JEE Main 2023 Sample Paper

Sample Paper

Full Test

Q.No. 1 The metal used for making X-ray tube window is :

(A) Na

(B) Ca

(C) Mg

(D) Be

Q.No. 2 The logical statement is equivalent to :

(A)

(B)

(C)

(D)

Q.No. 3 A particle Of mass m charge q has an initial velocity . If an electric field and magnetic field
act on the particle, its speed will double after a time:

(A)

(B)

(C)

(D)

Q.No. 4 In the circuit shown, find C if the effective capacitance of the whole circuit is to be 0.5 uF. All

values in the circuit are in uF.

(A)

(B) 4 μF

(C)

(D)

Q.No. 5 A point P moves on the line 2x - 3y +4=0. If Q(1,4) and R(3,-2) are fixed points, then the locus of
the centroid of PQR is a line :

(A) parallel to x-axis

(B) with slope 3/2

(C) with slope 2/3

(D) parallel to y-axis

Q.No. 6 For coagulation of arsenious sulphide sol, which one of the following salt solution will be most
effective ?

(A) Nacl

(B)

(C)

(D)

Q.No. 7 For , If x > 1, then is equal to:

(A)

(B)

(C)

(D)

Q.No. 8 A series AC circuit containing an inductor (20 mH), a capacitor and a resistor ( ) is
driven by an AC source of 24 V/50 Hz. The energy dissipated in the circuit in 60 s is:

(A)

(B)

(C)

(D)

Q.No. 9 In an a.c. circuit, the instantaneous e.m.f. and current are given by e=100 sin 30 t, i=20 sin (30t
- π/4) In one cycle of a.c., the average power consumed by the circuit and the wattless current are,
respectively :

(A) 50, 10

√

(B) 1000/√2, 10

(C) 50/√2 , 0

(D) 50 , 0

Q.No. 10 The compound that does not produce nitrogen gas by the thermal decomposition is :

(A) Ba(N₃)₂

(B) (NH₄)₂Cr₂O₇

(C) NH₄NO₂

(D) (NH₄)₂SO₄

Q.No. 11 Among the following four aromatic compounds, which one will have the lowest melting point ?

(A)

(B)

(C)

(D)

Q.No. 12 An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass M.
The piston and cylinder have equal cross sectional area A. When the piston is in equilibrium, the volume of
the gas is V0 and its pressure is P0. The piston is slightly displaced from the equilibrium position and
released. Assuming that the system is completely isolated from its surrounding, the piston executes a simple
harmonic motion with frequency:

(A)

(B)

(C)

(D)

Q.No. 13 If and then the value of f(1) is:

(A) -1/4

(B) 1/2

(C) 1/4

(D) -1/2

Q.No. 14 An ideal gas occupies a volume of 2 m3 at a pressure of 3 x 10⁶ Pa. The energy of the gas is :

(A) 9 x 10⁶ J

(B) 3 x 10² J

(C) 6 x 10⁴ J

(D) 10⁸ J

Q.No. 15 A resonance tube is old and has jagged end. It is still used in the laboratory to determine velocity of
sound in air. A tuning fork of frequency 512 Hz produces first resonance when the tube is filled with water to
a mark 11 cm below a reference mark, near the open end of the tube. The experiment is repeated with
another fork of frequency 256 Hz which produces first resonance when water reaches a mark 27 cm below
the reference mark. The velocity of sound in air, obtained in the experiment, is close to :

(A) 335

(B) 322

(C) 328

(D) 341

Q.No. 16 For a diatomic ideal gas in a closed system, which of the following plots does not correctly
describe the relation between various thermodynamic quantities?

(A)

(B)

(C)

(D)

Q.No. 17 If a, b and c be three distinct real numbers in G.P.and a+b+c=xb, then x cannot be:

(A) 4

(B) -3

(C) - 2

(D) 2

Q.No. 18 The area (in sq. units) bounded by the parabola y= x² - 1, the tangent at the point (2, 3) to it and the
y-axis is :

(A) 56/3

(B) 8/3

(C) 32/3

(D) 14/3

Q.No. 19 The function ƒ : R →[-1/2 , 1/2] defined as ƒ(x) = x/1+x² , is:

(A) injective but not surjective.

