JEE Main 2022 Answer Key | ENTRANCE INDIA

JEE Main Session 1 25th June 2022 Shift-1 Question Paper and Answer Key

December 6, 2022December 2, 2022 by suresh84

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 :

Answer: (C)

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

Answer: (C)

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

Answer: (B)

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

Answer: (B)

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

(D) g/9

Answer: (D)

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

(D) r³

Answer: (C)

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

Answer: (B)

8. In the figure, a very large plane sheet of positive charge is shown. P₁ and P₂ 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 E₁ and E₂ and P₁ and P₂ respectively are

(A) E₁ = σ/ε₀, E₂ = σ/2ε₀

(B) E₁ = 2σ/ε₀, E₂ = σ/ε₀

(D) E₁ = E₂ = σ/ε₀

Answer: (C)

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)

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

Answer: (A)

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 ∝ r²

(B) B ∝ r

(D) B ∝ 1/r

Answer: (B)

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

(A) Purely Resistive circuit

(B) Purely Inductive circuit

(D) RC series circuit only

Answer: (B)

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^–12C²N^–1m^–2)

(A) 5.65 Wm^–2

(B) 4.24 Wm^–2

(D) 56.5 Wm^–2

Answer: (B)

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

(D) 7 I

Answer: (B)

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°

(D) 60°

Answer: (D)

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.

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

Answer: (A)

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

(D) 2 : 1

Answer: (D)

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

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

Answer: (D)

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

(A) Coaxial cable

(B) Optical fibre

(D) Water

Answer: (B)

19. The difference of speed of light in the two media A and B(v_A – v_B) is 2.6 × 10⁷ 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 × 10⁸ms^–1)

(A) 1.303

(B) 1.318

(D) 0.12

Answer: (C)

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)

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

Answer: (B)

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.

Answer: (2)

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

Answer: (600)

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^–2s)

Answer: (100)

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 ___________ × 10³

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

Answer: (31)

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.

Answer: (80)

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

Answer: (6)

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.

Answer: (450)

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

Answer: (2)

29. The current in a coil of self-inductance 2.0 H is increasing according to I = 2sin(t²)A. The amount of energy spent during the period when current changes from 0 to 2A is _______ J.

Answer: (4)

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 _________

Answer: (2)

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) N₂

(D) C₂

(E) B₂

Choose the most appropriate answer from the options given below :

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

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

(D) (D) only

Answer: (C)

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.

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

Answer: (B)

3. The pair, in which ions are isoelectronic with Al³⁺ is:

(A) Br^– and Be²⁺

(B) Cl^– and Li⁺

(D) O^2– and Mg²⁺

Answer: (D)

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⁻

(D) [Au(CN)₄]²⁻ and [Zn (CN)₆]⁴⁻

Answer: (C)

5. Number of electron deficient molecules among the following PH₃, B₂H₆, CCl₄, NH₃, LiH and BCl₃ is

(A) 0

(B) 1

(D) 3

Answer: (C)

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

(A) Be²⁺

(B) Mg²⁺

(D) Sr²⁺

Answer: (D)

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

(A) [Ag(NH₃)₄]CI₂

(B) [Ag(CI)₂(NH₃)₂]

(D) [Ag(NH₃)CI]CI

Answer: (C)

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

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

Answer: (B)

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

(A) Mn³⁺

(B) Fe³⁺

(D) Cr³⁺

Answer: (A)

10. The eutrophication of water body results in:

(A) loss of Biodiversity.

(B) breakdown of organic matter.

(D) decrease in BOD.

Answer: (A)

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

(D) Sublimation

Answer: (C)

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

Answer: (C)

13. The products formed in the following reaction.

Answer: (B)

14. The IUPAC name of ethylidene chloride is:

(A) 1-Chloroethene

(B) 1-Chloroethyne

(D) 1, 1-Dichloroethane

Answer: (D)

15. The major product in the reaction

(A) t-Butyl ethyl ether

(B) 2, 2-Dimethyl butane

(D) 2-Methyl prop-1-ene

Answer: (D)

16. The intermediate X, in the reaction :

Answer: (C)

17. In the following reaction:

The compound A and B respectively are:

Answer: (C)

18. The reaction of with bromine and KOH gives RNH₂ as the end product. Which one of the following is the intermediate product formed in this reaction?

