**JEE Main Session 1 25 ^{th} July 2022 Shift 1**

**PHYSICS**

**Section-A**

**IMPORTANT INSTRUCTIONS:**

(1) The test is of **3 hours** duration:

(2) The Test Booklet consists of 90 questions. The maximum marks are 300.

(3) There are three parts in the question paper consisting of **Physics**, **Chemistry** and **Mathematics** having 30 questions in each part of equal weightage. Each part (subject) has two sections.

(i) **Section-A:** This section contains 20 multiple choice questions which have only one correct answer. each question carries **4 marks** for correct answer and **−1** mark for wrong answer.

(ii) **Section-B:** This section contains 10 questions. In Section-B, attempt any **five questions out of 10.** The answer to each of the questions is a numerical value. Each question carries 4 marks for correct answer and **−1 mark** for wrong answer. For Section-B, the answer should be rounded off to the nearest integer.

1. If momentum [P], area [A] and time [T] are taken as fundamental quantities, then the dimensional formula for the coefficient of viscosity is

(A) [PA^{–1}T^{0}]

(B) [PAT^{–1}]

(C) [PA^{–1}T]

(D) [PA^{–1}T^{–1}]

2. Which of the following physical quantities have the same dimensions?

(A) Electric displacement and surface charge density

(B) Displacement current and electric field

(C) Current density and surface charge density

(D) Electric potential and energy

3. A person moved from A to B on a circular path as shown in figure. If the distance travelled by him is 60 m, then the magnitude of displacement would be

(Given cos135°= –0.7)

(A) 42 m

(B) 47 m

(C) 19 m

(D) 40 m

4. A body of mass 0.5 kg travels on straight line path with velocity v = (3x^{2} + 4)m/s. The net workdone by the force during its displacement from x = 0 to x = 2 m is :

(A) 64 J

(B) 60 J

(C) 120 J

(D) 128 J

5. A solid cylinder and a solid sphere, having same mass M and radius R, roll down the same inclined plane from top without slipping. They start from rest. The ratio of velocity of the solid cylinder to that of the solid sphere, with which they reach the ground, will be

6. Three identical particle A, B and C of mass 100 kg each are placed in a straight line with AB = BC = 13 m. The gravitational force on a fourth particle P of the same mass is F, when placed at a distance 13 m from the particle B on the perpendicular bisector of the line AC. The value of F will be approximately :

(A) 21 G

(B) 100 G

(C) 59 G

(D) 42 G

7. A certain amount of gas of volume V at 27°C temperature and pressure 2 × 10^{7} Nm^{−}^{2} expands isothermally until its volume gets doubled. Later it expands adiabatically until its volume gets redoubled. The final pressure of the gas will be

(Use γ = 1.5)

(A) 3.536 × 10^{5} Pa

(B) 3.536 × 10^{6} Pa

(C) 1.25 × 10^{6} Pa

(D) 1.25 × 10^{5} Pa

8. Following statements are given:

(1) The average kinetic energy of a gas molecule decreases when the temperature is reduced.

(2) The average kinetic energy of a gas molecule increases with increase in pressure at constant temperature.

(3) The average kinetic energy of a gas molecule decreases with increase in volume.

(4) Pressure of a gas increases with increase in temperature at constant pressure.

(5) The volume of gas decreases with increase in temperature.

Choose the correct answer from the options given below:

(A) (1) & (4) only

(B) (1), (2) & (4) only

(C) (2) & (4) only

(D) (1), (2) & (5) only

9. In figure (A), mass ‘2 m’ is fixed on mass ‘m’ which is attached to two springs of spring constant k. In figure (B), mass ‘m’ is attached to two spring of spring constant ‘k’ and ‘2k’. If mass ‘m’ in (A) and (B) are displaced by distance ‘x’ horizontally and then released, then time period T1 and T2 corresponding to (A) and (B) respectively follow the relation.

