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The document outlines the instructions and structure for the JEE(Main) Enthusiast Course Part Test for the academic session 2024-2025, scheduled for January 5, 2025. It details the test format, including the number of questions, marking scheme, and rules for candidates during the examination. Additionally, it includes sections for physics questions and numerical value type questions, emphasizing the importance of following instructions and maintaining integrity during the test.
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0% found this document useful (0 votes)
367 views15 pages

Score Paper 11

The document outlines the instructions and structure for the JEE(Main) Enthusiast Course Part Test for the academic session 2024-2025, scheduled for January 5, 2025. It details the test format, including the number of questions, marking scheme, and rules for candidates during the examination. Additionally, it includes sections for physics questions and numerical value type questions, emphasizing the importance of following instructions and maintaining integrity during the test.
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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(1001CJA101021240034) )1001CJA101021240034) Test Pattern

CLASSROOM CONTACT PROGRAMME JEE(Main)


PART TEST
(Academic Session : 2024 - 2025) 05-01-2025

JEE(Main+Advanced) : ENTHUSIAST COURSE (SCORE-I)


Time : 3 Hours PAPER-1 (OPTIONAL) Maximum Marks : 300
IMPORTANT NOTE : Students having 8 digits Form No. must fill two zero before their Form No.
in OMR. For example, if your Form No. is 12345678, then you have to fill 0012345678.

READ THE INSTRUCTIONS CAREFULLY

Important Instructions :
1. Immediately fill in the form number on this page of the Test Booklet with Blue/Black Ball
Point Pen. Use of pencil is strictly prohibited.

DO NOT BREAK THE SEALS WITHOUT BEING INSTRUCTED TO DO SO BY THE INVIGILATOR


2. The candidates should not write their Form Number anywhere else (except in the specified
space) on the Test Booklet/Answer Sheet.
3. The Test Booklet consists of 75 questions.
4. There are three parts in the question paper 1,2,3 consisting of Physics, Chemistry and
Mathematics having 25 questions in each subject and each subject having Two sections.
(i) Section-I contains 20 multiple choice questions with only one correct option.
Marking scheme : +4 for correct answer, 0 if not attempted and –1 in all other cases.
(ii) Section-II contains 05 Numerical Value Type questions.
Marking scheme : +4 for correct answer, 0 if not attempted and –1 in all other cases.
5. No candidate is allowed to carry any textual material, printed or written, bits of papers,
mobile phone any electronic device etc, except the Identity Card inside the examination
hall/room.
6. Rough work is to be done on the space provided for this purpose in the Test Booklet only.
7. On completion of the test, the candidate must hand over the Answer Sheet to the invigilator
on duty in the Room/Hall. However, the candidate are allowed to take away this Test
Booklet with them.
8. Do not fold or make any stray marks on the Answer Sheet.
9. Take g = 10 m/s2 unless otherwise stated.
Name of the Candidate (in Capitals) _______________________________________________________

Form Number : in figures _______________________________________________________________

: in words ________________________________________________________________

Centre of Examination (in Capitals) : ______________________________________________________

Candidate’s Signature : ________________________ Invigilator’s Signature : ___________________

Your Target is to secure Good Rank in JEE(Main) 2025


ALLEN CAREER INSTITUTE Pvt. Ltd.
Registered & Corporate Office : ‘SANKALP’, CP-6, Indra Vihar, Kota (Rajasthan) INDIA-324005
Ph. : +91-744-3556677, +91-744-2757575|E-mail : info@allen.in|Website : www.allen.ac.in

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T

PART-1 : PHYSICS

SECTION-I : (Maximum Marks: 80) 3. During the propagation of electromagnetic waves