Answer: (C)

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.

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

Answer: (C)

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

(A) Bithional

(B) Alitame

(D) Lactose

Answer: (B)

SECTION-B

21. The number of N atoms in 681 g of C₇H₅N₃O₆ is x × 10²¹. The value of x is ______. (NA = 6.02 × 10²³ mol^–1) (Nearest Integer)

Answer: (5418)

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 × 10²³ mol^–1)

Answer: (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 × 10⁸ ms^–1)

Answer: (4)

24. The standard entropy change for the reaction 4Fe(s) + 3O₂(g) 2Fe₂O₃(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)

Answer: (300)

25. 1 L aqueous solution of H₂SO₄ contains 0.02 m mol H₂SO₄. 50% of this solution is diluted with deionized water to give 1 L solution (A). In solution (A), 0.01 m mol of H₂SO₄ are added. Total m mols of H₂SO₄ in the final solution is ______ × 10³ m mols.

Answer: (0)

26. The standard free energy change (ΔG°) for 50% dissociation of N₂O₄ into NO₂ 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]

Answer: (710)

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)

Answer: (23)

28. For a given chemical reaction

γ₁A + γ₂B → γ₃C + γ₄D

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.

Answer: (1)

29. If [Cu(H₂O)₄]²⁺ absorbs a light of wavelength 600 nm for d-d transition, then the value of octahedral crystal field splitting energy for [Cu(H₂O)₆]²⁺ will be _______ ×10^–21 [Nearest integer]

(Given : h = 6.63 × 10^–34 Js and c = 3.08 × 10⁸ ms^–1)

Answer: (765)

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]

Answer: (1143)

MATHEMATICS

SECTION-A

1. Let a circle C touch the lines L₁ : 4x – 3y +K₁ = 0 and L₂ : 4x – 3y + K₂ = 0, K₁, K₂∈ If a line passing through the centre of the circle C intersects L₁ at (–1, 2) and L₂ 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

(D) (x – 1)² + (y – 2)² = 16

Answer: (C)

2. The value of is equal to

(A) π²/4

(B) π²/2

(D) π/2

Answer: (C)

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

(D) 1

Answer: (A)

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

(D) 6

Answer: (C)

5. Let A be a 3 × 3 real matrix such that and If X = (x₁, x₂, x₃)T and I is an identity matrix of order 3, then the system has

(A) No solution

(B) Infinitely many solutions

(D) Exactly two solutions

Answer: (B)

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

(D) 91/49

Answer: (A)

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

(D) Both P1 and P2 are TRUE

Answer: (C)

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

(A) 1

(B) 2

(D) 5

Answer: (D)

9. Let f(x) be a polynomial function such that f(x) + f′(x) + f′′(x) = x⁵ + 64. Then, the value of

(A) −15

(B) −60

(D) 15

Answer: (A)

10. Let E₁ and E₂ be two events such that the conditional probabilities P(E₁|E₂) = 1/2, P(E₂|E₁) = 3/4 and P(E₁∩E₂) = 1/8. Then:

(A) P(E₁ ∩ E₂) = P(E₁) ∙ P(E₂)

(B) P(E’₁ ∩ E’₂) = P(E’₁) ∙ P(E₂)

(D) P(E’₁ ∩ E₂) = P(E₁) ∙ P(E₂)

Answer: (C)

11. Let If M and N are two matrices given by then MN² is

(A) a non-identity symmetric matrix

(B) a skew-symmetric matrix

(D) an identity matrix

Answer: (A)

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)

(D) g – g’ is increasing in (0, π/2)

Answer: (D)

13. Let f :R→R and g : R → R be two functions defined by f(x) = loge(x² + 1) – e^–x + 1 and Then, for which of the following range of α, the inequality holds?