10. A condenser of 2 μF capacitance is charged steadily from 0 to 5C. Which of the following graph represents correctly the variation of potential difference (V) across it’s plates with respect to the charge (Q) on the condenser ?

11. Two charged particles, having same kinetic energy, are allowed to pass through a uniform magnetic field perpendicular to the direction of motion. If the ratio of radii of their circular paths is 6 : 5 and their respective masses ratio is 9 : 4. Then, the ratio of their charges will be :

(A) 8 : 5

(B) 5 : 4

(C) 5 : 3

(D) 8 : 7

12. To increase the resonant frequency in series LCR circuit,

(A) Source frequency should be increased.

(B) Another resistance should be added in series with the first resistance.

(C) Another capacitor should be added in series with the first capacitor.

(D) The source frequency should be decreased.

13. A small square loop of wire of side l is placed inside a large square loop of wire L(L>>l). Both loops are coplanar and their centres coincide at point O as shown in figure. The mutual inductance of the system is :

14. The rms value of conduction current in a parallel plate capacitor is 6.9 μA. The capacity of this capacitor, if it is connected to 230 V ac supply with an angular frequency of 600 rad/s, will be :

(A) 5 pF

(B) 50 pF

(C) 100 pF

(D) 200 pF

15. Which of the following statement is correct?

(A) In primary rainbow, observer sees red colour on the top and violet on the bottom

(B) In primary rainbow, observer sees violet colour on the top and red on the bottom

(C) In primary rainbow, light wave suffers total internal reflection twice before coming out of water drops

(D) Primary rainbow is less bright than secondary rainbow

16. Time taken by light to travel in two different materials A and B of refractive indices μ_{A} and μ_{B} of same thickness is t_{1} and t_{2} If t_{2} – t_{1} = 5 × 10^{–10} s and the ratio of μ_{A} to μ_{B} is 1 : 2. Then, the thickness of material, in meter is: (Given v_{A} and v_{B} are velocities of light in A and B materials, respectively.)

(A) 5 × 10^{–10}v_{A} m

(B) 5 × 10-10^{–10} m

(C) 1.5 × 10^{–10}m

(D) 5 × 10^{–10}v_{B} m

17. A metal exposed to light of wavelength 800 nm and emits photoelectrons with a certain kinetic energy. The maximum kinetic energy of photo-electron doubles when light of wavelength 500 nm is used. The work function of the metal is:

(Take hc = 1230 eV-nm)

(A) 1.537 eV

(B) 2.46 eV

(C) 0.615 eV

(D) 1.23 eV

18. The momentum of an electron revolving in nth orbit is given by: (Symbols have their usual meanings)

(A) nh/2πr

(B) nh/2r

(C) nh/2π

(D) 2πr/nh

19. The magnetic moment of an electron (e) revolving in an orbit around nucleus with an orbital angular momentum is given by:

20. In the circuit, the logical value of A = 1 or B = 1 when potential at A or B is 5 V and the logical value of A = 0 or B = 0 when potential at A or B is 0 V.

The truth table of the given circuit will be:

**SECTION-B**

21. A car is moving with speed of 150 km/h and after applying the break it will move 27 m before it stops. If the same car is moving with a speed of one third the reported speed then it will stop after travelling ________ m distance.

22. For forces are acting at a point P in equilibrium as shown in figure. The ratio of force F_{1} to F_{2} is 1 : x where x =_________.

23. A wire of length L and radius r is clamped rigidly at one end. When the other end of the wire is pulled by a force F, its length increases by 5 cm. Another wire of the same material of length 4L and radius 4r is pulled by a force 4F under same conditions. The increase in length of this wire is __________ cm.

24. A unit scale is to be prepared whose length does not change with temperature and remains 20 cm, using a bimetallic strip made of brass and iron each of different length. The length of both components would change in such a way that difference between their lengths remains constant. If length of brass is 40 cm and length of iron will be ________ cm.