(B) surjective but not injective.

(C) neither injective nor surjective.

(D) invertible.

Q.No. 20 The area (in sq. units) of the region {(x, y) ∈ R2 [4x2 ≤ y ≤ 8x+ 12} is

(A) 135/3

(B) 128/3

(C) 124/3

(D) 127/3

Q.No. 21 Consider a tank made of glass(refractive index 5) with a thick bottom. It is filled with a liquid of
refractive index u. A student finds that, irrespective of what the incident angle i (see figure) is for a beam of
light entering the liquid, the light reflected from the liquid glass interface is never completely polarized. For

this to happen, the minimum value of u is :

(A)

(B)

(C)

(D)

Q.No. 22 The pair that does NOT require calcination is :

(A)

(B)

(C)

(D)

Q.No. 23 Two particles A, B are moving on two concentric circles of radii R₁ and R₂ with equal angular
speed ω. At t = 0, their positions and direction of motion are shown in the figure :

The relative velocity is given by:

(A)

(B)

(C)

(D)

Q.No. 24 If y=y(x) is the solution of the differential equation, satisfying y(1)=1, then y (½)
is equal to :

(A) 7/64

(B) 49/16

(C) ¼

(D) 13/16

Q.No. 25 In a building there are 15 bulbs of 45 W, 15 bulbs of 100 W, 15 small fans of 10 W and 2 heaters of
1 kW. The voltage of main 220 V. The minimum fuse capacity (rated value) of the building will be :

(A) 10 A

(B) 25 A

(C) 15 A

(D) 20 A

Q.No. 26 Which of the following statements is false ?

(A) Wheatstone bridge is the most sensitive when all the four resistances are of the same order of magnitude.

(B) In a balanced wheatstone bridge if the cell and the galvanometer are exchanged, the null point is
disturbed.

(C) A rheostat can be used as a potential divider.

(D) Kirchhoff’s second law represents energy conservation.

Q.No. 27 The reaction 2X B is a zeroth order reaction. If the initial concentration of X is 0.2 M, the half-life
is 6 h. When the initial concentration of X is 0.5 M, the time required to reach its final concentration of 0.2
M will be :

(A) 9.0 h

(B) 10 h

(C) 18.0 h

(D) 7.2 h

Q.No. 28 Which of the following, upon treatment with tert-BuONa followed by addition of bromine water,
fails to decolourize the colour of bromine ?

(A)

(B)

(C)

(D)

Q.No. 29 'The value of c in the Lagrange's mean value theorem for the function f(x) = x3 + 8x + 11, when x
∈ [0, 1] is :

(A)

(B)

(C) 2/3

(D)

Q.No. 30 If x, y, z are in A.P. and tan−1x, tan−1y and tan−1z are also in A.P., then

(A) 2x = 3y = 6z

(B) 6x = 3y = 2z

(C) 6x = 4y = 3z

(D) x = y = z

Q.No. 31 A block of mass 10 kg is kept on a rough inclined plane as shown in the figure. A force of 3 N is
applied on the block. The coefficient of static friction between the plane and the block is 0.6. What should be

the minimum value of force P, such that the block does not move downward ? (take g = 10 ms⁻²)

(A) 25 N

(B) 23 N

(C) 18 N

(D) 32 N

Q.No. 32 The dipole moments of CCl4, CHCl3 and CH4 are in the order:

(A) CHCl3 < CH4 = CCl4

(B) CCl4 < CH4 < CHCl3

(C) CH4 < CCl4 < CHCl3

(D) CH4 = CCl4 < CHCl3

Q.No. 33 A particle moves from the point m, at t=0, with an initial velocity .
It is acted upon by a constant force which produces a constant acceleration . What is the
distance of the particle from the origin at time 2 s?