(A) (2, 3)

(B) (–2, –1)

(D) (–1, 1)

Answer: (A)

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

(D) 7

Answer: (B)

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

(D) a point of inflection

Answer: (B)

16. If y = m₁x + c₁ and y = m₂x + c₂, m₁≠ m₂ are two common tangents of circle x² + y² = 2 and parabola y² = x, then the value of 8|m1m2| is equal to :

(A) 3 + 4√2

(B) −5 + 6√2

(D) 7 + 6√2

Answer: (C)

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 QR² is equal to :

(A) 2

(B) 5

(D) 11

Answer: (B)

18. If the solution curve y = y(x) of the differential equation y²dx + (x² – xy + y²)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

(D) π/6

Answer: (C)

19. Let x = 2t, y = t²/3 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

(D) 13/18

Answer: (D)

20. Let a circle C in complex plane pass through the points z₁ = 3 + 4i, z₂ = 4 + 3i and z₃ = 5i. If z(≠ z₁) is a point on C such that the line through z and z₁ is perpendicular to the line through z₂ and z₃, then arg(z) is equal to:

Answer: (B)

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, C₁ + 3⋅2 C₂ + 5⋅3 C₃ + … upto 10 terms then the value of α + β is equal to _____

Answer: (286*)

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

Answer: (63)

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

Answer: (576)

24. Let the abscissae of the two points P and Q be the roots of 2x² – rx + p = 0 and the ordinates of P and Q be the roots of x² – sx – q = 0. If the equation of the circle described on PQ as diameter is 2(x² + y²) – 11x – 14y – 22 = 0, then 2r + s – 2q + p is equal to _________.

Answer: (7)

25. The number of values of x in the interval for which 14cosec²x – 2 sin²x = 21 – 4 cos²x holds, is ___________.

Answer: (4)

26. For a natural number n, let a_n = 19ⁿ – 12ⁿ. Then, the value of is

Answer: (4)

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 ___________.

Answer: (2)

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 L₁ and L₂, then the value of a + b + d is equal to _______.

Answer: (5)

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 ____________.

Answer: (414)

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 ________.

Answer: (98)

JEE Main Session 1 24th June 2022 Shift 1 Question Paper and Answer Key

December 6, 2022December 2, 2022 by suresh84

JEE Main 2022 Session 1 June 24 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. The bulk modulus of a liquid is 3 × 10¹⁰ Nm⁻². The pressure required to reduce the volume of liquid by 2% is :

(A) 3 × 10⁸ Nm⁻²

(B) 9 × 10⁸ Nm⁻²

(D) 12 × 10⁸ Nm⁻²

Answer: (C)

2. Given below are two statements : One is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : In an uniform magnetic field, speed and energy remains the same for a moving charged particle.

Reason (R) : Moving charged particle experiences magnetic force perpendicular to its direction of motion.

(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)

(D) (A) is false but (R) is true.

Answer: (A)

3. Two identical cells each of emf 1.5 V are connected in parallel across a parallel combination of two resistors each of resistance 20Ω. A voltmeter connected in the circuit measures 1.2 V. The internal resistance of each cell is

(A) 2.5Ω

(B) 4Ω

(D) 10Ω

Answer: (C)

4. Identify the pair of physical quantities which have different dimensions :

(A) Wave number and Rydberg’s constant

(B) Stress and Coefficient of elasticity

(D) Specific heat capacity and Latent heat

Answer: (D)

5. A projectile is projected with velocity of 25 m/s at an angle θ with the horizontal. After t seconds its inclination with horizontal becomes zero. If R represents horizontal range of the projectile, the value of θ will be : [use g = 10 m/s²]

Answer: (D)

6. A block of mass 10 kg starts sliding on a surface with an initial velocity of 9.8 ms⁻¹. The coefficient of friction between the surface and bock is 0.5. The distance covered by the block before coming to rest is : [use g = 9.8 ms⁻²]

(A) 4.9 m

(B) 9.8 m

(D) 19.6 m

Answer: (B)