This section contains 20 questions. Each question has in vaccum:
4 options for correct answer. Multiple-Choice (A) Electrical field and magnetic field vibrates in
Questions (MCQs) Only one option is correct. For same direction.
each question, marks will be awarded as follows: (B) Electrical field and magnetic field vibrates in
Full Marks : +4 If correct answer is selected. same phase.
Zero Marks : 0 If none of the option is selected.
(C) Electric energy density is double of the
Negative Marks : –1 If wrong option is selected. magnetic energy density
1. A beam of natural unpolarised light falls on a system (D) Electric energy density is half of the magnetic
of 4 polaroids, which are arranged in succession such energy density.
that each polaroid is turned through 37° with respect
to the preceding one. The percentage of incident
4. A parallel-plate capacitor with plate area A and
separation between the plates d, is charged by a
intensity that passes through the system will be
constant current i. Consider a plane surface of area
(approximately):
A/4 parallel to the plates and drawn symmetrically
(A) 32% between the plates. Find the displacement current
(B) 20% through this area.
(C) 13% (A) i (B) i/2 (C) i/4 (D) zero
(D) 8% 5. For a partially polarized light, we can define the degree
2. In an experiment of Fraunhoffer diffraction at a of polarization. The degree of polarization of light is
single slit using light of wavelength λ , the first Imax − Imin
given by P= . Here Imax and Imin are
minimum is formed at an angle of 37°. Then the Imax + Imin
direction θ of the first secondary maximum is : maximum and minimum possible intensities in two
4 mutually perpendicular directions. For a given partially
(A) tan−1 ( )
3
polarized light beam, the value of P is 0.25. The
3
−1
(B) sin ( )
4 approximate ratio of maximum and minimum
9 amplitudes in two mutually perpendicular directions is:
(C) sin−1 ( )
10
3 (A) 4 (B) 1.66
(D) tan−1 ( )
4 (C) 1.3 (D) 9
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6. A string with a linear mass density of 36 × 10 – 3 kg/m 9. A sound source emits two sinusoidal sound waves,
is under tension of 360 N and is fixed at both ends. both of wavelength λ , along paths A and B as shown
in figure. The sound travelling along path B is
One of its resonance frequencies is 375 Hz. The next
reflected from four surfaces as shown and then
higher resonance frequency is 450 Hz. The mass of merges at point Q, producing minimum intensity at
the string is : that point. The minimum value of d in terms of λ is :
(A) 24 × 10 – 3 kg
(B) 36 × 10 – 3 kg
(C) 12 × 10 – 3 kg
(D) 4 × 10 – 3 kg
7. A point source of sound is kept at origin and a man
is hearing at distance 100 m from the source. (A) λ (B) λ (C) λ (D) λ
8 4 3 6
Calculate the displacement of the man towards the 10. In young's double slit experiment maximum
source so that the loudness heard by man increases intensity is I, then angular position of the point
by 20dB. [Assume that the motion of man is along where the intensity becomes I/4.
the line joining the source and the man] λ λ
(A) sin−1 ( ) (B) sin−1 ( )
3d 2d
(A) 30 m
2λ λ
(C) sin−1 ( ) (D) sin−1 ( )
(B) 90 m d 4d
(C) 20 m 11. The second overtone of an open pipe A and a
(D) 40 m closed pipe B have the same frequencies. The ratio
of fundamental frequency of A to the fundamental
8. The magnetic field in the plane electromagnetic wave frequency of B is:
is given by Bz = 2 × 10 – 7 sin(0.5 × 103x + 1.5 × 1011t)
(A) 3 : 5 (B) 5 : 3 (C) 5 : 6 (D) 6 : 5
tesla. The expression for electric field will be:
12. A ray is incident on the boundary of a medium
3 11
(A) Ez = 30√2 sin(0.5 × 10 x + 1.5 × 10 t)V /m from air at an angle of incidence of 53° such that
(B) Ez = 60 sin(0.5 × 103 x + 1.5 × 1011 t)V /m reflected ray is completely polarised, then
(C) Ey = −30√2 sin(0.5 × 1011 x + 1.5 × 103 t)V /m
refractive index of medium is:
5 5 4 25
(D) Ey = −60 sin(0.5 × 103 x + 1.5 × 1011 t)V /m (A) (B) (C) (D)
3 4 3 9
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13. A sonometer wire of length 2m is made of steel. By 16. The figure shows at time t = 0 second, a rectangular
varying the tension in the wire elastic strain is and triangular pulse on a uniform wire are
varied from 1% to 4%. What is magnitude of approaching each other. The pulse speed of both
change in fundamental frequency of wire if density pulses is 0.5 cm/s. The resultant pulse at t = 2
and young's modulus of steel are 7.7 × 103 kg m – 3 second is :
and 2.2 × 1011 Nm – 2 respectively?
(A) 265 Hz (B) 132.5 Hz
(C) 397.5 Hz (D) 198.75 Hz
14. A uniform rope of length ℓ and mass M hangs
vertically from a rigid support. A block of mass m
is attached to the free end of the rope. A transverse
pulse of wavelength λ is produced at the lower end
(A)
of the rope. The wavelength of the pulse, when it
reaches the top of the rope, is :