(α_{iron}= 1.2 × 10^{−5} K^{−1} and α_{brass} = 1.8 × 10^{−5} K^{−1})

25. An observer is riding on a bicycle and moving towards a hill at 18 kmh^{–1}. He hears a sound from a source at some distance behind him directly as well as after its reflection from the hill. If the original frequency of the sound as emitted by source is 640 Hz and velocity of the sound in air is 320 m/s, the beat frequency between the two sounds heard by observer will be _________ Hz.

26. The volume charge density of a sphere of radius 6 m is 2μC cm^{−}^{3}. The number of lines of force per unit surface area coming out from the surface of the sphere is _________ × 10^{10} NC^{−}^{1}.

(Given: Permittivity of vacuum = ∈_{0} = 8.85 × 10^{−}^{12}C^{2}N^{−}^{1}-m^{−}^{2}).

27. In the given figure, the value of V_{0} will be ______ V.

28. Eight copper wire of length l and diameter d are joined in parallel to form a single composite conductor of resistance R. If a single copper wire of length 2l have the same resistance (R) then its diameter will be ________ d.

29. The energy band gap of semiconducting material to produce violet (wavelength = 4000 Å) LED is _________ eV. (Round off to the nearest integer).

30. The required height of a TV tower which can cover the population of 6.03 lakh is h. If the average population density is 100 per square km and the radius of earth is 6400 km, then the value of h will be ________ m.

**CHEMISTRY**

**SECTION-A**

1. SO_{2}Cl_{2} on reaction with excess of water results into acidic mixture

SO_{2}Cl_{2} + 2H_{2}O → H_{2}SO_{4} + 2HCl

16 moles of NaOH is required for the complete neutralisation of the resultant acidic mixture. The number of moles of SO_{2}Cl_{2} used is :

(A) 16

(B) 8

(C) 4

(D) 2

2. Which of the following sets of quantum numbers is not allowed ?

3. The depression in the freezing point observed for a formic acid solution of concentration 0.5 mL L^{–1} is 0.0405°C. Density of formic acid is 1.05 g mL^{–1}. The Van’t Hoff factor of the formic acid solution is nearly (Given for water k_{f} = 1.86 k kg mol^{–1})

(A) 0.8

(B) 1.1

(C) 1.9

(D) 2.4

4. 20 mL of 0.1 M NH_{4}OH is mixed with 40 mL of 0.05 M HCl. The pH of the mixture is nearest to

(Given :K_{b}(NH_{4}OH) = 1 × 10^{–5}, log2 = 0.30, log3 = 0.48, log5 = 0.69, log7 = 0.84, log11 = 1.04)

(A) 3.2

(B) 4.2

(C) 5.2

(D) 6.2

5. Match List-I with List-II.

Choose the correct answer from the options given below :

(A) (A) – (II), (B) – (IV), (C) – (I), (D) – (III)

(B) (A) – (II), (B) – (I), (C) – (IV), (D) – (III)

(C) (A) – (III), (B) – (IV), (C) – (I), (D) – (II)

(D) (A) – (III), (B) – (I), (C) – (IV), (D) – (II)

6. The IUPAC nomenclature of an element with electronic configuration [Rn] 5f^{14}6d^{17}s^{2} is

(A) Unnilbium

(B) Unnilunium

(C) Unnilquadium

(D) Unniltrium

7. The compound(s) that is(are) removed as slag during the extraction of copper is

(1) CaO

(2) FeO

(3) Al_{2}O_{3}

(4) ZnO

(5) NiO

Choose the correct answer from the options given below :