7. A boy ties a stone of mass 100 g to the end of a 2 m long string and whirls it around in a horizontal plane. The string can withstand the maximum tension of 80 N. If the maximum speed with which the stone can revolve is A boy ties a stone of mass 100 g to the end of a 2 m long string and whirls it around in a horizontal plane. The string can withstand the maximum tension of 80 N. If the maximum speed with which the stone can revolve is

(A) 400

(B) 300

(D) 800

Answer: (C)

8. A vertical electric field of magnitude 4.9 × 10⁵ N/C just prevents a water droplet of a mass 0.1 g from falling. The value of charge on the droplet will be : (Given g = 9.8 m/s²)

(A) 1.6 × 10⁻⁹ C

(B) 2.0 × 10⁻⁹ C

(D) 0.5 × 10⁻⁹ C

Answer: (B)

9. A particle experiences a variable force in a horizontal x-y plane. Assume distance in meters and force is newton. If the particle moves from point (1, 2) to point (2, 3) in the x-y plane, the Kinetic Energy changes by

(A) 50.0 J

(B) 12.5 J

(D) 0 J

Answer: (C)

10. The approximate height from the surface of earth at which the weight of the body becomes 1/3 of its weight on the surface of earth is : [Radius of earth R = 6400 km and √3 = 1.732]

(A) 3840 km

(B) 4685 km

(D) 4267 km

Answer: (B)

11. A resistance of 40 Ω is connected to a source of alternating current rated 220 V, 50 Hz. Find the time taken by the current to change from its maximum value to rms value :

(A) 2.5 ms

(B) 1.25 ms

(D) 0.25 s

Answer: (A)

12. The equations of two waves are given by :

y₁ = 5 sin2π(x – vt) cm

y₂ = 3sin2π(x – vt + 1.5)cm

These waves are simultaneously passing through a string. The amplitude of the resulting wave is

(A) 2 cm

(B) 4 cm

(D) 8 cm

Answer: (A)

13. A plane electromagnetic wave travels in a medium of relative permeability 1.61 and relative permittivity 6.44. If magnitude of magnetic intensity is 4.5 × 10⁻² Am⁻¹ at a point, what will be the approximate magnitude of electric field intensity at that point ?

(Given : permeability of free space μ₀ = 4π × 10⁻⁷ NA⁻², speed of light in vacuum c = 3 × 10⁸ ms⁻¹)

(A) 16.96 Vm⁻¹

(B) 2.25 × 10⁻² V^m−1

(D) 6.75 × 10⁶ Vm⁻¹

Answer: (C)

14. Choose the correct option from the following options given below :

(A) In the ground state of Rutherford’s model electrons are in stable equilibrium. While in Thomson’s model electrons always experience a net-force.

(B) In the ground state of Rutherford’s model electrons are in stable equilibrium. While in Thomson’s model electrons always experience a net-force.

(D) The positively charged part of the atom possesses most of the mass in Rutherford’s model but not in Thomson’s model.

Answer: (C)

15. Nucleus A is having mass number 220 and its binding energy per nucleon is 5.6 MeV. It splits in two fragments ‘B’ and ‘C’ of mass numbers 105 and 115. The binding energy of nucleons in ‘B’ and ‘C’ is 6.4 MeV per nucleon. The energy Q released per fission will be :

(A) 0.8 MeV

(B) 275 MeV

(D) 176 MeV

Answer: (D)

16. A baseband signal of 3.5 MHz frequency is modulated with a carrier signal of 3.5 GHz frequency using amplitude modulation method. What should be the minimum size of antenna required to transmit the modulated signal ?

(A) 42.8 m

(B) 42.8 mm

(D) 21.4 m

Answer: (C)

17. A Carnot engine whose heat sinks at 27°C, has an efficiency of 25%. By how many degrees should the temperature of the source be changed to increase the efficiency by 100% of the original efficiency ?