(B)

(A) λ √
M −m (B) λ M +m
m m

(C) λ m (D) λ √
M +m

M +m m
15. A sound source of frequency 512 Hz approaches a
(C)

stationary observer with a velocity of 36 km/hr.


The speed of sound is 330 m/s. What is the
frequency heard by the observer ?
(A) 522 Hz (B) 528 Hz (D)
(C) 524 Hz (D) 532 Hz

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17. The figure shows a string at a certain moment as a 19. Certain plane wavefronts are shown in figure. The
transverse wave passes through it. Three particles A,
refractive index of medium is
B and C of the string are also shown. Match the
physical quantities in the List-I with the description
in the List-II.

List-I List-II
Downwards, if the (A) 2
(P) Velocity of A (1) wave is travelling
(B) 4
towards right.
Downwards, if the (C) 1.5
(Q) Acceleration of A (2) wave is travelling (D) Cannot be determined
towards left.
20. In Young’s double slit experiment, two slits are
Downwards, no matter
(R) Velocity of B (3) which way the illuminated with a light of wavelength 800 nm. The
wave is travelling. line joining A1P is perpendicular to A1A2 as shown
(S) Velocity of C (4) Zero in the figure. If the first minimum is detected at P,
(A) (P) → 2; (Q) → 1,2; (R) → 1; (S) → 4 the value of slits separation a will be: The distance
(B) (P) → 1; (Q) → 1,2; (R) → 4; (S) → 2 of screen from slits is D = 5 cm
(C) (P) → 1; (Q) → 1,2,3; (R) → 2; (S) → 4
(D) (P) → 4; (Q) → 3; (R) → 2; (S) → 1
18. Assertion : In a small segment of string
carrying sinusoidal wave, total energy is conserved.
Reason : Every small part of the string carrying a
sinusoidal wave, moves in SHM.
(A) Assertion is true, Reason is true and Reason is
the correct explanation for Assertion.
(A) 0.5 mm
(B) Assertion is true, Reason is true and Reason is (B) 0.1 mm
NOT the correct explanation for Assertion. (C) 0.4 mm
(C) Assertion is true, Reason is false.
(D) 0.2 mm
(D) Assertion is false, Reason is true.
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SECTION-II : (Maximum Marks: 20) 4. Two identical piano wires have a fundamental
This section contains 05 questions. frequency of 600 vib/sec, when kept under the same
The answer to each question is a Numerical Value. tension. What percentage increase in the tension of
one wire will lead to the occurrence of six beats per
For each question, enter the correct integer value (In
second when both wires vibrate simultaneously.
case of non-integer value, the answer should be
rounded off to the nearest Integer). 5. Two forks A and B when sounded together produce
4 beats/sec. The fork A is in unison with 30 cm
Answer to each question will be evaluated according to
length of a sonometer wire and B is in unison with
the following marking scheme:
25 cm length of the same wire at the same tension
Full Marks : +4 If correct answer is entered.
in same mode. If their frequency are fA and fB and
Zero Marks : 0 If the question is unanswered.
fA + fB = 11 N, then find the value of N.
Negative Marks : –1 If wrong answer is entered.
1. Two wires of different densities but same area of
cross-section are soldered together at one end and
are stretched to a tension T. The velocity of a
transverse wave in the first wire is half of that in
the second wire. Find the ratio of the density of the
first wire to that of the second wire.
2. Three waves of equal frequency having amplitudes
4 μ m, 3 μ m and 3 μ m arrive at a given point with a
successive phase difference of 2 π /3. The amplitude
of the resulting wave in μ m is given by :

