JEE Main Sample Paper 1

A projectile is fired at an angle of 45° with the horizontal with speed 20 m/s. The maximum height reached is (g = 10 m/s²):

1. A.5 m
2. B.10 m✓
3. C.15 m
4. D.20 m

Correct answer: B

A block of mass 2 kg rests on a rough horizontal surface with coefficient of friction 0.5. The minimum horizontal force required to just move the block is (g = 10 m/s²):

1. A.5 N
2. B.10 N✓
3. C.15 N
4. D.20 N

Correct answer: B

A body of mass 1 kg falls freely from a height of 5 m. Its kinetic energy just before hitting the ground is (g = 10 m/s²):

1. A.25 J
2. B.50 J✓
3. C.75 J
4. D.100 J

Correct answer: B

Two resistors of 4 Ω and 12 Ω are connected in parallel. The equivalent resistance of the combination is:

1. A.3 Ω✓
2. B.6 Ω
3. C.8 Ω
4. D.16 Ω

Correct answer: A

Two point charges of 1 μC each are placed 3 m apart in vacuum. The magnitude of the electrostatic force between them is F × 10⁻³ N. The value of F is:

Correct answer: 1

In a p-n junction diode under forward bias:

1. A.The depletion region width increases
2. B.The depletion region width decreases✓
3. C.The potential barrier increases
4. D.No current flows through the junction

Correct answer: B

The number of moles in 22 g of CO₂ (molar mass 44 g/mol) is:

1. A.0.25
2. B.0.5✓
3. C.1.0
4. D.2.0

Correct answer: B

The maximum number of electrons that can be accommodated in a subshell with azimuthal quantum number l = 2 is:

1. A.6
2. B.8
3. C.10✓
4. D.14

Correct answer: C

Which of the following molecules has a linear shape?

1. A.H₂O
2. B.CO₂✓
3. C.NH₃
4. D.CH₄

Correct answer: B

For the equilibrium N₂(g) + 3H₂(g) ⇌ 2NH₃(g), an increase in pressure shifts the equilibrium:

1. A.In the backward direction
2. B.In the forward direction✓
3. C.It has no effect
4. D.First forward, then backward

Correct answer: B

The IUPAC name of CH₃—CH(CH₃)—CH₂—CH₃ is:

1. A.2-Methylbutane✓
2. B.3-Methylbutane
3. C.Pentane
4. D.Isopentene

Correct answer: A

The oxidation state of iron in K₄[Fe(CN)₆] is:

1. A.+1
2. B.+2✓
3. C.+3
4. D.+4

Correct answer: B

If z = 1 + i, then |z|² equals:

1. A.1
2. B.2✓
3. C.√2
4. D.4

Correct answer: B

If A is a 3 × 3 matrix with det(A) = 5, then det(2A) equals:

1. A.10
2. B.20
3. C.40✓
4. D.80

Correct answer: C

The number of ways the letters of the word EXAM can be arranged is:

1. A.12
2. B.16
3. C.24✓
4. D.32

Correct answer: C

The number of terms in the expansion of (x + y)¹⁰ is:

1. A.10
2. B.11✓
3. C.20
4. D.21

Correct answer: B

The value of lim(x→0) sin(3x)/x is:

Correct answer: 3

Two fair coins are tossed together. The probability of getting exactly one head is:

1. A.1/4
2. B.1/2✓
3. C.3/4
4. D.1/3

Correct answer: B