(A) Increases by 18°C

(B) Increase by 200°C

(D) Increase by 73°

Answer: (B)

18. A parallel plate capacitor is formed by two plates each of area 30π cm² separated by 1 mm. A material of dielectric strength 3.6 × 10⁷ Vm⁻¹ is filled between the plates. If the maximum charge that can be stored on the capacitor without causing any dielectric breakdown is 7 × 10⁻⁶ C, the value of dielectric constant of the material is :

(A) 1.66

(B) 1.75

(D) 2.33

Answer: (D)

19. The magnetic field at the centre of a circular coil of radius r, due to current I flowing through it, is B. The magnetic field at a point along the axis at a distance r/2 from the centre is :

(A) B/2

(B) 2B

(C)

(D)

Answer: (C)

20. Two metallic blocks M₁ and M₂ of same area of cross-section are connected to each other (as shown in figure). If the thermal conductivity of M₂ is K then the thermal conductivity of M₁ will be : [Assume steady state heat conduction]

(A) 10 K

(B) 8 K

(D) 2 K

Answer: (B)

SECTION-B

21. 056 kg of Nitrogen is enclosed in a vessel at a temperature of 127°C. The amount of heat required to double the speed of its molecules is _____ k cal. (Take R = 2 cal mole⁻¹K⁻¹)

Answer: (12)

22. Two identical thin biconvex lenses of focal length 15 cm and refractive index 1.5 are in contact with each other. The space between the lenses is filled with a liquid of refractive index 1.25. The focal length of the combination is ______ cm.

Answer: (10)

23. A transistor is used in common-emitter mode in an amplifier circuit. When a signal of 10 mV is added to the base-emitter voltage, the base current changes by 10 μA and the collector current changes by 1.5 mA. The load resistance is 5 kΩ. The voltage gain of the transistor will be _____ .

Answer: (750)

24. As shown in the figure an inductor of inductance 200 mH is connected to an AC source of emf 220 V and frequency 50 Hz. The instantaneous voltage of the source is 0 V when the peak value of current is The value of a is ______.

Answer: (242)

25. Sodium light of wavelengths 650 nm and 655 nm is used to study diffraction at a single slit of aperture 0.5 mm. The distance between the slit and the screen is 2.0 m. The separation between the positions of the first maxima of diffraction pattern obtained in the two cases is ______ × 10⁻⁵

Answer: (3)

26. When light of frequency twice the threshold frequency is incident on the metal plate, the maximum velocity of emitted election 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 = x v₁, the value of x will be ______.

Answer: (2)

27. From the top of a tower, a ball is thrown vertically upward which reaches the ground in 6 s. A second ball thrown vertically downward from the same position with the same speed reaches the ground in 1.5 s. A third ball released, from the rest from the same location, will reach the ground in ________ s.

Answer: (3)

28. A ball of mass 100 g is dropped from a height h = 10 cm on a platform fixed at the top of vertical spring (as shown in figure). The ball stays on the platform and the platform is depressed by a distance h/2. The spring constant is _______ Nm⁻¹. (Use g = 10 ms⁻²)

Answer: (120)

29. In a potentiometer arrangement, a cell gives a balancing point at 75 cm length of wire. This cell is now replaced by another cell of unknown emf. If the ratio of the emf’s of two cells respectively is 3 : 2, the difference in the balancing length of the potentiometer wire in above two cases will be ______ cm.

Answer: (25)

30. A metre scale is balanced on a knife edge at its centre. When two coins, each of mass 10 g are put one on the top of the other at the 10.0 cm mark the scale is found to be balanced at 40.0 cm mark. The mass of the metre scale is found to be x × 10⁻² The value of x is _________.

Answer: (6)

CHEMISTRY

SECTION-A

1. A metre scale is balanced on a knife edge at its centre. When two coins, each of mass 10 g are put one on the top of the other at the 10.0 cm mark the scale is found to be balanced at 40.0 cm mark. The mass of the metre scale is found to be x × 10⁻² The value of x is

(A) 1188 g and 1296 g

(B) 2376 g and 2592 g

(D) 3429 g and 3142 g

Answer: (C)

2. Consider the following pairs of electrons

The pairs of electron present in degenerate orbitals is/are:

(A) Only A

(B) Only B

(D) (B) and (C)

Answer: (B)

3. Match List-I with List-II

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

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

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

Answer: (B)

4. For a reaction at equilibrium

the relation between dissociation constant (K), degree of dissociation (α) and equilibrium pressure (p) is given by :

Answer: (B)

5. Given below are two statements :

Statement I : Emulsions of oil in water are unstable and sometimes they separate into two layers on standing.

