitting diode (LED) has a voltage drop of 2V across it and passes a current of
10 mA. When it operates with a 6V battery through a limiting resistor R, the value of R is:
(A) 40 k (B) 4 k (C) 200 (D) 400
1. D
2. Two full turns of the circular scale of a screw gauge cover a distance of 1 mm on its main
scale. The total number of division on the circular scale is 50. Further, it is found that the
screw gauge has a zero error of – 0.03 mm. While measuring the diameter of a thing wire, a
student notes the main scale reading of 3 mm and the number of circular scale divisions in
line with the main scale as 35. The diameter of the wire is
(A) 3.73 mm (B) 3.67 mm (C) 3.38 mm (D) 3.32 mm
2. C
3. To radiate signals with high efficiency, the antennas should have a size ( is wavelength)
(A) (B) > (C) (D) > 4
4 4
3. C
5. The number densities of electrons and holes in a pure germanium at room temperature are
equal and its value is 3 ×1016 per m3. On doping with aluminium, the hole density increases
to 4.5 × 1022 per m3. Then the electron density in doped germanium is
(A) 2.5 × 1010 m–3 (B) 2 × 1010 m–3 (C) 4.5 × 109 m–3 (D) 3 × 109 m–3
5. B
7. In hydrogen atom, if potential energy of electron in ground state is assumed to be zero, then
(A) Total energy of first excited state = 23.8 eV
(B) Potential energy of first excited state = 20.4 eV
(C) Kinetic energy of first excited state = 6.8 eV
(D) Kinetic energy of first excited state = 3.4 eV
7. ABD
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8. Nucleus A decays to B with decay constant 1 and B decays to C with decay constant 2.
Initially at t = 0, number of nuclei of A and B are 2N0 and N0 respectively. At t = t0, number of
3N0
nuclei of B stop changing. If at this instant number of nuclei of B are .
2
1 4 1 1 4 1
(A) the value of t0 is ln (B) the value of t0 is ln
1 3 2 2 3 2
3N0 2 2N0 2
(C) the value of NA at t0 is (D) the value of NA at t0 is
2 1 3 1
8. AC
ab2
9. An experiment measures quantities a, b, c are x is calculated from x = 3 . If the
c
percentage errors in a, b, c are 1%, 3% and 2% respectively.
(A) The percentage error in x can be 13%
(B) The percentage error in x can be 7%
(C) The percentage error in x can be 20%
(D) The percentage error in x can be 26%
9. AB
11. Radiations of monochromatic waves of wavelength 400 nm are made incident on the
surface of metals Zn, Fe and Ni of work functions 3.4 eV, 4.8 eV and 5.9 eV respectively
(take hc = 12400 eV-Å) :
(A) maximum KE associated with photoelectrons from the surface of any metal is 0.3 eV.
(B) no photoelectrons are emitted from the surface of Ni.
(C) if the wavelength of source of radiation is doubled then KE of photoelectrons is also
doubled.
(D) photoelectrons will be emitted from the surface of all the three metals if the wavelength
of incident radiations is less than 200 nm.
11. BD
12. Due to annihilation of electron-positron of same kinetic energy 0.95 MeV, a photon is
produced which can also be produced by a photo-electron of energy E, the possible value of
E is (mass of electron = 9.1 10–31 kg, e = 1.6 10–19 Coulomb)
(A) 1.02 MeV (B) 2.42 MeV (C) 2.03 MeV (D) 2.93 MeV
12. CD
13. If the dimensions of length are expressed as Gx cy hz; where G, c and h are the universal
gravitational constant, speed of light and Planck’s constant respectively, then
1 1 1 1
(A) x = , y = (B) x = , z =
2 2 2 2
1 3 3 1
(C) y = , z = (D) y = − ,z =
2 2 2 2
13. BD
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14. The pitch of a screw gauge is 1 mm and there are 100 divisions on circular scale. When
there is nothing between the two ends (studs) of screw gauge 95th divisions of circular scale
is coinciding with screw gauge and in this situation zero of main scale is not visible. When a
wire is placed between the studs the linear scale reads 2 division and 20th divisions of
circular scale coincides with reference line. For this situation mark the correct statement(s).