(A) (3), (4) only

(B) (1), (2), (5) only

(C) (1), (2) only

(D) (2) only

8. The reaction of H_{2}O_{2} with potassium permanganate in acidic medium leads to the formation of mainly

(A) Mn^{2+}

(B) Mn^{4+}

(C) Mn^{3+}

(D) Mn^{6+}

9. Choose the correct order of density of the alkali metals.

(A) Li < K < Na <Rb< Cs

(B) Li < Na < K <Rb< Cs

(C) Cs <Rb< K < Na < Li

(D) Li < Na < K < Cs <Rb

10. The geometry around boron in the product ‘B’ formed from the following reaction is

(A) Trigonal planar

(B) Tetrahedral

(C) Pyramidal

(D) Square planar

11. The interhalogen compound formed from the reaction of bromine with excess of fluorine is a :

(A) hypohalite

(B) halate

(C) perhalate

(D) halite

12. The photochemical smog does not generally contain :

(A) NO

(B) NO_{2}

(C) SO_{2}

(D) HCHO

13. A compound ‘A’ on reaction with ‘X’ and ‘Y’ produces the same major product but different by product ‘a’ and ‘b’. Oxidation of ‘a’ gives a substance produced by ants.

‘X’ and ‘Y’ respectively are

(A) KMnO_{4}/H^{+} and dil. KMnO_{4}, 273 K

(B) KMnO_{4}(dilute), 273 Kand KMnO_{4}/H^{+}

(C) KMnO_{4}/H^{+} and O_{3}, H_{2}O/Zn

(D) O_{3}, H_{2}O/Zn and KMnO_{4}/H^{+}

14. Most stable product of the following reaction is :

15. Which one of the following reactions does not represent correct combination of substrate and product under the given conditions?

16. An organic compound ‘A’ on reaction with NH_{3} followed by heating gives compound B. Which on further strong heating gives compound C(C_{8}H_{5}NO_{2}). Compound C on sequential reaction with ethanolic KOH, alkyl chloride and hydrolysis with alkali gives a primary amine. The compound A is :

17. Melamine polymer is formed by the condensation of :

18. During the denaturation of proteins, which of these structures will remain intact?

(A) Primary

(B) Secondary

(C) Tertiary

(D) Quaternary

19. Drugs used to bind to receptors, inhibiting its natural function and blocking a message are called:

(A) Agonists

(B) Antagonists

(C) Allosterists

(D) Anti histaminists

20. Given below are two statements:

**Statement I:** On heating with KHSO4, glycerol is dehydrated and acrolein is formed.

**Statement II:**Acrolein has fruity odour and can be used to test glycerol’s presence.

Choose the correct option.

(A) Both Statement I and Statement II are correct.

(B) Both Statement I and Statement II are incorrect.

(C) Statement I is correct but Statement II is incorrect.

(D) Statement I is incorrect but Statement II is correct.

**SECTION-B**

21. Among the following species

the number of species showing diamagnetism is ________.

22. The enthalpy of combustion of propane, graphite and dihydrogen at 298 K are –2220.0 kJ mol^{–1}, –393.5 kJ mol^{–1} and –285.8 kJ mol^{–1}, respectively. The magnitude of enthalpy of formation of propane (C_{3}H_{8}) is _____ kJ mol^{–1}. (Nearest integer)

23. The pressure of a moist gas at 27°C is 4 atm. The volume of the container is doubled at the same temperature. The new pressure of the moist gas is ______ ×10^{–1} (Nearest integer)

(Given: The vapour pressure of water at 27°C is 0.4 atm.)

24. The cell potential for Zn|Zn^{2+}(aq)||Sn^{x+}|Sn is 0.801 V at 298 K. The reaction quotient for the above reaction is 10^{–2}. The number of electrons involved in the given electrochemical cell reaction is ________.