Statement II :For stabilisation of an emulsion, excess of electrolyte is added. In the light of the above statements, choose the most appropriate answer from the options given below :

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

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

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

Answer: (C)

6. Given below are the oxides:

Na₂O, As₂O₃, N₂O, NO and Cl₂O₇

Number of amphoteric oxides is:

(A) 0

(B) 1

(D) 3

Answer: (B)

7. Match List – I with List – II

Choose the most appropriate answer from the options given below:

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

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

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

Answer: (A)

8. The highest industrial consumption of molecular hydrogen is to produce compounds of element:

(A) Carbon

(B) Nitrogen

(D) Chlorine

Answer: (B)

9. Which of the following statements are correct ?

(A) Both LiCl and MgCl₂ are soluble in ethanol.

(B) The oxides Li₂O and MgO combine with excess of oxygen to give superoxide.

(D) Li₂O is more soluble in water than other alkali metal oxides.

Choose the most appropriate answer from the options given below:

(A) (A) and (C) only

(B) (A), C) and (D) only

(D) (A) and (C) only

Answer: (A)

10. Identify the correct statement for B₂H₆ from those given below.

(A) In B₂H₆, all B-H bonds are equivalent.

(B) In B₂H₆ there are four 3-centre-2-electron bonds.

(D) B₂H₆ can be synthesized form both BF₃ and NaBH₄.

(E) B₂H₆ is a planar molecule.

Choose the most appropriate answer from the options given below :

(A) (A) and (E) only

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

(D) (C) and (E) only

Answer: (C)

11. The most stable trihalide of nitrogen is:

(A) NF₃

(B) NCl₃

(D) NI₃

Answer: (A)

12. Which one of the following elemental forms is not present in the enamel of the teeth?

(A) Ca²⁺

(B) P³⁺

(D) P⁵⁺

Answer: (B)

13. In the given reactions sequence, the major product ‘C’ is :

Answer: (B)

14. Two statements are given below :

Statement I: The melting point of monocarboxylic acid with even number of carbon atoms is higher than that of with odd number of carbon atoms acid immediately below and above it in the series.

Statement II : The solubility of monocarboxylic acids in water decreases with increase in molar mass.

Choose the most appropriate option:

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

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

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

Answer: (A)

15. Which of the following is an example of conjugated diketone?

Answer: (C)

16.

The major product of the above reaction is

Answer: (D)

17. Which of the following is an example of polyester?

(A) Butadiene-styrene copolymer

(B) Melamine polymer

(D) Poly-β-hydroxybutyrate-co-β-hydroxy valerate

Answer: (D)

18. A polysaccharide ‘X’ on boiling with dil H₂SO₄ at 393 K under 2-3 atm pressure yields ‘Y’.

‘Y’ on treatment with bromine water gives gluconic acid. ‘X’ contains β-glycosidic linkages only. Compound ‘X’ is :

(A) starch

(B) cellulose

(D) amylopectin

Answer: (B)

19. Which of the following is not a broad spectrum antibiotic?

(A) Vancomycin

(B) Ampicillin

(D) Penicillin G

Answer: (D)

20. During the qualitative analysis of salt with cation y²⁺ , addition of a reagent (X) to alkaline solution of the salt gives a bright red precipitate. The reagent (X) and the cation (y²⁺) present respectively are:

(A) Dimethylglyoxime and Ni²⁺

(B) Dimethylglyoxime and Co²⁺

(D) Nessler‟s reagent and Ni²⁺

Answer: (A)

SECTION-B

21. Atoms of element X form hcp lattice and those of element Y occupy 2/3 Atoms of element X form hcp lattice and those of element Y occupy ________ (Nearest Integer)

