Assertion Reasoning Quiz

Question 1 of 8

Assertion (A): The sequence 3, -6, 12, -24, ... is a geometric progression.
Reason (R): The common ratio of this given sequence is 2.

A Both (A) and (R) are true and (R) is the correct explanation of (A) B Both (A) and (R) are true but (R) is NOT the correct explanation of (A) C (A) is true but (R) is false D (A) is false but (R) is true

Select one option. Answers are shown after the test.

Question 2 of 8

Assertion (A): The Virahānka-Fibonacci sequence is defined by the recursive rule \(V_1 = 1\), \(V_2 = 2\), and \(V_n = V_{n-1} + V_{n-2}\) for \(n \ge 3\).
Reason (R): A recursive formula is a rule that calculates the value of a term strictly based on its position number \(n\), without needing previous terms.

A Both (A) and (R) are true and (R) is the correct explanation of (A) B Both (A) and (R) are true but (R) is NOT the correct explanation of (A) C (A) is true but (R) is false D (A) is false but (R) is true

Select one option. Answers are shown after the test.

Question 3 of 8

Assertion (A): If the terms 5, 15, 45, 135 ... are in GP, then the ratio of the 10th term to the 9th term is 3.
Reason (R): In a Geometric Progression, the ratio of any term to its immediately preceding term is constant throughout the sequence.

A Both (A) and (R) are true and (R) is the correct explanation of (A) B Both (A) and (R) are true but (R) is NOT the correct explanation of (A) C (A) is true but (R) is false D (A) is false but (R) is true

Select one option. Answers are shown after the test.

Question 4 of 8

Assertion: The points corresponding to \((1,3),(2,6),(3,12),(4,24),(5,48)\) do not lie on one straight line.
Reason: The difference between the first two terms of the sequence \(3,6,12,24,48\) is \(3\).

A Both Assertion and Reason are true, and Reason is the correct explanation of Assertion. B Both Assertion and Reason are true, but Reason is not the correct explanation of Assertion. C Assertion is true, but Reason is false. D Assertion is false, but Reason is true.

Select one option. Answers are shown after the test.

Question 5 of 8

Assertion (A): The 5th triangular number is 15.
Reason (R): The explicit formula for the \(n^{th}\) triangular number is \(t_n = \frac{n(n+1)}{2}\).

A Both (A) and (R) are true and (R) is the correct explanation of (A) B Both (A) and (R) are true but (R) is NOT the correct explanation of (A) C (A) is true but (R) is false D (A) is false but (R) is true

Select one option. Answers are shown after the test.

Question 6 of 8

Assertion: A taxi charges a fixed booking fee of ₹200 and ₹40 per kilometre. The fares for journeys of \(1,2,3,\ldots\) km form the AP \(240,280,320,\ldots\), whose \(n\)th term is \(200+40n\).
Reason: Increasing the journey by one kilometre increases the fare by the constant amount ₹40.

A Both Assertion and Reason are true, and Reason is the correct explanation of Assertion. B Both Assertion and Reason are true, but Reason is not the correct explanation of Assertion. C Assertion is true, but Reason is false. D Assertion is false, but Reason is true.

Select one option. Answers are shown after the test.

Question 7 of 8

Assertion (A): For the sequence \(t_n = n^2 - 2n + 3\), the 5th term is 18.
Reason (R): The sequence defined by \(t_n = n^2 - 2n + 3\) is an arithmetic progression.

A Both (A) and (R) are true and (R) is the correct explanation of (A) B Both (A) and (R) are true but (R) is NOT the correct explanation of (A) C (A) is true but (R) is false D (A) is false but (R) is true

Select one option. Answers are shown after the test.

Question 8 of 8

Assertion: A ball is dropped from a height of \(80\) m and rises to \(60\%\) of its previous height after each bounce. Its height after the fifth bounce is \(6.2208\) m.
Reason: The successive bounce heights form an arithmetic progression because the ball loses \(40\%\) of its height each time.

A Both Assertion and Reason are true, and Reason is the correct explanation of Assertion. B Both Assertion and Reason are true, but Reason is not the correct explanation of Assertion. C Assertion is true, but Reason is false. D Assertion is false, but Reason is true.

Select one option. Answers are shown after the test.

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