JEE Advanced 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): Addition of a non-volatile solute lowers the freezing point of a solvent.

Reason (R): Solute molecules reduce the equilibrium vapor pressure of the solution according to Raoult's Law.

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 square root of 2 ($\sqrt{2}$) is an irrational real number.

Reason (R): The square root of any positive prime integer is an irrational number.

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

Assertion (A): If two linear equations represent coincident lines, the system has infinitely many solutions.

Reason (R): Two lines $a_1x + b_1y + c_1 = 0$ and $a_2x + b_2y + c_2 = 0$ coincide when $\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}$.

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?

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): If two linear equations represent coincident lines, the system has infinitely many solutions.

Reason (R): Two lines $a_1x + b_1y + c_1 = 0$ and $a_2x + b_2y + c_2 = 0$ coincide when $\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}$.

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

What geometric property distinguishes the vertex of the upward-opening parabola $y = ax^2 + c$ ($a > 0$)?

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): 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): 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: Optical Fibers and Total Internal Reflection in Medical Endoscopy' to answer:

Calculate the critical angle $\theta_c$ for the optical fiber described in the passage ($n_1 = 1.52, n_2 = 1.48$).

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

During the chlor-alkali process, which chemical product is evolved at the positively charged anode?

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

Assertion (A): If two linear equations represent coincident lines, the system has infinitely many solutions.

Reason (R): Two lines $a_1x + b_1y + c_1 = 0$ and $a_2x + b_2y + c_2 = 0$ coincide when $\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}$.

Refer to the Case Study 'Case Study: Optical Fibers and Total Internal Reflection in Medical Endoscopy' to answer:

In clinical medicine, why are coherent fiber bundles used in flexible endoscopes rather than non-coherent bundles?

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

Why is sodium hydroxide ($NaOH$) formed specifically in the cathode compartment?

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: The Chlor-Alkali Electrochemical Process in Chemical Industry' to answer:

During the chlor-alkali process, which chemical product is evolved at the positively charged anode?

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

Which of the following is a major industrial application of the chlorine gas generated by the chlor-alkali process?

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

Assertion (A): Electric current in a conductor is treated as a scalar physical quantity.

Reason (R): Although electric current has both magnitude and direction, it does not obey the laws of vector addition.

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: Optical Fibers and Total Internal Reflection in Medical Endoscopy' to answer:

Calculate the critical angle $\theta_c$ for the optical fiber described in the passage ($n_1 = 1.52, n_2 = 1.48$).

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): If two linear equations represent coincident lines, the system has infinitely many solutions.

Reason (R): Two lines $a_1x + b_1y + c_1 = 0$ and $a_2x + b_2y + c_2 = 0$ coincide when $\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}$.

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.