Answer: (43)

22. 2O₃(g) ⇌ 3O₂(g)

At 300 K, ozone is fifty percent dissociated. The standard free energy change at this temperature and 1 atm pressure is (–) _______J mol ^–1 (Nearest integer) [Given: ln 1.35 = 0.3 and R = 8.3 J K^–1 mol^–1]

Answer: (747)

23. The osmotic pressure of blood is 7.47 bar at 300 K. To inject glucose to a patient intravenously, it has to be isotonic with blood. The concentration of glucose solution in gL–1 is _______ (Molar mass of glucose = 180 g mol^–1 R = 0.083 L bar K^–1 mol^–1) (Nearest integer)

Answer: (54)

24. The cell potential for the following cell

Pt|H₂(g)|H⁺(aq)||Cu²⁺(0.01M)|Cu(s)

is 0.576 V at 298 K. The pH of the solution is ___. (Nearest integer)

Answer: (5)

25. The rate constants for decomposition of acetaldehyde have been measured over the temperature range 700 –1000 K. The data has been analysed by plotting In k vs 10³/T graph. The value of activation energy for the reaction is___ kJ mol^–1. (Nearest integer) (Given : R = 8.31 J K^–1 mol^–1)

Answer: (154)

26. The difference in oxidation state of chromium in chromate and dichromate salts is _______

Answer: (0)

27. In the cobalt-carbonyl complex: [Co₂(CO)₈], number of Co-Co bonds is “X” and terminal CO ligands is “Y”. X + Y =______

Answer: (7)

28. A 0.166 g sample of an organic compound was digested with cone. H2SO4 and then distilled with NaOH. The ammonia gas evolved was passed through 50.0 mL of 0.5 N H₂SO₄. The used acid required 30.0 mL of 0.25 N NaOH for complete neutralization. The mass percentage of nitrogen in the organic compound is____.

Answer: (63)

29. Number of electrophilic centre in the given compound is _______

Answer: (3)

30. The major product ‘A’ of the following given reaction has _____ sp² hybridized carbon atoms. 2,7 – Dimethyl1 – 2, 6 – octadiene

Answer: (2)

MATHEMATICS

SECTION-A

1. Let A = {z ∈ C : 1 ≤ |z – (1 + i) |≤2 and

B = {z ∈ A : | z – (1 – i) | = 1}. Then, B:

(A) is an empty set

(B) contains exactly two elements

(D) is an infinite set

Answer: (D)

2. The remainder when 3²⁰²² is divided by 5 is

(A) 1

(B) 2

(D) 4

Answer: (D)

3. The surface area of a balloon of spherical shape being inflated, increases at a constant rate. If initially, the radius of balloon is 3 units and after 5 seconds,, it becomes 7 units, then its radius after 9 seconds is :

(A) 9

(B) 10

(D) 12

Answer: (A)

4. Bag A contains 2 white, 1 black and 3 red balls and bag B contains 3 black, 2 red and n white balls. One bag is chosen at random and 2 balls drawn from it at random, are found to be 1 red and 1 black. If the probability that both balls come from Bag A is 6/11, then n is equal to _____ .

(A) 13

(B) 6

(D) 3

Answer: (C)

5. Let x² + y² + Ax + By + C = 0 be a circle passing through (0, 6) and touching the parabola y = x² at (2, 4). Then A + C is equal to______.

(A) 16

(B) 88/5

(D) −8

Answer: (A)

6. The number of values of α for which the system of equations :

x + y + z = α

x + 2 αy + 3z = −1

x + 3 αy + 5z = 4

is inconsistent, is

(A) 0

(B) 1

(D) 3

Answer: (B)

7. If the sum of the squares of the reciprocals of the roots α and β of the equation 3x² + λx – 1 = 0 is 15, then 6(α³ + β³) is equal to :

(A) 18

(B) 24

(D) 96

Answer: (B)

8. The set of all values of k for which (tan⁻¹ x)³ + (cot⁻¹ x)³ = kπ³, x ∈ R, is the interval:

Answer: (A)

9. Let S = {√n : 1 ≤ 1 ≤ n ≤ 50 and n is odd}

Let a ∈ S and

If then λ is equal to

(A) 218

(B) 221

(D) 1717

Answer: (B)

10. f(x) = 4 log_e(x – 1) –2x² + 4x +5, x > 1, which one of the following is NOT correct ?