Each division on the main scale to 1 mm.
(A) LC of the instrument is 0.01 mm.
(B) Zero correction for the instrument is +0.05 mm.
(C) Thickness of wire is 1.20 mm
(D) Thickness of the wire is 2.25 mm.
14. ABD
Comprehension Type
Paragraph for question nos. 15 – 16
In van der Waal’s equation: [P + (a/V2)](V − b) = RT. Then answer the following questions.
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Section – II (Chemistry)
PART – A
(Single Correct Choice 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 be correct.
1. Which of the following gas is not formed in the reaction between NaBr and conc. H2SO4?
(A) Br2 (B) HBr (C) SO2 (D) O2
1. D
2. CrCl3 ⎯⎯ X
→ green ppt. ⎯⎯
Y
→ Yellow solution
In the above reaction X and Y are respectively
(A) H2SO4 and Cl2 water (B) NaOH and Na2O2
(C) H2O2 and NaOH (D) NH4OH and NH4Cl
2. B
3. C
Ba( OH)
4. CO2 ⎯⎯⎯⎯
2
→ P ( White )
Ba( OH)
SO2 ⎯⎯⎯⎯ → Q ( White ) ⎯⎯⎯
( )
→ S ( White )
2 R
P and Q are soluble in dil. mineral acids S is insoluble in dil. mineral acids but partially
soluble in conc. HCl.
Which of the following is(R)?
(A) NaOH (B) Zn/HCl (C) Cl2/H2O (D) Ca(OH)2
4. C
5. B
6. A
7. Which of the following metallurgical process(es) is/are carried out in order to extract zinc
from zinc blend?
(A) Froth flotation (B) Roasting (C) Carbon reduction (D) Distillation
7. ABCD
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8. BD
9. Which of the following metallurgical process(es) is/are used to separate Cu from CuSO4 in a
single step?
(A) Electrolysis (B) Hydrometallurgy
(C) Aluminothermic reduction (D) Calcination
9. AB
10. NaNO3 solution is treated with the following reagents. In which case(s) the product(s) or the
observation(s) is/are correct?
(A) ⎯⎯⎯⎯⎯⎯⎯
Conc.H2SO4 ,FeSO4
Heat
→ Yellow solution (B) ⎯⎯⎯⎯
Zn dust
Heat
→ NH3 gas
(C) ⎯⎯⎯→
Dil.HCl
NO2 gas (D) ⎯⎯⎯⎯⎯⎯
Conc.H2SO4
Copper turnings
→ Blue solution
10. ABD
11. AB
Soluble (P )
+
⎯⎯→
H
Pb( CH COO )
12. Na2CrO4 ⎯⎯⎯⎯⎯→
3 2
Yellow ppt.
→ Soluble ( Q )
−
⎯⎯⎯
OH
The anions present in the soluble compounds of (P) and (Q) in the above reaction is/are
(A) [Pb(OH)4]2– (B) Cr2O72− (C) [PbH4]2– (D) CrO54−
12. AB
13. The absorption of atmosphere N2 gas by soil takes place through the following reactions.
N2 + O2 ⎯⎯→h
P ( gas ) ⎯⎯
O2
→ Q ( gas )
⎯
( S ) ⎯⎯⎯⎯⎯⎯Alkali
Subs tances in soil (R ) ⎯⎯⎯⎯
Rain water
13. CD
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14. AB
Comprehension Type
Paragraph for question nos. 15 – 16
The presence of Fe3+ ion in a solution is checked by adding K4[Fe(CN)6] in slightly acidic medium.
The reaction mixture turns blue and a blue ppt. is formed.
15. C
16. Which of the following compound can dissolve the blue precipitate?
(A) NaOH (B) KCl (C) H2SO4 (D) NH4Cl
16. A
In the extraction of iron from Fe2O3, CaCO3 is used as a flux and MnO2 is used to line the blast
furnace. Coke is used as the reducing agent.
