JEE FULL TEST (30.08.2025)

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Welcome to your JEE FULL TEST (30.08.2025)

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IMPORTANT INSTRUCTIONS

1. The test is of 3 hours duration and Test Booklet contains 75 questions. Each question carried 4 marks for each correct response, the candidate will get 4 marks. For each incorrect response, one mark will be deducted from the total scores. The maximum marks are 300.
2. There are three subject in the question paper containing Physics, Chemistry, Mathematics and having 25 questions in each part.
3. Use of Cell phone/Electronics gadgets/Calculator etc. are not allowed.

PHYSICS

1. An object is placed on the principal axis of a concave mirror at a distance of 1.5 f (f is the focal length). The image will be at,

1) 5f
2) −1.5f
3) 3f
4) −3f

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2. A thin prism having refracting angle 10∘ is made of glass of refracting index 1.42. This prism is combined with another thin prism of glass of refractive index 1.7. This combination produces dispersion without deviation. The refracting angle of second prism should be:

1) 6°
3) 10°
2) 8°
4) 4°

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3. Two thin convex lenses of focal length 20 cm and 25 cm are placed at a finite distance apart. The power of the combination is 8 D. Distance between the lenses is

1) 5 cm
3) 8 cm
2) 10 cm
4) 4 cm

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4. A ray of light strikes a transparent rectangular slab of refractive index √2 at an angle of incidence of 45∘. The angle between the reflected and refracted rays is

1) 75°
3) 105°
2) 90°
4) 120°

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5. A concave shaving mirror has a radius of curvature of 35.0cm. It is positioned so that the (upright) image of man’s face is 2.50 times the size of the face. How far is the mirror from the face?

1) 5.25cm
2) 21.0cm
3) 10.5cm
4) 42cm

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6. A body of mass 1 kg is dropped from a height of 500 m above the ground and undergoes inelastic collision. If the impulse imparted to the ground is 150 Ns, then the maximum height reached by the ball after collision is (take g = 10 m/s²)

1) 100 m
2) 200 m
3) 150 m
4) 125 m

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7. In the figure below, find the contact force between the 8 kg and the 5 kg block.

1) 32 N
2) 35 N
3) 20 N
4) 37 N

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8. In the diagram below, the normal reaction between the 2 kg and 3 kg is (consider the surface to be smooth: take g = 10 m/s²)

1) 39 N
2) 25 N
3) 12 N
4) 35 N

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9. A ball with initial momentum strikes a wall and bounces off. If the ball comes back along the same path with a quarter of its initial velocity, then the initial velocity of the ball if the change in momentum is -10 Ns is

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10. A 40 kg mass is initially at rest on a rough bench and a 10 kg mass is attached to it as shown. A frictional force of 20 N opposes the motion of the 40 kg mass. The speed of the 10 kg mass after 5 seconds of their motion is (take g = 10 m/s²)

1) 0 m/s
2) 3.2 m/s
3) 4 m/s
4) 8 m /s

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11. Two charges +3q and -q are placed at the vertices B and C of an isosceles triangle as shown in the figure. The potential at the vertex A is

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12. Work done in carrying a charge Q once around a circle of radius R with charge Q at the centre of a circle is

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13. Two points P and Q are maintained at the potentials 10V and 4V respectively. The work done in moving an electron from P to Q is

1) 9.6×10^-19 J
2) -9.6×10^-19 J
3) 2.24×10^-19 J
4) -.24×10^-19 J

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14. Two charges of 4μC each are placed at the corners A and B of an equilateral triangle of side length 0.2 m in air. The electric potential at C is

1) 9×4 V
2) 18×10⁴V
3) 36×10⁴ V
4) 36×10^-4 V

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15. A metallic sphere of radius 10 m is charged such that potential at its surface is 120 V. The potential at the centre of the sphere is

1) 120 V
2) Zero
3) 12 V
4) 1200 V

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16. Consider the following statements:
a) Acceleration due to gravity depends only on mass of the body.
b) linear momentum of a planet is constant.
c) acceleration due to gravity depends on mass of planet.
d) Kepler’s laws apply only to the planets that move around the sun.
Which of the above statements are NOT correct?

