Polytechnic & Diploma Engineering Entrances (JEECUP, POLYCET & DTED) 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): 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.

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

What is the primary function of the outer cladding layer in the fiber structure?

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): 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.

Engineering Analysis & Principles: In technical analysis of 'Ohm Law Resistors in Series Parallel and Heating Effect' within Mechanics, Electricity & Magnetism, which governing relationship or mathematical model determines optimal system response under equilibrium conditions?

Engineering Analysis & Principles: In technical analysis of 'Magnetic Effect of Current Electromagnets and Electric Motor' within Mechanics, Electricity & Magnetism, which governing relationship or mathematical model determines optimal system response under equilibrium conditions?

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.

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

What essential conditions must be satisfied for total internal reflection to occur within the optical fiber?

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): 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.

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?

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): 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): The quadratic equation $x^2 - 6x + 9 = 0$ has real and equal roots.

Reason (R): A quadratic equation $ax^2 + bx + c = 0$ has real and equal roots if and only if its discriminant $D = b^2 - 4ac = 0$.

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

Assertion (A): 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): 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): 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): 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): The quadratic equation $x^2 - 6x + 9 = 0$ has real and equal roots.

Reason (R): A quadratic equation $ax^2 + bx + c = 0$ has real and equal roots if and only if its discriminant $D = b^2 - 4ac = 0$.

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.

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): 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.

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.