(Given and

25. The half-life for the decomposition of gaseous compound A is 240 s when the gaseous pressure was 500 torr initially. When the pressure was 250 torr, the half-life was found to be 4.0 min. The order of the reaction is ______. (Nearest integer)

26. Consider the following metal complexes:

[Co(NH_{3})_{6}]^{3+}

[CoCl(NH_{3})_{5}]^{2+}

[Co(CN)_{6}]^{3–}

[Co(NH_{3})_{5}(H_{2}O)]^{3+}

The spin-only magnetic moment value of the complex that absorbs light with shortest wavelength is _______ B.M. (Nearest integer)

27. Among Co^{3+}, Ti^{2+}, V^{2+} and Cr^{2+} ions, one if used as a reagent cannot liberate H_{2} from dilute mineral acid solution, its spin-only magnetic moment in gaseous state is________ B.M. (Nearest integer)

28. While estimating the nitrogen present in an organic compound by Kjeldahl’s method, the ammonia evolved from 0.25 g of the compound neutralized 2.5 mL of 2 M H_{2}SO_{4}. The percentage of nitrogen present in organic compound is ________.

29. The number of sp^{3} hybridised carbons in an acyclic neutral compound with molecular formula C_{4}H_{5}N is ________.

30. In the given reaction,

(where Et is –C_{2}H_{5})

The number of chiral carbon(s) in product A is _________.

**MATHEMATICS**

**SECTION-A**

1. The total number of functions, f : {1, 2, 3, 4} ● {1, 2, 3, 4, 5, 6} such that f(1) + f(2) = f(3), is equal to

(A) 60

(B) 90

(C) 108

(D) 126

2. If α, β, γ, δ are the roots of the equation x^{4} + x^{3} + x^{2} + x + 1 = 0, then α^{2021} + β^{2021} + γ^{2021} + δ^{2021} is equal to

(A) −4

(B) −1

(C) 1

(D) 4

3. For n ∈ N, let and Then the number of elements in the set {n ∈ N : S_{n}∩T_{n} = ϕ} is :

(A) 0

(B) 2

(C) 3

(D) 4

4. The number of q∈ (0, 4π) for which the system of linear equations

3(sin 3θ) x – y + z = 2

3(cos 2θ) x + 4y + 3z = 3

6x + 7y + 7z = 9

has no solution, is

(A) 6

(B) 7

(C) 8

(D) 9

5. If then 8(α + β) is equal to :

(A) 4

(B) −8

(C) −4

(D) 8

6. If the absolute maximum value of the function in the interval [−3, 0] is f(α), then:

(A) α = 0

(B) α = −3

(C) α∈ (−1, 0)

(D) α∈ (−3, −1)

7. The curve y(x) = ax^{3} + bx^{2} + cx + 5 touches the x-axis at the point P(–2, 0) and cuts the y-axis at the point Q, where y′ is equal to 3. Then the local maximum value of y(x) is

(A) 27/4

(B) 29/4

(C) 37/4

(D) 9/2

8. The area of the region given by A = {(x, y); x^{2}≤ y ≤ min{x + 2, 4 – 3x}} is

(A) 31/8

(B) 17/6

(C) 19/6

(D) 27/8

9. For any real number x, let [x] denote the largest integer less than equal to x. Let f be a real valued function defined on the interval [–10, 10] by . Then the value of is:

(A) 4

(B) 2

(C) 1

(D) 0

10. The slope of the tangent to a curve C : y = y(x) at any point (x, y) on it is If C passes through the points then e^{α} is equal to:

11. The general solution of the differential equation (x – y^{2})dx + y(5x + y^{2})dy = 0 is :

(A) (y^{2} + x)^{4} = C|(y^{2} + 2x)^{3}|

(B) (y^{2} + 2x)^{4} = C|(y^{2} + 2x)^{3}|

(C) |(y^{2} + x)^{3}| = C(2y^{2} + x)^{4}

(D) |(y^{2} + 2x)^{3}| = C(2y^{2} + x)^{4}

12. A line, with the slope greater than one, passes through the point A(4, 3) and intersects the line

x – y – 2 = 0 at the point B. If the length of the line segment AB is√29/3, then B also lies on the line:

