DIRECTIONS

In the following questions, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option.

Question 1

Statement A (Assertion): If product of two numbers is 5780 and their HCF is 17, then their LCM is 340.

Statement R (Reason): HCF is always a factor of LCM.

• (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
• (b) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A).
• (c) Assertion (A) is true but reason (R) is false.
• (d) Assertion (A) is false but reason (R) is true.

Question 2

Statement A (Assertion): If HCF of 510 and 92 is 2, then the LCM of 510 and 92 is 32460.

Statement R (Reason): Since HCF (a, b) × LCM (a, b) = a × b.

• (a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
• (b) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
• (c) Assertion (A) is true but Reason (R) is false.
• (d) Assertion (A) is false but Reason (R) is true.

Question 3

Statement A (Assertion): If the co-ordinates of the mid-points of the sides AB and AC of ΔABC are D (3, 5) and E (⎼3, ⎼3) respectively, then BC = 20 units

Statement R (Reason): The line joining the mid points of two sides of a triangle is parallel to the third side and equal to half of it.

• (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
• (b) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A).
• (c) Assertion (A) is true but reason (R) is false.
• (d) Assertion (A) is false but reason (R) is true.

Question 4

Statement A (Assertion): The ratio in which the line segment joining (2, ⎼3) and (5, 6) internally divided by x-axis is 1 : 2.

Statement R (Reason): The formula for the internal division is ((𝑚𝑥2 + 𝑛𝑥1)/(𝑚 + 𝑛), (𝑚𝑦2 + 𝑛𝑦1)/(𝑚 + 𝑛)).

• (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
• (b) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A).
• (c) Assertion (A) is true but reason (R) is false.
• (d) Assertion (A) is false but reason (R) is true.

Question 5

Statement A (Assertion): If one root of the quadratic equation 6x2xk = 0 is 2/3, then the value of k is 2.

Statement R (Reason):  The quadratic equation ax2 + bx + c = 0, a ≠ 0 has almost two roots.

• (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
• (b) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A).
• (c) Assertion (A) is true but reason (R) is false.
• (d) Assertion (A) is false but reason (R) is true.

Question 6

Statement A (Assertion): (2x – 1)2 – 4x2 + 5 = 0 is not a quadratic equation.

Statement R (Reason):  An equation of the form ax2 + bx + c = 0, a ≠ 0, where a, b, c ∈ ℝR is called a quadratic equation.

• (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
• (b) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A).
• (c) Assertion (A) is true but reason (R) is false.
• (d) Assertion (A) is false but reason (R) is true.