Sample JEE paper

 Creating a sample JEE (Joint Entrance Examination) paper requires combining questions from multiple sections of the exam. The JEE exam has two main components:

• JEE Main: This is an undergraduate admission test for various engineering courses in India, mainly focusing on Physics, Chemistry, and Mathematics.
• JEE Advanced: This is the second stage of the JEE exam, intended for students who qualify the JEE Main. It is more complex and covers more challenging questions.

Here’s a sample JEE paper that covers all three subjects: Physics, Chemistry, and Mathematics.

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JEE Main Sample Paper

Physics (Time: 1 Hour 30 Minutes)

Section A: Multiple Choice Questions (MCQs)

1. The electric field inside a conductor is zero under electrostatic conditions. Which of the following is true?

   • A) The electric field inside is zero only when the conductor is uncharged.
   • B) The electric field inside is zero only in the absence of external electric fields.
   • C) The electric field inside is zero only when the temperature of the conductor is zero Kelvin.
   • D) The electric field inside is zero under electrostatic conditions regardless of external factors.

2. A body is projected vertically upward with a speed of 20 m/s. What is the maximum height it will reach? (Take g = 10 m/s²)

   • A) 20 m
   • B) 40 m
   • C) 100 m
   • D) 50 m

3. In a parallel plate capacitor, the distance between the plates is doubled while the potential difference remains constant. How will the capacitance change?

   • A) It will remain the same.
   • B) It will be doubled.
   • C) It will be halved.
   • D) It will be quadrupled.

Section B: Numerical Answer Type

4. A metal rod of length 2 m is moving with a velocity of 5 m/s in a magnetic field of strength 0.2 T perpendicular to its length. What is the induced EMF across the ends of the rod?

5. A body with a mass of 10 kg is moving with a velocity of 15 m/s. What is the kinetic energy of the body?

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Chemistry (Time: 1 Hour 30 Minutes)

Section A: Multiple Choice Questions (MCQs)

1. Which of the following elements has the highest ionization energy?

   • A) Lithium
   • B) Oxygen
   • C) Neon
   • D) Sodium

2. The reaction: NaOH + HCl → NaCl + H₂O is an example of:

   • A) Redox reaction
   • B) Precipitation reaction
   • C) Neutralization reaction
   • D) Displacement reaction

3. Which of the following is the correct IUPAC name of the compound CH₃-CH₂-CH=CH₂?

   • A) 1-Butene
   • B) 2-Butene
   • C) Propene
   • D) Butane

Section B: Numerical Answer Type

4. Calculate the pH of a solution that has a hydrogen ion concentration of 1 × 10⁻⁴ M.

5. If the molar mass of CO₂ is 44 g/mol, how many grams of CO₂ are present in 2 moles of CO₂?

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Mathematics (Time: 1 Hour 30 Minutes)

Section A: Multiple Choice Questions (MCQs)

1. The solution set of the equation (x² + 5x + 6 = 0) is:

   • A) x = -1, -6
   • B) x = 1, 6
   • C) x = -2, -3
   • D) x = 2, 3

2. What is the value of the determinant of the matrix $\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$?

   • A) -2
   • B) 2
   • C) 1
   • D) 0

3. If a point (x, y) lies on the line y = 2x + 3, what is the value of y when x = 4?

   • A) 8
   • B) 7
   • C) 11
   • D) 12

Section B: Numerical Answer Type

4. Find the area of a triangle with vertices at A(0, 0), B(4, 0), and C(4, 3).

5. A car moves along a straight line with a velocity given by v(t) = 3t² + 2t. What is the total displacement of the car after 2 seconds?

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Answer Key

Physics

1. D: The electric field inside a conductor is zero under electrostatic conditions regardless of external factors.
2. B: Maximum height = $\frac{v^2}{2g} = \frac{20^2}{2 \times 10} = 20 \, \text{m}$.
3. C: Capacitance $C = \frac{\epsilon_0 A}{d}$. When $d$ is doubled, $C$ is halved.
4. Induced EMF = Blv = 0.2 \times 2 \times 5 = 2 V.
5. Kinetic Energy = $\frac{1}{2}mv^2 = \frac{1}{2} \times 10 \times 15^2 = 1125 \, \text{J}$.

Chemistry

1. C: Neon has the highest ionization energy.
2. C: It is a neutralization reaction.
3. B: The correct IUPAC name is 2-Butene.
4. pH = -log(1 × 10⁻⁴) = 4.
5. Mass of CO₂ = 2 × 44 = 88 g.

Mathematics

1. C: The roots of the quadratic equation are $x = -2, -3$.
2. A: Determinant = $(1 \times 4) - (2 \times 3) = -2$.
3. C: $y = 2(4) + 3 = 11$.
4. Area = ( \frac{1}{2} \times \text{Base} \times \text{Height} = \frac{1}{2} \times 4 \times 3 = 6 , \text{sq. units}.
5. Displacement = ( \int_0^2 (3t^2 + 2t) dt = [t^3 + t^2]_0^2 = (8 + 4) - (0) = 12 , \text{m}.

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This sample paper provides a range of problems from each subject and covers the basic types of questions one would encounter in a JEE exam, including both multiple-choice and numerical answer type questions.