2024-Mock JEE Main-10 - Paper
2024-Mock JEE Main-10 - Paper
2024-Mock JEE Main-10 - Paper
General Instructions
1. The test is of 3 hours duration and the maximum marks is 300.
2. The question paper consists of 3 Parts (Part I: Physics, Part II: Chemistry, Part III: Mathematics). Each Part
has two sections (Section 1 & Section 2).
3. Section 1 contains 20 Multiple Choice Questions. Each question has 4 choices (A), (B), (C) and (D), out of
which ONLY ONE CHOICE is correct.
4. Section 2 contains 10 Numerical Value Type Questions Out of which ONLY 5 (any) questions have to be
attempted. You will NOT be allowed to attempt the sixth question. If you wish to attempt any other
question apart from the five already attempted, then you will have to delete any one response from the
five previously answered and then proceed to answer the new one.
The answer to each question should be rounded off to the nearest integer.
5. No candidate is allowed to carry any textual material, printed or written, bits of papers, pager, mobile
phone, any electronic device, etc. inside the examination room/hall.
6. On completion of the test, the candidate must hand over the Answer Sheet to the Invigilator on duty in the
Room/Hall. However, the candidates are allowed to take away this Test Booklet with them.
Marking Scheme
1. Section – 1: +4 for correct answer, –1 (negative marking) for incorrect answer, 0 for all other cases.
2. Section – 2: +4 for correct answer, –1 (negative marking) for incorrect answer, 0 for all other cases.
Roll Number :
(A) 100 103 W (B) 50 103 W (C) 500 103 W (D) 33.3 103 W
3. What is the value of inductance ‘L’ for which the current is maximum in a series LCR circuit with
C 10 F and 1000 s 1 ?
(A) 1mH (B) 10 mH (C) 100mH (D) 1000 mH
3
5. If a man at the equator would weight th of his weight, the angular speed of the earth is:
5
2g g R 2R
(A) (B) (C) (D)
5R R g 5g
6. The ratio for the speed of the electron in the 3rd orbit of He to the speed of the electron in the 3rd orbit
of hydrogen atom will be:
(A) 1:1 (B) 1:2 (C) 4:1 (D) 2:1
7. A block of mass 1 kg is placed on a rough horizontal surface connected by a light string passing over
two smooth pulleys as shown. Another block of 1Kg is connected to the other end of the string. The
acceleration of the system is: [Coefficient of friction 0.2]
8. A stone of mass 1.5Kg is tied at the end of 0.5m long string and whirled in a vertical circular path at
constant speed of 2 ms 1. The maximum tension in the string is: [ g 10 ms 2 ]
(A) 27 N (B) 3N (C) 90 N (D) 15 N
CP
9. Two moles of a monoatomic gas is mixed with 3 moles of a diatomic gas. Find of mixture of gases.
CV
11 21 21 31
(A) (B) (C) (D)
21 11 31 21
10. A series combination of R, L and C is connected to an A.C. source. If the resistance is 3 and reactance
is 4 . The power factor of the circuit is:
(A) 0.4 (B) 0.6 (C) 0.8 (D) 1.0
++
11. The energy provided to an Li atom in ground state so that it can emit only three different photons will
be:
(A) 13.6 eV (B) 91.8 eV (C) 108.8 eV (D) 12.1 eV
12. The pressure and volume of 1 mole ideal gas are related as PV 3/4 constant. The work done by gas
when its temperature is increased from T0 to 3T0 is:
(A) 4RT0 (B) 8RT0 (C) 16RT0 (D) 32RT0
13. The length (l) and acceleration due to gravity (g) was measured in the laboratory as l = (5 ± 0.05) m,
g (10 0.20) m / s 2 . The percentage error in time period of simple pendulum is:
(A) 0.5% (B) 1% (C) 1.5% (D) 2%
14. A particle is projected with a velocity v such that its range on the horizontal plane is twice the greatest
height attained by it. The range of the projectile is (where g is acceleration due to gravity)
4v 2 4g v2 4v 2
(A) (B) (C) (D)
5g 5v 2 g 5g
15. A thin sheet of glass ( 1.5) of thickness 6 microns introduced in the path of one of interfering beams
of a double slit experiment shifts the central fringe to a position previously occupied by fifth bright
fringe. Then the wavelength of the light used is:
(A) 6000 Å (B) 3000 Å (C) 4500 Å (D) 7500 Å
16. The pitch of a screw gauge is 1 mm and there are 200 divisions on the circular scale. The least count of
the screw will be:
(A) 0.5m (B) 1m (C) 5m (D) 10m
17. Given below are two statements: One is labelled as Assertion (A) and the other is labelled as Reason
(R).