3. Two pulses traveling on the same string are described


2 −2
by y1 = 2
, y2 = 2
.
(2x − t) + 1 (2x + t − 4) + 1
The time (in sec.) when two waves cancel everywhere
is :-

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PART-2 : CHEMISTRY

SECTION-I : (Maximum Marks: 80) 4. A graph between the number of O-atoms in a


This section contains 20 questions. Each question has compound vs weight of the compound is given below.
4 options for correct answer. Multiple-Choice
Questions (MCQs) Only one option is correct. For
each question, marks will be awarded as follows:
Full Marks : +4 If correct answer is selected.
Zero Marks : 0 If none of the option is selected.
Negative Marks : –1 If wrong option is selected. Calculate number of "O" atoms per formula unit of

1. Sum of oxidation number of underlined atom of the


the compound ?
[Given : Molecular weight of substance = 60,
following species that act as only oxidising agent.
NA = 6 × 1023]

(A) 8 (A) 4 (B) 2 (C) 1 (D) 3


(B) 10 5. Average atomic mass of a mixture containing two
elements having successive atomic masses and
(C) 11 equal mole fractions is 10, then atomic mass of
(D) 14 elements respectively (in amu).
2. Which of the following is an example of (A) 8.5, 9.5 (B) 9.5, 10.5
comproportionation reaction ? (C) 9, 10 (D) 8, 9
(A) NH4NO2 → N2 + 2H2O 6. 140 gm organic compound was processed via
(B) KC ℓ O3 → KC ℓ + KC ℓ O4 Kjeldahl method and was found to produce 51 gm
NH3 gas. Then mass percent of 'N' in organic
(C) PC ℓ 5 → PC ℓ 3 + C ℓ 2
compound is :
(D) Mg + N2 → Mg3N2
(A) 3% (B) 30% (C) 15% (D) 60%
3. How many moles of Fe0.8O will completely oxidise 7. Standard reduction potential values for some metals
0.2 M, 10 L K2Cr2O7 solution in acidic medium ? are given below :
(A) 20 A = 0.45 V , B = 0.75 V
C = – 0.45 , D = 0.6 V
(B) 30 Which metal will produce hydrogen gas in an
(C) 10 acidic solution in standard conditions ?
(D) 25 (A) A (B) B (C) C (D) D
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8. Calculate cell potential of given Galvanic cell. 12. The pair of compounds whose boiling point
difference is less than 20°C are seperated by :-
Pt | H2(1 atm) | H+ (pH = 2) || H+ (pH = 3) | H2 (4 atm) | Pt
(A) Steam distillation
2.303 RT
[Given : = 0.06, log 2 = 0.30] (B) Fractional distillation
F
(A) 0.078 V (C) Distillation under reduced pressure
(B) – 0.078 V (D) Chromatography.
(C) 0.068 V 13.
(D) – 0.068 V
9. Which of the following is incorrect for electrolysis
Configuration across chiral centre is:-

of CuSO4(aq.) using platinum electrode. (A) 2R, 3R (B) 2S, 3S


(C) 2R, 3S (D) 2S, 3R
(A) O2 gas produce at anode
(B) Cu deposited at cathode
14. Which of following is correct order of acidic
strength?
(C) H2 gas produce at cathode
(D) Nature of solution becomes acidic (A) > >
10. Ratio of equivalent conductance to molar conductance
for Na2SO4 in aqueous solution is :
1
>
(A) 3 (B)
3
(C) 2 1
(D) (B) O - methoxy benzoic acid > Benzoic acid
2