(A) 5 m

(B) 20 √2 m

(C) 10 √2 m

(D) 15 m

Q.No. 34 The increasing basicity order of the following compounds is :

(A) ( D) < ( C) < ( A) < ( B)

(B) ( A) < ( B) < C < ( D)

(C) ( D) < ( C) < ( B) < ( A)

(D) ( A) < ( B) < ( D) < ( C)

Q.No. 35

(A) 1/16

(B) 1/8

(C) 1/4

(D) 1/24

Q.No. 36 Let and then k is

(A) 3/2

(B) 4/3

(C) 2/3

(D) ⅓

Q.No. 37 The time period of revolution of the electron in its ground state orbit in a hydrogen atom is 1.6 x 10
-16 s. The frequency of revolution of the electron in its first excited state (in s-1) is :

(A) 1.6 x 1014

(B) 7.8 x 1014

(C) 6.2 x 10 15

(D) 5.6 x 10 12

Q.No. 38 Which of the following arrangements does not represent the correct order of the property stated
against it ?

(A) Ni2+ < Co2+ < Fe2+ < Mn2+ : ionic size

(B) Co3+ < Fe3+ < Cr3+ < Sc3+ : stability in aqueous solution

(C) Sc < Ti < Cr < Mn : number of oxidation states

(D) V2+ > Cr2+ > Mn2+ > Fe2+ : paramagnetic behaviour

Q.No. 39 Which of the following molecules is least resonance stabilized ?

(A)

(B)

(C)

(D)

Q.No. 40 Which hydrogen in compound (E) is easily replaceable during bromination reaction in presence of
light?

(A) hydrogen

(B) hydrogen

(C) hydrogen

(D) hydrogen

Q.No. 41 A bag contains 30 white balls and 10 red balls. 16 balls are drawn one by one randomly from the
bag with replacement. If X be the number of white balls drawn, then is equal to:

(A) 4

(B)

(C)

(D)

Q.No. 42 Twenty meters of wire is available for fencing off a flower-bed in the form of a circular sector.
Then the maximum area (in sq. m) of the flower-bed, is :

(A) 10

(B) 25

(C) 30

(D) 12.5

Q.No. 43 The temporary hardness of water is due to :

(A)

(B)

(C)

(D) Nacl

Q.No. 44 Which of the graphs shown below does not represent the relationship between incident light and
the electron ejected from metal surface?

(A)

(B)

(C)

(D)

Q.No. 45 The maximum area (in sq. units) of a rectangle having its base on the x-axis and its other two
vertices on the parabola, y=12-x² such that the rectangle lies inside the parabola, is:

(A) 36

(B)

(C)

(D) 32

Q.No. 46 If λ be the ratio of the roots of the quadratic equation in x, 3m²x² +m(m - 4)x+2=0, then the least
value of m for which , is:

(A)

(B)

(C)

(D)

Q.No. 47 IF (α∊R) is a purely imaginary number |z|=2, then a value of a is:

(A) 1

(B)

(C) ½

(D) 2

Q.No. 48 Which of the following statements is correct ?

(A) Gluconic acid can form cyclic (acetal/ hemiacetal) structure

(B) Gluconic acid is a dicarboxylic acid

(C) Gluconic acid is a partial oxidation product of glucose

(D) Gluconic acid is obtained by oxidation of glucose with HN03

Q.No. 49 Water samples with BOD values of 4 ppm and 18 ppm, respectively, are:

(A) Clean and Highly polluted

(B) Highly polluted and Highly polluted

(C) Highly polluted and Clean

(D) Clean and Clean

Q.No. 50 If the magnetic field of a plane electromagnetic wave is given by (The speed of light=
) then the maximum electric field associated
with it is :

(A)

(B)

(C)

(D)

Q.No. 51 The values of for the following reactions at 300 K are, respectively : (At 300 K,

(A)

(B)

(C)

(D)

Q.No. 52 Let C₁ and C₂ be the centres of the circles x²+y²-2x-2y-2=0 and x²+y²-6x-6y +14=0 respectively. If
P and Q are the points of intersection of these circles, then the area (in sq. units) of the quadrilateral PC₁QC₂,
is :

(A) 8

(B) 4

(C) 6

(D) 9

Q.No. 53 A tetrahedron has vertices P(1, 2, 1), Q(2,1,3), R(-1, 1, 2) and O(0, 0, 0). The angle between the

faces OPQ and PQR is :

(A)

(B)

(C)

(D)

Q.No. 54 If , and equals :

(A)

(B)

(C)

(D)

Q.No. 55 The total number of irrational terms in the binomial expansion of is:

(A) 55

(B) 54

(C) 48

(D) 49

Q.No. 56 Which dicarboxylic acid in presence of a dehydrating agent is least reactive to give an anhydride ?

