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

**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.

**PHYSICS**

**Section-A**

1. If then the relative error in Z will be :

2. is a vector quantity such that Which of the following expressions is true for

3. Which of the following relations is true for two unit vector making an angle θ to each other?

4. If force acts on a particle having position vector then, the torque about the origin will be :-

5. The height of any point P above the surface of earth is equal to diameter of earth. The value of acceleration due to gravity at point P will be (Given g = acceleration due to gravity at the surface of earth).

(A) g/2

(B) g/4

(C) g/3

(D) g/9

6. The terminal velocity (v_{t}) of the spherical rain drop depends on the radius (r) of the spherical rain drop as

(A) r^{1/2}

(B) r

(C) r^{2}

(D) r^{3}

7. The relation between root mean square speed (v_{rms}) and most probable speed (v_{p}) for the molar mass M of oxygen gas molecule at the temperature of 300 K will be

8. In the figure, a very large plane sheet of positive charge is shown. P_{1} and P_{2} are two points at distance l and 2l from the charge distribution. If σ is the surface charge density, then the magnitude of electric fields E_{1} and E_{2} and P_{1} and P_{2} respectively are

(A) E_{1} = σ/ε_{0}, E_{2} = σ/2ε_{0}

(B) E_{1} = 2σ/ε_{0}, E_{2} = σ/ε_{0}

(C) E_{1} = E_{2} = σ/2ε_{0}

(D) E_{1} = E_{2} = σ/ε_{0}

9. Match List-I with List-II

Choose the correct answer from the options given below:-

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

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

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

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

10. A long straight wire with a circular cross-section having radius R, is carrying a steady current I. The current I is uniformly distributed across this cross-section. Then the variation of magnetic field due to current I with distance r (r < R) from its centre will be

(A) B ∝ r^{2}

(B) B ∝ r

(C) B ∝ 1/r^{2}

(D) B ∝ 1/r

11. If wattless current flows in the AC circuit, then the circuit is :

(A) Purely Resistive circuit

(B) Purely Inductive circuit

(C) LCR series circuit

(D) RC series circuit only

12. The electric field in an electromagnetic wave is given by E = 56.5 sinω(t – x/c) NC^{–1}. Find the intensity of the wave if it is propagating along x-axis in the free space.

(Given ∈_{0} = 8.85 × 10^{–12}C^{2}N^{–1}m^{–2})

(A) 5.65 Wm^{–2}

(B) 4.24 Wm^{–2}

(C) 1.9 × 10^{–7} Wm^{–2}

(D) 56.5 Wm^{–2}

13. The two light beams having intensities I and 9I interfere to produce a fringe pattern on a screen. The phase difference between the beams is π/2 at point P and π at point Q. Then the difference between the resultant intensities at P and Q will be:

(A) 2 I

(B) 6 I

(C) 5 I

(D) 7 I

14. A light wave travelling linearly in a medium of dielectric constant 4, incidents on the horizontal interface separating medium with air. The angle of incidence for which the total intensity of incident wave will be reflected back into the same medium will be :

(Given : relative permeability of medium μ_{r}= 1)

(A) 10°

(B) 20°

(C) 30°

(D) 60°

15. Given below are two statements :

**Statement I:** Davisson-Germer experiment establishes the wave nature of electrons.

**Statement II:** If electrons have wave nature, they can interfere and show diffraction.

In the light of the above statements choose the correct answer from the option given below :

(A) Both statement I and statement II are true.

(B) Both statement I and statement II are false.

(C) Statement I is true but statement II is false.

(D) Statement I is false but statement II is true.

16. 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

17. The photodiode is used to detect the optical signals. These diodes are preferably operated in reverse biased mode because :

(A) fractional change in majority carriers produce higher forward bias current

(B) fractional change in majority carriers produce higher reverse bias current

(C) fractional change in minority carriers produce higher forward bias current

(D) fractional change in minority carriers produce higher reverse bias current

18. A signal of 100 THz frequency can be transmitted with maximum efficiency by :

(A) Coaxial cable

(B) Optical fibre

(C) Twisted pair of copper wires

(D) Water

19. The difference of speed of light in the two media A and B(v_{A} – v_{B}) is 2.6 × 10^{7} m/s. If the refractive index of medium B is 1.47, then the ratio of refractive index of medium B to medium A is: (Given: speed of light in vacuum C = 3 × 10^{8}ms^{–1})

(A) 1.303

(B) 1.318

(C) 1.13

(D) 0.12

20. A teacher in his physics laboratory allotted an experiment to determine the resistance (G) of a galvanometer. Students took the observations for 1/3 deflection in the galvanometer. Which of the below is true for measuring value of G?