11. Br2 /CCl4


Cis- But-2-ene −−−−−−→ product mixure1 (C) Propan-1-amine > Prop-1-yne
KMnO4 /OH − (D) Floroform > Chloroform
Trans But-2-ene −−−−−−−−−→ Product mixure2
Correct statement is :
273K
15. Which of following is correct order of basic strength?
(A) O - methyl Aniline > Aniline
(A) Product mixure 1 is optically active.
(B) Pyridine > Aniline
(B) Product mixure 2 is optically active.
(C) Urea > Guanidine
(C) Product mixure 1 is Erythro.
(D) Phenol > Benzyl alcohol
(D) Product mixure 2 is Threo.

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16. In which of following species hypercongugation 19. Compound (I) & (II) are related as :
take place ?
(A) CH3 – BH2 (B)

(C) (D)

Na
17. ←−−−−−− (P )
Dry ether (A) Enantiomers
Mg ND4 Cl
−−−−−−→ (Q) −−−−→ (R) (B) Diastereomers
Dry ether
(C) Homomers
R is :
(D) Structural isomers

(A) 20. In which of following there is correct order of enol


content ?
(B) CH3 – CH2 – D

(A)
(C)

(D)
(B)

18.
(C)
(A)

(B)
(D)
(C)

(D)

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SECTION-II : (Maximum Marks: 20) 4. (i)O3 /Zn
−−−−−−−−−⊕−−→ Total nunmber of
This section contains 05 questions. (ii)NH2 −OH/H

The answer to each question is a Numerical Value. localised lone pair in product ?
For each question, enter the correct integer value (In
case of non-integer value, the answer should be 5. How many of below are soluble in NaOH as well as
rounded off to the nearest Integer). release CO2(g) on reaction with sodium bicarbonate?
Answer to each question will be evaluated according to
the following marking scheme: , ,
Full Marks : +4 If correct answer is entered.
Zero Marks : 0 If the question is unanswered.
Negative Marks : –1 If wrong answer is entered. Picric acid, P-nitro phenol, Hydrochloric acid,
1. For a sparingly soluble salt K4[M(CN)6] following
data is given :
,
Solubility product of K4[M(CN)6] = 256 × 10 – 10.
Given : λ m∞ ( K + ) = 150 Ohm−1 mol−1 cm2

λ m∞ ([M(CN)6 ]

) = 400 Ohm−1 mol−1 cm2

Specific resistance of K4[M(CN)6] is [in ohm. cm]


2. A mixture containing 10 mole each of Na2CO3,
NaHCO3 and NaOH is titrated against 2M HCl
solution. Then required volume of HCl for complete
titration (in Litre) is :
3. A sample of water has hardness due to presence of
only CaCl2. 10 kg of hard water required 10.6 gm
of Na2CO3 for complete removal of hardness. What
is degree of hardness of hard water sample (in ppm
CaCO3) ?
[Atomic mass : Na = 23, Ca = 40, Cl = 35.5]

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PART-3 : MATHEMATICS

SECTION-I : (Maximum Marks: 80) 4. Consider the curve S1 : 4y = x2, S2 : y = x


and
This section contains 20 questions. Each question has
2
S3 : y2 = 4x then area bounded by the curve S1, S2, S3
4 options for correct answer. Multiple-Choice
Questions (MCQs) Only one option is correct. For is equal to : (for x ≥ 2)
each question, marks will be awarded as follows: (A) 27
Full Marks : +4 If correct answer is selected. (B) 15
Zero Marks : 0 If none of the option is selected.
(C) 22
Negative Marks : –1 If wrong option is selected.
3
π /2 49
1. The value of ∫
|tan−1 tan 2x| − |sin−1 sin 2x|
−1
dx
(D)
3
|tan−1 tan 2x| + |sin sin 2x|
is equal to :
0
5. Let region S = {(x, y) : y ≥ x2 – 1, y ≤ x + 1} then

