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 6x2 – x – k = 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 ∈ ℝ 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.
Question ⑦
Statement A (Assertion): 2 is a prime number.
Statement R (Reason): The square of an irrational number is always a prime number.
- (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 ⑧
Statement A (Assertion): √2 is an irrational number.
Statement R (Reason): If m is a natural number which is not a perfect square, then √m is irrational.
- (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 ⑨
Statement A (Assertion): The HCF of two numbers is 6 and their product is 18144, then their LCM is 3024.
Statement R (Reason): HCF × LCM = Product of two given numbers.
- (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 ⑩ [CBSE Practice Set-1 2023]
A number q is prime factorised as 32 × 72 × b, where b is a prime number other than 3 and 7.
Statement A (Assertion): q is definitely an odd number.
Statement R (Reason): 32 × 72 is an odd number.
- (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 ⑪
① Statement A (Assertion): When a positive integer a is divided by 4, the values of remainder can be 0, 1, 2 or 3.
Statement R (Reason): According to Euclid’s Division Lemma a = bq + r, where 0 ≤ r < b and r is an integer.
(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.