(A) 1/3 deflection method cannot be used for determining the resistance of the galvanometer.

(B) 1/3 deflection method can be used and in this case the G equals to twice the value of shunt resistance(s)

(C) 1/3 deflection method can be used and in this case, the G equals to three times the value of shunt resistance(s)

(D) 1/3 deflection method can be used and in this case the G value equals to the shunt resistance(s)

**SECTION-B**

21. A uniform chain of 6 m length is placed on a table such that a part of its length is hanging over the edge of the table. The system is at rest. The co-efficient of static friction between the chain and the surface of the table is 0.5, the maximum length of the chain hanging from the table is __________m.

22. A 0.5 kg block moving at a speed of 12 ms^{–1 }compresses a spring through a distance 30 cm when its speed is halved. The spring constant of the spring will be ___ Nm^{–1}.

23. The velocity of upper layer of water in a river is 36 kmh^{–1}. Shearing stress between horizontal layers of water is 10^{–3} Nm^{–2}. Depth of the river is _____________ m. (Co-efficient of viscosity of water is 10^{–2}s)

24. A steam engine intakes 50 g of steam at 100°C per minute and cools it down to 20°C. If latent heat of vaporization of steam is 540 cal g^{–1}, then the heat rejected by the steam engine per minute is ___________ × 10^{3}

(Given : specific heat capacity of water : 1 cal g^{–1} °C^{–1})

25. The first overtone frequency of an open organ pipe is equal to the fundamental frequency of a closed organ pipe. If the length of the closed organ pipe is 20 cm. The length of the open organ pipe is __________ cm.

26. The equivalent capacitance between points A and B in below shown figure will be _______μF.

27. A resistor develops 300 J of thermal energy in 15 s, when a current of 2 A is passed through it. If the current increases to 3 A, the energy developed in 10 s is _______ J.

28. The total current supplied to the circuit as shown in figure by the 5 V battery is _________A.

29. The current in a coil of self-inductance 2.0 H is increasing according to I = 2sin(t^{2})A. The amount of energy spent during the period when current changes from 0 to 2A is _______ J.

30. A force on an object of mass 100 g is The position of that object at t = 2s is after starting from rest. The value of a/b will be _________

**CHEMISTRY**

**SECTION-A**

1. Bonding in which of the following diatomic molecule(s) become(s) stronger, on the basis of MO Theory, by removal of an electron?

(A) NO

(B) N_{2}

(C) O_{2}

(D) C_{2}

(E) B_{2}

Choose the most appropriate answer from the options given below :

(A) (A), (B), (C) only

(B) (B), (C), (E) only

(C) (A), (C) only

(D) (D) only

2. Incorrect statement for Tyndall effect is :

(A) The refractive indices of the dispersed phase and the dispersion medium differ greatly in magnitude.

(B) The diameter of the dispersed particles is much smaller than the wavelength of the light used.

(C) During projection of movies in the cinemas hall, Tyndall effect is noticed.

(D) It is used to distinguish a true solution from a colloidal solution.

3. The pair, in which ions are isoelectronic with Al^{3+} is:

(A) Br^{–} and Be^{2+}

(B) Cl^{–} and Li^{+}

(C) S^{2–} and K^{+}

(D) O^{2–} and Mg^{2+}

4. Leaching of gold with dilute aqueous solution of NaCN in presence of oxygen gives complex [A], which on reaction with zinc forms the elemental gold and another complex [B]. [A] and [B], respectively are :

(A) [Au(CN)_{4}]^{−} and [Zn(CN)_{2} (OH)_{2}]^{2−}

(B) [Au(CN)_{2}]^{−} and [Zn (OH)_{4}]^{2−}

(C) [Au(CN)_{2}]^{−} and [Zn (CN)_{4}]^{2−}

(D) [Au(CN)_{4}]^{2−} and [Zn (CN)_{6}]^{4−}

5. Number of electron deficient molecules among the following PH_{3}, B_{2}H_{6}, CCl_{4}, NH_{3}, LiH and BCl_{3} is

(A) 0

(B) 1

(C) 2

(D) 3

6. Which one of the following alkaline earth metal ions has the highest ionic mobility in its aqueous solution?

(A) Be^{2+}

(B) Mg^{2+}

(C) Ca^{2+}

(D) Sr^{2+}

7. White precipitate of AgCI dissolves in aqueous ammonia solution due to formation of:

(A) [Ag(NH_{3})_{4}]CI_{2}

(B) [Ag(CI)_{2}(NH_{3})_{2}]

(C) [Ag(NH_{3})_{2}]CI

(D) [Ag(NH_{3})CI]CI

8. Cerium (IV) has a noble gas configuration. Which of the following is correct statement about it?

(A) It will not prefer to undergo redox reactions.