Assertion (A) : Clothes containing oil or grease stains cannot be cleaned by water wash.
Reason (R) : Because the angle of contact between the oil/grease and water is obtuse.
In the light of the above statements, choose the correct answer from the option given below:
(A) Both (A) and (R) are true and (R) is the correct explanation of (A)
(B) Both (A) and (R) are true but (R) is not the correct explanation of (A)
(C) (A) is true but (R) is false
(D) (A) is false but (R) is true
18. A ball is projected with horizontal velocity 0 9 gR at the bottom most point attached with
inextensible string of length R and fixed at O as shown. Tension in the string in horizontal position:
(A) 2 volt (B) 0.80 volt (C) 1.33 volt (D) 1.60 volt
20. Two capacitor of equal capacitance are connected according to figure shown below. Now switch is
closed. The decrease in energy of the combined system is:
3 1 9
(A) CV 2 (B) CV 2 (C) 2CV 2 (D) CV 2
4 4 4
SPACE FOR ROUGH WORK
SECTION-2
Section 2 contains 10 Numerical Value Type Questions Out of which ONLY 5 (any) questions have to be attempted.
The answer to each question should be rounded off to the nearest integer.
1. A particle is moving in one dimension (along x-axis) under the action of variable force. The variation of
t3
its position (x) with time (t) is given as x 2t 2 4t 3, where x is in m and t is in sec. The
3
acceleration of the particle when its velocity becomes zero is _______ m / s 2 .
2. A source of frequency 10 kHz when vibrated over the mouth of a closed organ pipe is in unison at 250K
temperature. The beats produced when temperatures rises by 1 K is _______ Hz.
3. An ideal fluid of density 800 kg m3 , flows smoothly through a bent pipe (as shown in the figure) that
a
tapers in cross-sectional area from a to . The pressure difference between the wide and narrow sections
2
x 1
of pipe is 4100 Pa. At wider section, the velocity of fluid is ms for x = _______.
6
[Given : g 10 m / s 2 ]
5. In an electrical circuit, a battery is connected to pass 20C of charge through it in a certain given time. The
potential difference between two plates of the battery is maintained at 15V. The work done by the battery
is _______ J.
6. Focal length of a convex lens of refractive index 1.5 is 2 cm. Focal length of lens when immersed in a
liquid of refractive index of 1.25 will be _______ cm.
7. The position of the centre of mass of a uniform semi-circular wire of radius ‘R’ placed in x-y plane with
xR
its centre at the origin and the line joining its ends as x-axis is given by 0, . Then, the value of | x |
is _______.
8. Flux (in weber) in a closed circuit of resistance 10 varies with time ‘t’ (in seconds) according to the
equation 6t 2 4t 1. The magnitude of the induced current in the circuit at t = 2 is _____ Ampere.
9. When light of frequency twice the threshold frequency is incident on the metal plate, the maximum
velocity of emitted electron is v1. When the frequency of incident radiation is increased to five times the
threshold value, the maximum velocity of emitted electron becomes v2 . If v2 xv1, the value of x will
be _______.
10. Two identical conducting spheres with negligible volume have 2.1 nC and –0.1 nC charges, respectively.
They are brought into contact and then separated by a distance of 0.5 m. The electrostatic force acting
between the spheres is _______ 109 N .
SECTION-1
This section contains 20 Multiple Choice Questions. Each question has 4 choices (A), (B), (C) and (D), out of which
ONLY ONE CHOICE is correct.
1. Correct order of reactivity in electrophilic substitution reaction of the following compounds?
i ii iii iv v
(A) i > ii > iii > iv > v (B) v > iii > ii > iv > i
(C) v > iii > i > ii > iv (D) iii > i > v > ii > iv
2. For atoms/ions of Isoelectronic series, which of the following is same for all atoms/Ions:
(A) Size (B) Number of protons and electrons
(C) Nuclear charge (D) Principal quantum number
4. We have three aqueous solutions of 0.2 M Urea (A), 0.1 M NaCl (B), 0.01 M MgCl2 (C) respectively.
The value of van’t Hoff factor (i) for these solutions will be in the order:
[Consider NaCl, MgCl2 are strong electrolyte]
(A) i A iC i B (B) iA iB iC (C) i A i B iC (D) i A i B iC
7. In acidic medium, KMnO 4 shows oxidising action as represented in the half reaction:
MnO 4 XH Ye A ZH 2O
X, Y, Z and A respectively are:
(A) 8, 4, 5 and MnO 2 (B) 4, 3, 2 and MnO 2
15. Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason
(R).