(A)

(B)

(C)

(D)

Q.No. 57 The correct structure of product 'p' in the following reaction is :

(A)

(B)

(C)

(D)

Q.No. 58 The value of (²¹C₁ − ¹⁰C₁) + (²¹C₂ − ¹⁰C₂) + (²¹C₃ − ¹⁰C₃) + (²¹C₄ − ¹⁰C₄) + .........+(²¹C₁₀ − ¹⁰C₁₀) is :

(A) 2²¹ − 2¹⁰

(B) 2²⁰ − 2⁹

(C) 2²⁰ − 2¹⁰

(D) 2²¹ − 2¹¹

Q.No. 59 An observer is moving with half the speed of light towards a stationary microwave source emitting
waves at frequency 10 GHz. What is the frequency of the microwave measured by the observer ? (speed of
light=3×108 ms−1)

(A) 10.1 GHz

(B) 12.1 GHz

(C) 17.3 GHz

(D) 15.3 GHz

Q.No. 60 The mean and the variance of five observations are 4 and 5.20, respectively. If three of the
observations are 3, 4 and 4; then the absolute value of the difference of the other two observations, is:

(A) 3

(B) 1

(C) 7

(D) 5

Q.No. 61 The supply voltage to a room is 120 V. The resistance of the lead wires is 6 Ω. A 60 W bulb is
already switched on. What is the decrease of voltage across the bulb, when a 240 W heater is switched on in
parallel to the bulb?

(A) 2.9 Volt

(B) 13.3 Volt

(C) 10.04 Volt

(D) zero volt

Q.No. 62 It is found that if a neutron suffers an elastic collinear collision with deuterium at rest, fractional
loss of its energy is pd ; while for its similar collision with carbon nucleus at rest, fractional loss of energy is
Pc. The values of pd and pc are respectively :

(A) (.89, .28)

(B) (.28, .89)

(C) (0, 0)

(D) (0, 1)

Q.No. 63 The area (in sq. units) of the region {(x,y) : x≥0, x+y≤3, x²≤4y and y≤1 + √x} is:

(A) 3/2

(B) 7/3

(C) 5/2

(D) 59/12

Q.No. 64 Consider the following reactions
Which of the following reactions will not produce Saytzeff product ?

(A) [a], [c] and [d]

(B) [d] only

(C) [c] only

(D) [b] and [d]

Q.No. 65 Wilkinson catalyst is :

(A)

(B)

(C)

(D)

Q.No. 66 A sonometer wire of length 1.5 m is made of steel. The tension in it produces an elastic strain of 1
%. What is the fundamental frequency of steel if density and elasticity of steel are 7.7 × 103 kg/m3 and 2.2 ×
1011N/m2 respectively?

(A) 178.2 Hz

(B) 200.5 Hz

(C) 770 Hz

(D) 188.5 Hz

Q.No. 67 A parallel plate capacitor of capacitance 90 pF is connected to a battery of emf 20 V. If a dielectric
material of dielectric constant K = 5/3 is inserted between the plates, the magnitude of the induced charge
will be :

(A) 1.2 n C

(B) 0.3 n C

(C) 2.4 n C

(D) 0.9 n C

Q.No. 68 A particle is executing simple harmonic motion (SHM) of amplitude A, along the x-axis, about r=0.
When its potential Energy (PE) equals kinetic energy (KE), the position of the particle will be:

(A) A

(B) A/√2

(C) A/2√2

(D) A/2

Q.No. 69 Sodium salt of an organic acid ‘X’ produces effervescence with conc. H2SO4. ‘X’ reacts with the
acidified aqueous CaCl2 solution to give a white precipitate which decolourises acidic solution of
KMnO4.‘X’ is :

