Karnataka Board - Class 9 previous year questions (PYQ)

ವಿದ್ಯುಚ್ಛಕ್ತಿ ಅಧ್ಯಾಯದಲ್ಲಿ ರೋಧಕಗಳ 'ನಮ್ಮ ಸುತ್ತಲಿನ ಪರಿಸರದಲ್ಲಿರುವ ದ್ರವ್ಯ' ಜೋಡಣೆಯ ಸಮಾನ ರೋಧದ ಸೂತ್ರವೇನು?

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 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:

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): An employer is vicariously liable for tortious civil wrongs committed by an employee during the authorized course of employment.

Reason (R): The doctrine of vicarious liability is founded on the legal maxims *respondeat superior* (let the master answer) and *qui facit per alium facit per se*.