(B) It will prefer to gain electron and act as an oxidizing agent

(C) It will prefer to give away an electron and behave as reducing agent

(D) It acts as both, oxidizing and reducing agent.

9. Among the following which is the strongest oxidizing agent?

(A) Mn^{3+}

(B) Fe^{3+}

(C) Ti^{3+}

(D) Cr^{3+}

10. The eutrophication of water body results in:

(A) loss of Biodiversity.

(B) breakdown of organic matter.

(C) increase in biodiversity.

(D) decrease in BOD.

11. Phenol on reaction with dilute nitric acid, gives two products. Which method will be most efficient for large scale separation?

(A) Chromatographic separation

(B) Fractional crystallisation

(C) Steam distillation

(D) Sublimation

12. In the following structures, which one is having staggered conformation with maximum dihedral angle?

13. The products formed in the following reaction.

14. The IUPAC name of ethylidene chloride is:

(A) 1-Chloroethene

(B) 1-Chloroethyne

(C) 1, 2-Dichloroethane

(D) 1, 1-Dichloroethane

15. The major product in the reaction

(A) t-Butyl ethyl ether

(B) 2, 2-Dimethyl butane

(C) 2-Methyl pent-1-ene

(D) 2-Methyl prop-1-ene

16. The intermediate X, in the reaction :

17. In the following reaction:

The compound A and B respectively are:

18. The reaction of with bromine and KOH gives RNH_{2} as the end product. Which one of the following is the intermediate product formed in this reaction?

19. Using very little soap while washing clothes, does not serve the purpose of cleaning of clothes, because:

(A) soap particles remain floating in water as ions.

(B) the hydrophobic part of soap is not able to take away grease.

(C) the micelles are not formed due to concentration of soap, below its CMC value.

(D) colloidal structure of soap in water is completely distributed.

20. Which one of the following is an example of artificial sweetner?

(A) Bithional

(B) Alitame

(C) Salvarsan

(D) Lactose

**SECTION-B**

21. The number of N atoms in 681 g of C_{7}H_{5}N_{3}O_{6} is x × 10^{21}. The value of x is ______. (NA = 6.02 × 10^{23} mol^{–1}) (Nearest Integer)

22. The distance between Na^{+} and Cl^{–} ions in solid NaCl of density 43.1 g cm^{–3} is ____ × 10^{–10} (Nearest Integer)

(Given : NA = 6.02 × 10^{23} mol^{–1})

23. The longest wavelength of light that can be used for the ionisation of lithium atom (Li) in its ground state is x × 10^{–8} The value of x is ______. (Nearest Integer)

(Given : Energy of the electron in the first shell of the hydrogen atom is –2.2 x 10^{–18} J;

h = 6.63 × 10^{–34} Js and c = 3 × 10^{8} ms^{–1})

24. The standard entropy change for the reaction 4Fe(s) + 3O_{2}(g) 2Fe_{2}O_{3}(s) is –550 J K^{–1} at 298 K.

[Given: The standard enthalpy change for the reaction is –165 kJ mol^{–1}]. The temperature in K at which the reaction attains equilibrium is ________. (Nearest Integer)

25. 1 L aqueous solution of H_{2}SO_{4} contains 0.02 m mol H_{2}SO_{4}. 50% of this solution is diluted with deionized water to give 1 L solution (A). In solution (A), 0.01 m mol of H_{2}SO_{4} are added. Total m mols of H_{2}SO_{4} in the final solution is ______ × 10^{3} m mols.

26. The standard free energy change (ΔG°) for 50% dissociation of N_{2}O_{4} into NO_{2} at 27°C and 1 atm pressure is –x J mol^{–1}. The value of x is _____. (Nearest Integer)

[Given : R = 8.31 J K^{–1} mol^{–1}, log 1.33 = 0.1239 ln 10 = 2.3]

27. In a cell, the following reactions take place

The standard electrode potential for the spontaneous reaction in the cell is x × 10^{–2} V at 208 K. The value of x is _______. (Nearest Integer)

28. For a given chemical reaction

γ_{1}A + γ_{2}B → γ_{3}C + γ_{4}D

Concentration of C changes from 10 mmol dm^{–3} to 20 mmol dm^{–3} in 10 seconds. Rate of appearance of D is 1.5 times the rate of disappearance of B which is twice the rate of disappearance A. The rate of appearance of D has been experimentally determined to be 9 mmol dm^{–3} s^{–1}. Therefore, the rate of reaction is _____ mmol dm^{–3} s^{–1}.