(A) f is increasing in (1, 2) and decreasing in (2, ∞)

(B) f(x)= –1 has exactly two solutions

(D) f(x) = 0 has a root in the interval (e, e +1)

Answer: (C)

11. The tangent at the point (x₁, y₁) on the curve y = x³ +3x² + 5 passes through the origin, then (x₁, y₁) does NOT lie on the curve :

Answer: (D)

12. The sum of absolute maximum and absolute minimum values of the function f(x) = |2x² + 3x – 2| + sin x cos x in the interval [0, 1] is:

Answer: (B)

13. If where n is an even integer , is an arithmetic progression with common difference 1, and then n is equal to:

(A) 48

(B) 96

(D) 104

Answer: (B)

14. If x = x(y) is the solution of the differential equation x (1) = 0; then x(e) is equal to :

(A) e³(e^e – 1)

(B) e^e(e³ – 1)

(D) e^e(e² – 1)

Answer: (A)

15. Let λx – 2y = μ be a tangent to the hyperbola a²x² – y² = b². Then is equal to :

(A) −2

(B) −4

(D) 4

Answer: (D)

16. Let be unit vectors. If be a vector such that the angle between is π/12, and is equal to

(A) 6(3 – √3)

(B) 3 + √3

(D) 6(√3 + 1)

Answer: (C)

17. If a random variable X follows the Binomial distribution B (33, p) such that 3P(X = 0) = P(X = 1), then the value of is equal to

(A) 1320

(B) 1088

(D) 1088/1089

Answer: (A)

18. The domain of the function

Answer: (*)

19. Let If then T + n(S) is equal

(A) 7 + √3

(B) 9

(D) 10

Answer: (B)

20. The number of choices of ∆ ∈ {⋀, ⋁, ⇒, ⟺}, such that (p∆q) ⇒ ((p∆~q) ⋁ ((~p)∆q)) is a tautology, is

(A) 1

(B) 2

(D) 4

Answer: (B)

SECTION-B

21. The number of one-one function f : {a, b, c, d} → {0, 1, 2, … .,10} such that 2f(a) – f(b) + 3f(c) + f(d) = 0 is _____.

Answer: (31)

22. In an examination, there are 5 multiple choice questions with 3 choices, out of which exactly one is correct There are 3 marks for each correct answer, −2 marks for each wrong answer and 0 mark if the question is not attempted. Then, the number of ways a student appearing in the examination gets 5 marks is________.

Answer: (*)

23. Let be a fixed point in the xy-plane. The image of A in y-axis be B and the image of B in x-axis be C. If D(3 cos θ, a sin θ) is a point in the fourth quadrant such that the maximum area of ∆ACD is 12 square units, then a is equal to _______.

Answer: (8)

24. Let a line having direction ratios 1, −4, 2 intersect the lines and at the point A and B. Then (AB)² is equal to __________.

Answer: (84)

25. The number of points where the function

[t] denotes the greatest integer ≤ t, is discontinuous is _________.

Answer: (7)

26. Let Then the value of is __________.

Answer: (1)

27. Let If then α₁ + α₂ is equal to __________

Answer: (34)

28. If two tangents drawn from a point (α, β) lying on the ellipse 25x² + 4y² = l to the parabola y2 = 4x are such that the slope of one tangent is four times the other, then the value of (10α + 5)² + (16β² + 50)² equals __________

Answer: (2929)

29. Let S be the region bounded by the curves y = x³ and y² = x. The curve y = 2|x| divides S into two regions of areas R₁ and R₂.

If max {R₁, R₂} = R₂, then R₂/R₁ is equal to __________.

Answer: (19)

30.If the shortest distance between the line and then the integral value of a is equal to

Answer: (2)