1) (a) and (b) only
2) (a), (b) and (d) only
3) (a), (b) and (c) only
4) (b) and (c) only

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17. A projectile is fired from the surface of the earth with a velocity of 9.8 m/s and angle 𝜃 with the horizontal. Another projectile fired from another planet with a velocity of 4.9 m/s at the same angle follows a trajectory of the projectile fired from the earth. The value of the acceleration due to gravity on the planet is (given, g = 9.8 m/s2):

1) 2.45
2) 3.45
3) 4.25
4) 5.25

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18. A car of mass 1000 kg is moving with a velocity of 20 m/s. If the engine of the car can provide a constant power of 50 kW, then the car will attain a velocity of 40 m/s in:

1) 10 seconds
2) 12 seconds
3) 14 seconds
4) 18 seconds

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19. A point mass ′m′ is moved in a vertical circle of radius ′r′ with the help of a string. The velocity of the mass is √πgr at the lowest point. The tension in the string at the lowest point is:

1). mg(1+π)
2). mg(1-π)
3). mg/π
4). None of these

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20. A pump delivers water at the rate of V cubic meter per second. By what factor its power should be raised so that it delivers water at the rate of nV cubic metre per second?:

1). n³
2). √n
3). n
4). n²

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21. The acceleration due to gravity at height 1 km above the earth’s surface is same as at a depth d below the earth’s surface, then d equals:

1) 1 km
2) 2 km
3) 3 km
4) 4 km

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22. For a particle moving in a vertical circle, the total energy at different position along the path is:

1) Decreases
2). Increases
3) May increase or decrease
4) Conserved

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23. An engine is used to pump a liquid of density ρ through a pipe of cross-sectional area A. If the speed of flow of liquid is v, then the rate at which kinetic energy is being imparted to the liquid is:

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24. A man does a given amount of work in 10 sec. Another man does the same amount of work in 20 sec. The ratio of the output power of the first man to the second man is:

1) 1
2) 2
3) 1/2
4) 2/1

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25. Study the two statements labelled as Assertion (A) and Reason (R).
Assertion: Power of the machine gun is determined by both the number of bullets fired per seconds and kinetic energy of bullets.
Reason: Power of any machine is defined as work done per unit time.
Mark the correct choice as, if:

1) Both, A and R, are true and R is the correct explanation of A
2) Both, A and R, are true but R is not the correct explanation of A
3) If A is true but R is false
4) If A is false but R is true

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CHEMISTRY

26. The number of radial and angular nodes in 4p orbital are

1) 2, 0
2) 2,1
3) 2
4) 1

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27. The ionization enthalpy of H- atom is 1.312 X 10⁶ J/mol. The energy required to excite the electron in the atom from n=1 to n=2 is

1) 1.46 X 10 ⁵ J/mol
2) 9.1 X 10 ⁵ J/mol
3) 9.85 X 10 ⁵ J/mol
4) 1. 57 X 10 ⁶ J/mol

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28. The uncertainty in momentum of an electron is 1× 10^-5 m/s. The uncertainty in its position will be (h=6.62X10^-34 kg /s)

1) 1.25 X 10^-34 m
2) 3.01 X 10^-34 m
3) 5.27 x 10^-30 m
4) 5.27 x 10^-20 m

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29. The following quantum numbers are possible for how many orbitals n=3, l=2, m_l =0

1) 5
2) 4
3) 1
4) 3

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30. Maximum number of electrons in a subshell with l=2, n=3 is

1) 8
2) 10
3) 18
4) 32

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31. The de-Broglie wavelength of a cricket ball of mass 60g moving with a velocity of 10meters per second is approximately (h = 6.63 X 10^-34 Js)

1) 1.1 X 10 ^-31 meters
2) 1.1 X 10 ^-30 meters
3) 1.1 X 10 ^-28 meters
4) 1.1 X 10 ^-33 meters

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32. Which of the following set is non permissible?

1) n=4, l= 3, m=0
2) n=4, l= 2, m= 1
3) n= 4, l= 4, m=1
4) n=4, l=0, m= 0

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33. The following solutions were prepared by dissolving 10g of glucose (C₆H₁₂O₆) in 250ml of water (P1). 10g of urea (CH₄N₂O) in 250ml of water(P₂) and 10g of sucrose (C₁₂H₂₂O₁₂) in 250ml of water(P₃). The decreasing order of osmotic pressure of these solutions is:

1) P₂ > P₃ > P₁
2) P₃ > P₁ > P₂3) P₂ > P₁ > P₃
4) P₁ > P₂ > P₃

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34. The correct option for the value of vapour pressure of a solution at 45^oC with benzene to octane in a molar ratio 3:2 is: [At 45^oC vapour pressure of benzene is 280 mmHg and that of octane is 420 mmHg. Assume ideal Gas]