(A) π /2 (B) π (C) 3 π /2 (D) 0 area of region S is equal to :

2. Let y(x) is the solution of the differential equation (A) 4


dy 3
(1 + x) – y – 2x(1 + x)2sinx = 0 and y(0) = 1 (B)
dx 2
then 1 – y(2 π ) is equal to : (where x > – 1) 2
1
(A) 2 π (B) 2 π (1 + 4 π ) (C) ∫ [x] dx −
2
1
(C) π 2 (D) 2 π 2
4
3
3. If ∫
3 sin x
4 + sin x ⋅ cos x
dx =
−1
2
f(x) −
3
√7
g(x) + C
(D) ∫ [x] dx −
2
1

−π
and f π
b
(
4
) = 0, g (
4
) = 0 then
6. Let I = ∫ (x3 − x2 − 2x) dx. If I is minimum then
a
5π 3π
f( ) + g( ) is equal to :
4 4 (a, b) is : (where b > a > – 1)
(A) 0 (A) ( – 1, 2)
(B) π (B) ( – 1, 0)
(C) ℓ n2 + π (C) (0, 2)
(D) ℓ n2 + 2 π (D) ( – 1, 1)
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7. The value of

∫ [|sin x − cos x|] dx is : (where [·]


10. The area bounded by f(x) = minimum { x, sin x,
1
2
},

0 x-axis and the ordinate x = – π , x = π is :


denotes greatest integer function)
(A) π 2 + 2 √3
(A) 6 π π
(B) 2+ + 2 − √3
3π 3
(B)
2 (C) π2 π
+ + 2 − √3
5π 2 3
(C) π
2 (D) + 3 − √3
3
(D) 3 π
11. The solution of differential equation
8. If f(x) = ∫ (sin(2ℓnx) + 2 cos(2ℓnx)) dx and dy
+ 2x(x + y) = x(x + y)2 − 1 and y(0) = 1 is :
dx
f(e π ) = 1 then value of f
π
e 8 ) is :
(A) y = 2 x2 − x
(

π 1+e
(A) e8 + 1
(B) x + y = 2 or x + y = 0
π
(B) √ 2e + 18 2
(C) x + y − 2 = yex
π
e8
(C) +1 (D) Both A & B are correct
√ 2
(D)
π
e8 − 1 12. If n→∞
lim
xn − x−n
xn + x−n
= f(x) (0 < x < 1) then value of
9. Let a differentiable function 1
sgn(−f(x))ℓn (x + √1 + x2 ) dx
1 ∫ is :
⎛ ⎞

f ′ (x) = x + ex ⎜∫ f(t)dt⎟ and f(0) = 2 then value √ 1 + x2


0
⎝ ⎠
0
of f(2) is : (where sgn(x) is signum function)

13 (e2 − 1) (A) ℓn2


(A) +4 2
6 (3 − e) 2
(B) ( ℓn (√2 + 1))
13
(B) +1
6 (3 − e) 2
1 (C) ℓn√2
(C) +1
2
6 (3 − e)
−11 ℓn (√2 + 1)
(D) +2 (D)
6 (3 − e) 2
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13. ∫