29. If [Cu(H_{2}O)_{4}]^{2+} absorbs a light of wavelength 600 nm for d-d transition, then the value of octahedral crystal field splitting energy for [Cu(H_{2}O)_{6}]^{2+} will be _______ ×10^{–21} [Nearest integer]

(Given : h = 6.63 × 10^{–34} Js and c = 3.08 × 10^{8} ms^{–1})

30. Number of grams of bromine that will completely react with 5.0 g of pent-1-ene is ______ × 10^{–2} (Atomic mass of Br = 80 g/mol) [Nearest integer]

**MATHEMATICS**

**SECTION-A**

1. Let a circle C touch the lines L_{1} : 4x – 3y +K_{1} = 0 and L_{2} : 4x – 3y + K_{2} = 0, K_{1}, K_{2 }∈ If a line passing through the centre of the circle C intersects L_{1} at (–1, 2) and L_{2} at (3, –6), then the equation of the circle C is :

(A) (x – 1)^{2} + (y – 2)^{2} = 4

(B) (x + 1)^{2} + (y – 2)^{2} = 4

(C) (x – 1)^{2} + (y + 2)^{2} = 16

(D) (x – 1)^{2} + (y – 2)^{2} = 16

2. The value of is equal to

(A) π^{2}/4

(B) π^{2}/2

(C) π/4

(D) π/2

3. Let a, b and c be the length of sides of a triangle ABC such that If r and R are the radius of incircle and radius of circumcircle of the triangle ABC, respectively, then the value of R/r is equal to

(A) 5/2

(B) 2

(C) 3/2

(D) 1

4. Let f : N→R be a function such that f(x + y) = 2f(x) f(y) for natural numbers x and y. If f(1) = 2, then the value of α for which holds, is

(A) 2

(B) 3

(C) 4

(D) 6

5. Let A be a 3 × 3 real matrix such that and If X = (x_{1}, x_{2}, x_{3})T and I is an identity matrix of order 3, then the system has

(A) No solution

(B) Infinitely many solutions

(C) Unique solution

(D) Exactly two solutions

6. Let f : R→R be defined as f(x) = x3 + x – 5 If g(x) is a function such that f(g(x)) = x, ∀ x ∈ R, then g′ (63) is equal to _______.

(A) 1/49

(B) 3/49

(C) 43/49

(D) 91/49

7. Consider the following two propositions :

P1 : ~ (p → ~ q)

P2: (p ∧ ~q) ∧ ((-~p) ∨ q)

If the proposition p → ((~p) ∨ q) is evaluated as FALSE, then :

(A) P1 is TRUE and P2 is FALSE

(B) P1 is FALSE and P2 is TRUE

(C) Both P1 and P2 are FALSE

(D) Both P1 and P2 are TRUE

8. If then the remainder when K is divided by 6 is

(A) 1

(B) 2

(C) 3

(D) 5

9. Let f(x) be a polynomial function such that f(x) + f′(x) + f′′(x) = x^{5} + 64. Then, the value of

(A) −15

(B) −60

(C) 60

(D) 15

10. Let E_{1} and E_{2} be two events such that the conditional probabilities P(E_{1}|E_{2}) = 1/2, P(E_{2}|E_{1}) = 3/4 and P(E_{1}∩E_{2}) = 1/8. Then:

(A) P(E_{1} ∩ E_{2}) = P(E_{1}) ∙ P(E_{2})

(B) P(E’_{1} ∩ E’_{2}) = P(E’_{1}) ∙ P(E_{2})

(C) P(E_{1} ∩ E’_{2}) = P(E_{1}) ∙ P(E_{2})

(D) P(E’_{1} ∩ E_{2}) = P(E_{1}) ∙ P(E_{2})

11. Let If M and N are two matrices given by then MN^{2} is

(A) a non-identity symmetric matrix

(B) a skew-symmetric matrix

(C) neither symmetric nor skew-symmetric matrix

(D) an identity matrix

12. Let g : (0, ∞) → R be a differentiable function such that for all x > 0, where c is an arbitrary constant. Then.

(A) g is decreasing in (0, π/4)

(B) g’ is increasing in (0, π/4)

(C) g + g’ is increasing in (0, π/2)

(D) g – g’ is increasing in (0, π/2)

13. Let f :R→R and g : R → R be two functions defined by f(x) = loge(x^{2} + 1) – e^{–x} + 1 and Then, for which of the following range of α, the inequality holds?