1) 336 mm of Hg
2) 350 mm of Hg
3) 160 mm of Hg
4) 168 mm of Hg

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35. The freezing point depression constant (K_f) of benzene is 5.12Kkgmol^-1. The freezing point depression for the solution of molality 0.078m containing a non-electrolyte solute in benzene is (rounded off upto two decimal places):

1) 0.40K
2) 0.60K
3) 0.20K
4) 0.80K

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36. At 100^oC the vapour pressure of a solution of 6.5g of a solute in 100g of water is 732 mm. If K_b = 0.52, the boiling point of this solution will be:

1) 103^oC
2) 101^oC
3) 100^oC
4) 102^oC

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37. Which one of the following electrolytes has the same value of van’t Hoff’s factor (i) as tht of Al₂(SO₄)₃ (If all are 100% ionised)

1) K₄[Fe (CN)₆]
2) K₂SO₄3) K₃[Fe (CN)₆]
4) Al (NO₃)₃

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38. If osmotic pressure of 4% (w/v) solution of sucrose is same as 2% (w/v) solution of “X”, then the molecular mass of X (g/mol) is

1) 171
2) 205.2
3) 570
4) 150

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39. How much NaNO₃ must be weighed out to make 40 mL of an aqueous solution containing 65 mg of Na+ ions per mL ?

1) 12.9 g
2) 9.6 g
3) 8.5 g
4) 6.7 g

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40. In the reaction
4NH3 (g) + 5O2 (g) —-> 4NO (g) + 6H2O (l)
When 1 mole of Ammonia and 1 mole of O2 are
made to react to completion then :
1) 1 mole of H2O is produced
2) 1 mole of NO will be produced
3) All the Oxygen will be consumed
4) All the Ammonia will be consumed

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41. Volume of CO₂obtained by the complete decomposition of 9.85 g BaCO₃ at STP is (Gram atomic mass of Ba = 137.33 g per mole)

1) 2.24 L
2) 1.12 L
3) 0.84 L
4) 0.56 L

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42. 15 g of hydrofluoric acid gas occupies 5.6 litres of volume at NTP. If the Empirical formula of the gas is HF, then its molecular formula will be

1) HF
2) H₂F₂3) H₃F₃4) H₄F₄

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43. Two elements X (atomic mass 16) and Y (atomic mass 14) combine to form compounds A,B and C. The ratio of different masses of Y which combine with a fixed mass of X in A,B and C is 1:3:5. If 32 parts by mass of X combines with 84 parts by mass of Y in B, then in C, 8 parts by mass of X will combine with how many parts by mass of Y ?

1) 28
2) 70
3) 35
4) 50

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44. 1 litre of mixture of CO and CO₂is passed through red hot charcoal in tube. The new volume becomes 1.4 litre. Find out % composition of mixture by volume. All measurements are made at same P and T.

1) 50% CO, 50% CO₂
2) 40% CO, 60% CO₂
3) 60% CO, 40% CO₂
4) 10% CO, 90% CO₂

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45. Given below are two statements:
Statement I: o-Nitrophenol is steam volatile due to intramolecular hydrogen bonding.
Statement II: o-Nitrophenol has high melting point due to hydrogen bonding.
In the light of the above statements, choose the most appropriate answer from the options given below:

1) Both Statement I and Statement II are false
2) Statement I is true but Statement II is false
3) Both Statement I and Statement II are true
4) Statement I is false but Statement II is true

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46. Which one of the following compounds does not decolourize bromine water?

1) Phenol
2) aniline
3) cyclohexane
4) Ethene

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47. Which of the following conformation is most stable?

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48. In Kjeldahl’s method, nitrogen present is estimated as

1) N₂
2) NO
3) NH₃4) NO₂

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49. The correct stability order for the following species is

1) (II)> (IV)> (I)> (III)
2) (I)> (III)> (II) >(IV)
3) (I) >(II) >(III)> (IV)
4) (II) > (I)> (IV) >(III)

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50. The I.U.P.A.C. name of

1) 3–Methyl cyclohexene
2) 1–methyl cylohex–2–ene.
3) 6–methyl cyclohexene
4) 1–methyl cyclohex5–ene

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MATHEMATICS

(Attempt only 25 questions)

51. f:R →R is defined by f(x) = x² – 2x + 1. Find f(f(x))

1) x⁴ + 4x³ – 4x²
2) x⁴ – 4x³ + 4x²3) x⁴ + 4x³ + 4x²
4) x⁴ – 4x³ – 4x²

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53. Let ω₁ be a point obtained by the rotation of z₁=5+4i about the origin through a right angle in the anticlockwise direction, and ω₂ be the point through a right angle in the clockwise direction. Then the principal argument ω₁-ω₂ is equal to