1 + sin x
dx is equal to :
17. An inverted conical tank of 3m radius and 9m

cos(

+ x) height is initially full of water has an outlet at
2
bottom. The outlet is opened at some instant. The
(A) 2cot – 1(cosec x) + c 1
rate of flow through the outlet at anytime t is 4h 2
(B) 2cot−1 (√cos ec x − 1) + c where h is height of water level above the outlet at
(C) tan – 1 (cosec x – 1) + c time t, then time it takes to empty the tank, is :
2π 27π
(D) −2tan−1 (√cos ec x) + c (A) unit (B) unit
7 10
14. The value of (C) π
unit (D) π
unit
1 2 3 6 7 6
lim((
n→∞ 1 + n2
) +
4+n 2
+
9+n 2
+. . . +
37n
)
18. Assertion : If f satisfies the equation
is : 8

f(x+y) = f(x) + f(y) ∀ x, y ∈ R then ∫ 2f(x) dx = 0


1 1
(A) ℓn2 (B) ℓn10 −8
2 2 a

(C) 1
ℓn37 (D) ℓ n37 Reason : If f is an odd function then ∫ f(x) dx = 0
2
15.
−a
Orthogonal trajectories of the family of curves (A) Both Assertion & Reason are true and the
xy = k + x is : reason is the correct explanation of the
(A) family of circles assertion
(B) family of straight lines (B) Both Assertion & Reason are true but the
reason is not the correct explanation of the
(C) family of parabola
assertion
(D) family of hyperbola
(C) Assertion is true statement but Reason is false
16. Statement - I : The general solution of dydx + xy = x (D) Both Assertion and Reason are false statements
−x2
is y = 1 + ce . 4απ

Statement - II : The number of arbitrary constants 19. If Iα = ∫ |sin x| [sin x]dx ∀ α ∈ N (where [·]
in the general solution of the differential equation −4απ

is equal to order of differential equation. denotes greatest integer function) then value of
(A) Statement - I is true and Statement - II is false ∑
20
Iα is :
(B) Statement - I is false and Statement - II is true α=1

(C) Statement - I and Statement - II both are true


(A) 210 (B) 1680

(D) Statement - I and Statement - II both are false


(C) 840 (D) 0
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20. 1. If f(x) is an even function such that f(12 – x) = f(x)
List-I List-II 6 12

(Differential (Solution of and ∫ f(x)dx = 9 then ∫ f(x)dx is :

Equation) differential 0 0

Equation) 2. If the solution of differential equation


yx2dy – xdx = e−y dx is Kxey = Cx3 − 2 then
2 2
(A) xdy – ydx = xdx (P) y = x ℓ nx + cx

x(xy – 1) dy 3
value of K is : (where C is integration constant)
(B) (Q) 3Ay = 2(Ax + B) 2 +C 1
+ y (xy+2) dx = 0
2y
3. The value of ∫ ((
1
1 − x5 ) 2 − (1 − x2 ) 5 ) dx is :
1

1 √

3
d y 2
2 tan−1 ( ) 0
dy d y
(C)
(
dx dx3
) + (
dx2
)

(R)
√ 2
1
x
2y 2
4. If f : R+ → R be a differentiable function satisfying
dy − ℓ n (1 + ) x
= 0( > 0) 2 x2 f(t)
dx f(x) = x ℓ nx – x – ∫ dt ∀ x ∈ R+ then value
= ℓ nx + c t ℓ nt
1

(D) (x − 2y)
dy
=x+y (S) xy = ℓ nxy – 3 ℓ nx + c of [f(e)] is :
dx (where [·] represents greatest integer function)
(A) A → P ; B → S ; C → Q ; D → R 1
ex
dx
(B) A → Q ; B → S ; C → R ; D → P
5.

1+x
0
Find the value of 1
is :
(C) A → P ; B → R ; C → S ; D → Q ∫
x3 dx
4 −1
0 ex ( 2−x4 )
(D) A → S ; B → Q ; C → P ; D → Q
SECTION-II : (Maximum Marks: 20)
This section contains 05 questions.
The answer to each question is a Numerical Value.
For each question, enter the correct integer value (In
case of non-integer value, the answer should be
rounded off to the nearest Integer).
Answer to each question will be evaluated according to
the following marking scheme:
Full Marks : +4 If correct answer is entered.
Zero Marks : 0 If the question is unanswered.
Negative Marks : –1 If wrong answer is entered.
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