Assertion-Reason Questions
Q1: Assertion (A): If \(-2x+1 > 9\), then \(x < -4\).
Reason (R): Dividing each side of an inequality by a negative number, reverses the inequality.
Step 1: Start with the given inequality:
-2x + 1 > 9
Step 2: Subtract 1 from both sides:
-2x > 8
Step 3: Divide both sides by -2 (reverse the inequality):
x < 8 / -2
x < -4
Step 4: Compare with Assertion (A):
Assertion (A) is correct because solving the inequality gives x < -4.
Step 5: Check Reason (R):
Reason (R) is also correct because dividing by a negative number indeed reverses the inequality.
Step 6: Is Reason (R) the correct explanation of Assertion (A)?
Yes, the process of dividing by -2 (a negative number) directly leads to the solution x < -4.
Answer: a. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A)
Q2: Assertion (A): If 6x + 15 > 0, x ∈ N, then the solution set is {0, 1, 2, 3, …}
Reason (R): Solution set consists of all those values of the variable which satisfy the given inequation.
Step 1: Start with the inequality:
6x + 15 > 0
Step 2: Subtract 15 from both sides:
6x > -15
Step 3: Divide both sides by 6:
x > -15/6 = -5/2
Step 4: x ∈ N = {1, 2, 3, …} (natural numbers start from 1)
So the solution set is x ∈ {1, 2, 3, …}
Step 5: Compare with Assertion (A):
Assertion says solution set is {0, 1, 2, 3, …}. But 0 ∉ N, so Assertion (A) is **false**.
Step 6: Check Reason (R):
Reason is true because solution sets **always include all values satisfying the inequation**.
Answer: d. Assertion (A) is false but Reason (R) is true
Leave a Comment