17. Which reaction takes place in the slag formation zone of the blast furnace?
(A) C + O2 ⎯⎯ →CO2 (B) FeO + C ⎯⎯ → Fe + CO
(C) CaO + SiO2 ⎯⎯
→ CaSiO3 (D) FeO + CO ⎯⎯
→Fe + CO2
17. C
18. C
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1. In a group of students, mean weight of boys is 80 kg and mean weight of girls is 50 kg. If the
mean weight of all the students taken together is 60 kg, then the ratio of number of boys to
that of girls is
(A) 2 : 1 (B) 1 : 2
(C) 2 : 3 (D) none of these
1. B
1 −2 / 2
2. If be a complex cube root of unity, then 1 1 1 =
1 −1 0
(A) 0 (B) 1
(C) (D) 2
2. A
sin2 x cos2 x 1
3. cos2 x sin2 x 1 =
−10 12 2
(A) 0 (B) 12cos2 x − 10sin2 x
(C) 12sin2 x − 10cos2 x − 2 (D) 10 sin 2x
3. A
4. The coefficient of variation of a series is 50. Its S.D. is 21.2. Its arithmetic means is
(A) 42.4 (B) 22.6
(C) 26.6 (D) 36.1
4. A
5. If a variable takes values 0, 1, 2, …, n with frequencies 1, nC1, nC2, …, nCn then the A.M. is
(A) n ((B) (2n/n)
(C) n+1 (D) (n/2)
5. D
6. The mean deviation about the median of the series of batsman in ten innings 54, 38, 42, 44,
46, 48, 54, 55, 56, 76 is
(A) 8.6 (B) 7.6
(C) 8 (D) none of these
6. A
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1 2 2
7. If A = 2 1 −2 is a matrix satisfying the equation AA T = 9I, where I is 3 3 identity
a 2 b
matrix, then
(A) b – a = 1 (B) a – 2b = 1
(C) b + a + 3 = 0 (D) 2a – 3b = 2
7. AC
1 4 4
8. If the adjoint of a 3 3 matrix P is 2 1 7 , then the possible value(s) of the determinant
1 1 3
of P is (are)
(A) –2 (B) –1
(C) 1 (D) 2
8. AD
9. ABC
10. CD
0 1
, the values of , such that ( l + A ) = A 2 are
2
11. If A =
−1 0
1 1 1 1
(A) , (B) ,
2 2 2 2
i i i i
(C) , (D) ,
2 2 2 2
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11. AD
bc − a2 ca − b2 ab − c 2 2 2 2
12. If ca − b2 ab − c 2 bc − a2 = 2 2 2 , then
ab − c 2 bc − a2 ca − b2 2 2 2
(A) 2 = a2 + b2 + c 2 (B) 2 = ab + bc + ca
(C) 2 = ab + bc + ca (D) 2 = a2 + b2 + c2
12. AB
( 2 + ) ( 2 + 2 ) ( 2 + 3 )
2 2 2
= −684
( 3 + ) ( 3 + 2 ) ( 3 + 3 )
2 2 2
(A) –4 (B) 9
(C) –9 (D) 4
13. BC
1 1 0
14. For the matrix A = 1 2 1 , which of the following is correct
2 1 0
2 3 3
(A) A = 5 6 2
2
(B) A 3 − 3A 2 − I = 0
3 1 7
7 9 3
(C) A + 2A − I = 0
3 2
(D) A = 15 19 6
3
9 12 4
14. BD
Comprehension Type
Paragraph for question nos. 15 – 16
A square matrix A is said to be unitary matrix iff A.A* = I = A * A , where A* is the conjugate
1 1 + i
transpose of A. Let A= k , where k R
1 − i −1
15. C
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cos sin 20
16. If Q = ABA* where B= , then the value of X = A* Q A is
− sin cos
cos sin cos 20 sin 20
(A) (B)
− sin cos − sin 20 cos 20
cos 20 − sin 20 cos 20 − sin 20
(C) (D)
sin 20 cos 20 − sin 20 cos 20
16. B
1 0 0
Let A = 2 1 0 and U1,U2 and U3 are columns of a 3 3 matrix U. If column matrices
3 2 1
1 2 2
U1,U2,U3 satisfy AU1 = 0 , AU2 = 3 , AU3 = 3 , then answer the following questions
0 0 1
17. A
18. B
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SECTION – II (Physics)
Part – A
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