(A) CH3COONa

(B) Na2C2O4

(C) C6H5COONa

(D) HCOONa

Q.No. 70 The least count of the main scale of a screw gauge is 1 mm. The minimum number of divisions on
its circular scale required to measure 5μm diameter of a wire is :

(A) 50

(B) 100

(C) 200

(D) 500

Q.No. 71 The major product of following reaction is :

(A) RCOOH

(B) RCHO

(C) RCONH₂

(D) RCH₂NH₂

Q.No. 72 The tangent to the curve , parallel to the line 2y=4x +1, also passes through the
point :

(A)

(B)

(C)

(D)

Q.No. 73 The correct match between Item 1 and Item II is : Item I ( A) Benzaldehyde ( B) Alumina ( C)
Acetonitrile Item II (P) Mobile phase (Q) Adsorbent (R) Adsorbate Options

(A) ( A) →(Q); ( B)→(P); ( C)→ (R)

(B) ( A) →(R); ( B)→(Q): ( C)→(P)

(C) ( A) →(P); ( B)→(R); ( C)→ (Q)

(D) ( A) →(Q); ( B)→(R); ( C) →(P)

Q.No. 74 A bag contains 4 red and 6 black balls. A ball is drawn at random from the bag, its colour is
observed and this ball along with two additional balls of the same colour are returned to the bag. If now a
ball is drawn at random from the bag, then the probability that this drawn ball is red, is

(A) 3/10

(B) 2/5

(C) 1/5

(D) 3/4

Q.No. 75 The correct option with respect to the Pauling electronegativity values of the elements is :

(A) Si < Al

(B) Te > Se

(C) P > S

(D) Ga < Ge

Answer Sheet
Q.No Answer
Q.No. 1 (D)
Q.No. 2 (D)
Q.No. 3 (C)
Q.No. 4 (C)
Q.No. 5 (C)
Q.No. 6 (B)
Q.No. 7 (A)
Q.No. 8 (D)
Q.No. 9 (B)
Q.No. 10 (D)
Q.No. 11 (B)
Q.No. 12 (B)
Q.No. 13 (C)
Q.No. 14 (A)
Q.No. 15 (C)
Q.No. 16 (C)
Q.No. 17 (D)
Q.No. 18 Answer is missing
Q.No. 19 (B)
Q.No. 20 (B)
Q.No. 21 (C)
Q.No. 22 (C)
Q.No. 23 (C)
Q.No. 24 (B)
Q.No. 25 (D)

Q.No. 26 (B)
Q.No. 27 (C)
Q.No. 28 (C)

Q.No. 29 (B)
Q.No. 30 (D)
Q.No. 31 (D)
Q.No. 32 (D)
Q.No. 33 (B)
Q.No. 34 (A)
Q.No. 35 (A)
Q.No. 36 (C)
Q.No. 37 (B)
Q.No. 38 (B)
Q.No. 39 (B)
Q.No. 40 (B)
Q.No. 41 (C)
Q.No. 42 (B)
Q.No. 43 (C)
Q.No. 44 (A)
Q.No. 45 (D)
Q.No. 46 (B)
Q.No. 47 (D)
Q.No. 48 (C)
Q.No. 49 (A)
Q.No. 50 (A)
Q.No. 51 (D)
Q.No. 52 (B)
Q.No. 53 (B)
Q.No. 54 (B)
Q.No. 55 (B)
Q.No. 56 (C)
Q.No. 57 (A)
Q.No. 58 (C)
Q.No. 59 (C)
Q.No. 60 (C)
Q.No. 61 (C)
Q.No. 62 (A)
(C)

Q.No. 63
Q.No. 64 (C)
Q.No. 65 (C)
Q.No. 66 (A)

Q.No. 67 (A)
Q.No. 68 (B)
Q.No. 69 (B)
Q.No. 70 (C)
Q.No. 71 (B)
Q.No. 72 (D)
Q.No. 73 (B)
Q.No. 74 (B)
Q.No. 75 (D)