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54. A set S contains 3 elements, the number of which of the following sets is 256

1) S
2) P(S)
3) P(P(S))
4) P(P(P(S)))

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55. The value of for which the system of equations 2x-y+2z=2, x-2y+z=-4, x+y+λz=4 has no solution is

1) 0
2) 2
3) 4
4) 5

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56. Let n(U)=700, n(A)=200, n(B)=300, n(A∩B)=100, then n(A’∩B’) is equal to

1) 400
2) 600
3) 300
4) None of these

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57. Let A={1,2,3} and let R={(1,1),(2,2),(3,3),(1,3),(3,2),(1,2)}. Then R is

1) reflexive and symmetric but not reflexive
2) reflexive and transitive but not symmetric
3) symmetric and transitive but not reflexive
4) an equivalence relation

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1) (-1,1)
2) {-1,1}
3) (-∞,-1)
4) (1,∞)

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60. Let S={1,2,3}. The function f:S→S defined as below have inverse for

1) f={(1,2),(2,2),(3,3)}
2) f={(1,2),(2,1),(3,1)}
3) f={(1,3),(3,2),(2,1)}
4) f={(1,3),(2,3),(2,1)}

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61. The system of equations, +y+z=6, x+2y+3z=14, x+3y+5z=20 has

1) infinitely many solutions
2) a unique solution
3) only finitely many solutions
4) no solution

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62. Consider the following statements:

I: If A = {x: x is an even natural number} and B = {y: y is a natural number}, A subset B.
II: Number of subsets for the given set A = {5, 6, 7, 8) is 15.
III: Number of proper subsets for the given set A = {5, 6, 7, 8) is 15.
Which of the following statement(s) is/are correct?

1) I and II
2) I and III
3) II and III
4) None of the above

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63. The region represented by {z=x_iy∈C:|z|-Re(z)≤1} is also given by the inequality

1) y²≥2(x+1)
2) y²≤2x+1
3) y²≤(x+1/2)
4) y²≥x+1

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64. Let A = {1, 2, 3, …, 50} and R be the relation “is square of” on 𝐴. Then 𝑅 as a subset of A×A is written as:

1) {(1,1),(2,2),(3,3),(4,4),(5,5),(6,6), (7, 7)}
2) {(1, 1), (2, 5), (3, 9), (4, 15) (5, 25), (6, 36), (7, 49)}
3) {(1, 1), (4, 4), (9, 9), (16, 16) (25, 25), (36, 36), (49, 49)}
4) {(1, 1), (4, 2), (9, 3), (16, 4) (25, 5), (36, 6), (49, 7)}Deselect Answer

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65. If f(0)=0, f(1)=1, f(2)=2 and f(x)=f(x-2)+f(x-3) for x=3, 4, 5, &.., then f(9)=

1) 12
2) 13
3) 14
4) 10

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66. If A and B are two sets, then A∩(B-A) is:

1) A
2) ϕ
3) B
4) None of these

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67. If A={1, 2, 3}, and B={3, 6} then the number of relations from A to B is

1) 3²2) 2³3) 2⁴4) 2⁶

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68. Given the relation R={(1,2),(2,3)} on the set {1,2,3}, the minimum number of ordered pairs which when added to R make it an equivalence

1) 5
2) 6
3) 8
4) 7

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69. Which one of the following is correct? Here P(A) denotes the power set of a set A.

1) A∪P(A)=P(A)
2) A∩P(A)=A
3) A-P(A)=A
4) P(A)-{A}=P(A)

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72. The equation |z-i|=|z-1|, represents

1) a circle of radius 1/2
2) a circle of radius 1
3) the line through the origin with slope 1
4) none of these

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1) identity matrix
2) symmetric matrix
3) skew symmetric matrix
4) none of these

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78. Let A={1,2,3,4,5,6,7,8,9,10}. Then the number of subsets of A containing exactly two elements is

1) 45
2) 20
3) 35
4) 40

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79. The smallest positive integer for which is is

1) n=8
2) n=16
3) n=12
4) n=4

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1) k=7
2) k=-7
3) k=0
4) none of these

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Drawing Test (For B. Achitecture students only)
Answer any two.

1. You are a bird and you are flying above a city. Draw the view.
2. Imagine you are inside a pencil box. Draw the view
3. Imagine and draw a scene from a local cultural festival or fair
4. Draw from memory your grandparents’ face

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