(A) 2x + y = 9

(B) 3x – 2y = 7

(C) x + 2y = 6

(D) 2x – 3y = 3

13. Let the locus of the centre (α, β), β > 0, of the circle which touches the circle x^{2} +(y – 1)^{2} = 1 externally and also touches the x-axis be L. Then the area bounded by L and the line y = 4 is :

(A) 32√2/3

(B) 40√2/3

(C) 64/3

(D) 32/3

14. Let P be the plane containing the straight line and perpendicular to the plane containing the straight lines If d is the distance P from the point (2, –5, 11), then d^{2} is equal to :

(A) 147/2

(B) 96

(C) 32/3

(D) 54

15. Let ABC be a triangle

(A) Both (S1) and (S2) are true

(B) Only (S1) is true

(C) Only (S2) is true

(D) Both (S1) and (S2) are false

16. If the sum and the product of mean and variance of a binomial distribution are 24 and 128 respectively, then the probability of one or two successes is :

(A) 33/2^{32}

(B) 33/2^{29}

(C) 33/2^{28}

(D) 33/2^{27}

17. If the numbers appeared on the two throws of a fair six faced die are α and β, then the probability that x^{2} + αx + β > 0, for all x ∈ R, is :

(A) 17/36

(B) 4/9

(C) 1/2

(D) 19/36

18. The number of solutions of |cos x| = sinx, such that –4π ≤ x ≤ 4π is :

(A) 4

(B) 6

(C) 8

(D) 12

19. A tower PQ stands on a horizontal ground with base Q on the ground. The point R divides the tower in two parts such that QR = 15 m. If from a point A on the ground the angle of elevation of R is 60° and the part PR of the tower subtends an angle of 15° at A, then the height of the tower is :

(A) 5(2√3 + 3) m

(B) 5(√3 + 3)m

(C) 10(√3 + 1) m

(D) 10(2√3 + 1) m

20. Which of the following statements is a tautology?

(A) ((~p) ∨ q) ⇒ p

(B) p⇒ ((~p) ∨ q)

(C) ((~p) ∨ q) ⇒ q

(D) q⇒ ((~p) ∨ q)

**SECTION-B**

21. Let and B = A – I. If

then the number of elements in the set {n ∈ {1, 2, …, 1000} : A^{n} + (ωB)^{n} = A + B} is equal to _________.

22. The letters of the work ‘MANKIND’ are written in all possible orders and arranged in serial order as in an English dictionary. Then the serial number of the word ‘MANKIND’ is ______.

23. If the maximum value of the term independent of t in the expansion of is K, then 8K is equal to _________.

24. Let a, b be two non-zero real numbers. If p and r are the roots of the equation x^{2} – 8ax + 2a = 0 and q and s are the roots of the equation x^{2} + 12bx + 6b = 0, such that are in A.P., then a^{−}^{1} – b^{−}^{1} is equal to _________.

25. Let a_{1} = b_{1} = 1, a_{n} = a_{n – 1} + 2 and b_{n} = a_{n} + b_{n – 1} for every natural number n ≥ 2. Then is equal to _________.

26. Let where [α] denotes the greatest integer less than or equal to α. Then the number of points in R where f is not differentiable is _________.

27. If then the integral value of k is equal to _______.

28. Let the equation of two diameters of a circle x^{2} + y^{2} – 2x + 2fy + 1 = 0 be 2px – y = 1 and 2x + py = 4p. Then the slope m ∈ (0, ∞) of the tangent to the hyperbola 3x^{2} – y^{2} = 3 passing through the centre of the circle is equal to _______.

29. The sum of diameters of the circles that touch (i) the parabola 75x^{2} = 64(5y – 3) at the point (8/5, 6/5) and (ii) the y-axis is equal to _______.

30. The line of shortest distance between the lines and makes angle of with the plane P :ax – y – z = 0, (a > 0). If the image of the point (1, 1, –5) in the plane P is (α, β, γ), then α + β – γ is equal to ________.

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