(A) (2, 3)

(B) (–2, –1)

(C) (1, 2)

(D) (–1, 1)

14. Let a_{i} > 0, i = 1, 2, 3 be a vector which makes equal angles with the coordinate axes OX, OY and OZ. Also, let the projection of on the vector be 7. Let be a vector obtained by rotating with 90°. If and x-axis are coplanar, then projection of a vector is equal to

(A) √7

(B) √2

(C) 2

(D) 7

15. Let y = y(x) be the solution of the differential equation (x + 1)y′ – y = e^{3x}(x + 1)^{2}, with y(0) = 1/3. Then, the point x = −4/3 for the curve y = y(x) is:

(A) not a critical point

(B) a point of local minima

(C) a point of local maxima

(D) a point of inflection

16. If y = m_{1}x + c_{1} and y = m_{2}x + c_{2}, m_{1 }≠ m_{2} are two common tangents of circle x^{2} + y^{2} = 2 and parabola y^{2} = x, then the value of 8|m1m2| is equal to :

(A) 3 + 4√2

(B) −5 + 6√2

(C) −4 + 3√2

(D) 7 + 6√2

17. Let Q be the mirror image of the point P(1, 0, 1) with respect to the plane S: x + y + z = 5. If a line L passing through (1, –1, –1), parallel to the line PQ meets the plane S at R, then QR^{2} is equal to :

(A) 2

(B) 5

(C) 7

(D) 11

18. If the solution curve y = y(x) of the differential equation y^{2}dx + (x^{2} – xy + y^{2})dy = 0, which passes through the point (1,1) and intersects the line y = √3 x at the point (α, √3α), then value of log_{e}(√3α) is equal to

(A) π/3

(B) π/2

(C) π/12

(D) π/6

19. Let x = 2t, y = t^{2}/3 be a conic. Let S be a conic. Let S be the focus and B be the point on the axis of the conic such that SA⊥BA, where A is any point on the conic. If k is the ordinate of the centroid of the ΔSAB, then equal to

(A) 17/18

(B) 19/18

(C) 11/18

(D) 13/18

20. Let a circle C in complex plane pass through the points z_{1} = 3 + 4i, z_{2} = 4 + 3i and z_{3} = 5i. If z(≠ z_{1}) is a point on C such that the line through z and z_{1} is perpendicular to the line through z_{2} and z_{3}, then arg(z) is equal to:

**SECTION-B**

21. Let C_{r} denote the binomial coefficient of x^{r} in the expansion of (1 + x)^{10}. If for α, β ∈ R, C_{1} + 3⋅2 C_{2} + 5⋅3 C_{3} + … upto 10 terms then the value of α + β is equal to _____

22. The number of 3-digit odd numbers, whose sum of digits is a multiple of 7, is ________.

23. Let θ be the angle between the vectors where Then is equal to _________

24. Let the abscissae of the two points P and Q be the roots of 2x^{2} – rx + p = 0 and the ordinates of P and Q be the roots of x^{2} – sx – q = 0. If the equation of the circle described on PQ as diameter is 2(x^{2} + y^{2}) – 11x – 14y – 22 = 0, then 2r + s – 2q + p is equal to _________.

25. The number of values of x in the interval for which 14cosec^{2}x – 2 sin^{2}x = 21 – 4 cos^{2}x holds, is ___________.

26. For a natural number n, let a_{n} = 19^{n} – 12^{n}. Then, the value of is

27. Let f : R → R be a function defined by If the function g(x) = f (f (f (x))) + f (f (x)), then the greatest integer less than or equal to g(1) is ___________.

28. Let the lines

intersect at the point S. If a plane ax + by – z + d = 0 passes through S and is parallel to both the lines L_{1} and L_{2}, then the value of a + b + d is equal to _______.

29. Let A be a 3 × 3 matrix having entries from the set {–1, 0, 1}. The number of all such matrices A having sum of all the entries equal to 5, is ____________.

30. The greatest integer less than or equal to the sum of first 100 terms of the sequence 1/3, 5/9, 19/27, 65/81, … is equal to ________.

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