Assertion (A) : H 2S has lower boiling point than H 2O.
Reason (R) : Substances with hydrogen bonding tend to have unusually low boiling points.
In the light of the above statements, choose the most appropriate answer from the options given below:
(A) Both (A) and (R) are correct but (R) is not the correct explanation of (A)
(B) Both (A) and (R) are correct and (R) is the correct explanation of (A)
(C) (A) is correct but (R) is not correct.
(D) (A) is not correct but (R) is correct.
(A) A= B=
(B) A= B=
(C) A= B=
(D) A= B=
19. Arrange the bonds in order of increasing ionic character in the molecules.
LiF, KF, O 2 , CO 2 and Na 2O
(A) O 2 CO2 Na 2O KF LiF (B) LiF KF Na 2O CO 2 O 2
(C) O 2 CO2 Na 2O LiF KF (D) Na 2O O 2 CO 2 LiF KF
20. In H-atom, if ‘x’ is the radius of first Bohr orbit, de Broglie wavelength of an electron in 5th orbit is:
(A) 6x (B) 10x (C) 10x (D) 5x
SPACE FOR ROUGH WORK
SECTION-2
Section 2 contains 10 Numerical Value Type Questions Out of which ONLY 5 (any) questions have to be attempted.
The answer to each question should be rounded off to the nearest integer.
If 60 mmol of FeCl3 is mixed with 48 mmol of K 4 [Fe(CN)6 ]3 , then the amount of Fe 4 [Fe(CN)6 ]3
formed is _______ mmol (Nearest integer).
4. Among the following oxides, number of oxides having only acidic nature is _______.
Cl 2O7 , CO, PbO2 , N 2O, NO, Al2 O3 , SiO 2 , N 2 O5 , Na 2 O, Mn 2 O7 , CrO3 , SO 2
5. The cell Pt, H 2 (1atm) | H (pH ?) || I (2M) | AgI (s) , Ag (s) | Pt has emf E 298K 0. The standard
electrode potentials for the reaction AgI e Ag I is –0.162 volt. pH of the solution is _______.
[Given : 2.303 RT/F = 0.06 V, log (2) = 0.3]
6. The lowest oxidation state of an atom in a compound A3B is –3. The group number of that element
is_______.
7. A sample of U 238 (Half-life 4.5 109 years) ore is found to contain 11.9 g U 238 and 30.9 g of
Pb 206 . If the age of the ore is x 109 years, then value of x is _______.
8. Total number of activating groups in aromatic electrophilic substitution reaction among the following
is_______.
10. K a for CH 3COOH is 1.6 105 and K b for NH 4 OH is 1.6 105. The degree of hydrolysis of
0.05 M CH3COONH 4 is x 101 . Value of x is _______. (Nearest integer)
SECTION-1
This section contains 20 Multiple Choice Questions. Each question has 4 choices (A), (B), (C) and (D), out of which
ONLY ONE CHOICE is correct.
1 1
2. If 3 f ( x) 2 f 2
1 x 0 and y 5 x 2 f ( x) then y is strictly decreasing in:
x x
1 1 1 1
(A) , 0 , (B) , 0,
2 2 2 2
1 1 1 1
(C) , , (D) ,
2 2 2 2
3. Let 5, a, b, c be in AP and 1, a – 6, b – 4, c + 10 be in G.P., then sum of first 5 terms of the GP is:
(A) 242 (B) 121 (C) 363 (D) 726
4. If the area enclosed by the curves xy + 4y = 16 and x + y = 6 is (a – bln2) square units, then value of
a + b is:
(A) 2 (B) 60 (C) 62 (D) 32
5. There are two urns U1 and U 2 . U1 contains n white and 3 black balls whereas U 2 contains 5 white and
4 black balls. One of the urns is selected at random and a ball is drawn from it. If the drawn ball is white
9
then probability that it is drawn from urn U1 is , then n =
17
(A) 4 (B) 5 (C) 6 (D) 9
ln x, x 0 x, x 0
6. Let f : R R and g : R R be such that f ( x ) x and g ( x ) x , then
e , x 0 e , x 0
fog : R R is:
(A) Neither one-one nor onto (B) Both one-one and onto
(C) Onto but not one-one (D) One-one but not onto
7. If n is the number of ways in which 7 people can stay in 5 indistinguishable rooms of a hotel, when no
room remains empty, then n is equal to:
(A) 135 (B) 240 (C) 140 (D) 90
ax sin x (b 1)esin x
, x0
x2
8. Let f : R R be defined as f ( x ) 2 x 2 cx 1, 0 x 1.
x 2, x 1
If f is continuous x R and m is the number of points where f ( x ) is NOT differentiable then
mabc
(A) 2 (B) 4 (C) 1 (D) 3
/6
x dx
9. The value of integral sin (3 x) cos 4 (3 x)
4
equals to:
0
2
2 2 2 2 2 2 2
(A) (B) (C) (D)
36 72 64 18
10. If M is a 3 × 3 matrix such that M 2 O, then det (( I M ) 50 50 M )
(Where I is an identity matrix of order 3 3 and O is null matrix)
(A) 3 (B) 50 (C) 0 (D) 1
x 2y z 4
11. If the system of equations x y 3 z 2 has infinitely many solutions, then 48 is equal to:
2 x y z 1
(A) 289 (B) 179 (C) 279 (D) 286
dy
12. Let y y ( x) be the solution of the differential equation y (ln x ) (1 (ln x))e x , y (1) e then
dx
2
1
y 2
1 2
(A) (B) e (C) (D) 2e
e e
13. Let a 2iˆ ˆj kˆ, b iˆ 2 ˆj 3kˆ and c ((( a b ) iˆ) ˆj ) kˆ then c (2iˆ ˆj kˆ)
(A) –7 (B) –12 (C) –10 (D) –14
14. Let C : x 2 y 2 4 and C : x 2 y 2 8x 9 0 be two circles. If the set of all values of , so that
the circles C and C intersect at two distinct points, is R – [a, b], then the point (48a + 40, 80b – 60) lies
on the curve
(A) y 2 24 x (B) 7 x 2 y 2 10
(C) (5 x)2 y 2 50 (D) 5 x 2 y 2 50
x2 y2 3
15. Let 2
2
1, a > b be an ellipse, whose eccentricity isand length of latus rectum is 5, then
a b 2
x2 y2
square of eccentricity of conjugate hyperbola of the hyperbola 2 2 1 is:
a b
5
(A) 3 (B) 7 (C) 5 (D)
2
16.
Let S z C : | z 3 | 1 and (1+ 5 3i) z (1 5 3i ) z 0 .
Let z1, z2 S be such that | z1 | max | z | and | z 2 | min | z | then | z1 z2 |
z S zS
(A) 8 (B) 6 (C) 7 (D) 5
1 x
17. If tan A ( x 3 x 2 x 1 )1/2 , tan B and tan C . where,
2 2
x x x 1 x x 1
0 A, B, C then, (A – B) is equal to:
2
(A) C (B) C (C) C (D) C
2 2
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18. Let the median and mean deviation about the median of 7 observations. 170, 125, 230, 190, 210, a, b be
241
210 and respectively, then mean of all seven data is:
7
(A) 202 (B) 203 (C) 204 (D) 201
x y 2 z 1 x 3 y 1 z 2
19. If the shortest distance between the lines and is 2, then
2 1 1 1 2 1
sum of squares of all possible values of is:
(A) 27 (B) 24 (C) 36 (D) 30
20. For 0 , if the eccentricity of the hyperbola x 2 y 2 sec 2 5 is 7 times of the eccentricity
2
of the ellipse x 2 sec 2 y 2 5, then the value of is:
5
(A) (B) (C) (D)
4 12 6 3
SPACE FOR ROUGH WORK
SECTION-2
Section 2 contains 10 Numerical Value Type Questions Out of which ONLY 5 (any) questions have to be attempted.
The answer to each question should be rounded off to the nearest integer.
1. Let 2, 7, 12, 17, ….., 404 terms and 3, 5, 7, 9….up to 200 terms be two arithmetic progressions, then the
sum of the common terms in them, is equal to _______.
2. Let the line L : x 3 y passes through the point of the intersection P (in the first quadrant) of the
circle x 2 y 2 4 and the parabola y 2 3x. Let the line L touch two circles C1 and C2 of equal
radius 2. If the centres Q1 and Q2 of the circles C1 and C2 lie on the x-axis, then the square of the
area of the triangle PQ1Q2 is equal to _______.
/4
4 2 cos 2 x
3. If x 4 4
dx log e ( 2 1) where , are integers, then
/4 (1 (2024) ) (sin x cos x)
2 2 equals _______.