JEE Main previous year questions (PYQ)

Directions: In the question below, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option:

Assertion (A): A convex mirror is commonly used as a driver's rear-view mirror in automobiles.

Reason (R): A convex mirror always forms an erect, virtual, and diminished image, providing a much wider field of view.

Directions: In the question below, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option:

Assertion (A): Diamond sparkles brilliantly with internal radiance.

Reason (R): Total internal reflection of light occurs inside diamond because its critical angle is exceptionally small (approximately 24.4°).

Directions: In the question below, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option:

Assertion (A): Heavy water ($D_2O$) is utilized as a moderator in thermal nuclear power reactors.

Reason (R): Deuterium nuclei slow down energetic fission neutrons through elastic collisions without substantial parasitic neutron absorption.

Directions: In the question below, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option:

Assertion (A): An aqueous solution of pure glucose does not conduct electric current.

Reason (R): Glucose is a covalent molecular compound that does not dissociate into free mobile ions in water.

Directions: In the question below, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option:

Assertion (A): Carboxylic acids exhibit higher acidity than corresponding phenols.

Reason (R): The carboxylate anion is stabilized by two equivalent resonance structures where negative charge resides on electronegative oxygen atoms.

Refer to the Case Study 'Case Study: Parabolic Cable Geometry in Civil Engineering Suspension Bridges' to answer:

What is the vertical height of the suspension cable at a horizontal distance of $25\text{ m}$ from the bridge center?

Directions: In the question below, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option:

Assertion (A): Rusting of iron in moist air is an exothermic chemical oxidation process.

Reason (R): Rusting requires continuous absorption of thermal energy from ambient surroundings to proceed.

Directions: In the question below, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option:

Assertion (A): Metallic copper does not evolve hydrogen gas when reacted with dilute hydrochloric acid.

Reason (R): Copper has a positive standard reduction potential ($E^\circ = +0.34\text{ V}$) and lies below hydrogen in the electrochemical series.

Directions: In the question below, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option:

Assertion (A): A concave mirror can form both real inverted images and virtual erect images.

Reason (R): When an object is placed between the pole and focus of a concave mirror, it forms an erect, magnified, virtual image.

Refer to the Case Study 'Case Study: The Chlor-Alkali Electrochemical Process in Chemical Industry' to answer:

What reaction occurs at the cathode during brine electrolysis?

Refer to the Case Study 'Case Study: Parabolic Cable Geometry in Civil Engineering Suspension Bridges' to answer:

Determine the parameter $c$ in the parabolic equation $y = ax^2 + c$ from the vertex information.

Directions: In the question below, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option:

Assertion (A): The value of $\sin\theta$ cannot exceed 1 for any real angle $\theta$.

Reason (R): In any right-angled triangle, the hypotenuse is the strictly longest side, ensuring the ratio $\text{Perpendicular}/\text{Hypotenuse} \le 1$.

Refer to the Case Study 'Case Study: Parabolic Cable Geometry in Civil Engineering Suspension Bridges' to answer:

Using the tower coordinates $(x = 50\text{ m}, y = 25\text{ m})$, determine the value of the quadratic coefficient $a$.

Directions: In the question below, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option:

Assertion (A): Noble gases possess positive or zero electron gain enthalpy.

Reason (R): Noble gases have completely filled stable electronic valence shell configurations ($ns^2 np^6$).