Assertion Reasoning Quiz

Question 1 of 8

Assertion (A): 308 is the 62nd term of the sequence given by the explicit rule \(S_n = 5n - 2\).
Reason (R): The sequence \(1, 3, 5, 7, \dots\) 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 2 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 3 of 8

Assertion: The \(23\)rd term of the AP \(11,7,3,-1,\ldots\) is \(-77\).
Reason: An arithmetic progression may have a negative common difference.

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 4 of 8

Assertion (A): The sequence 11, 7, 3, -1, -5, ... is an AP with a common difference of 4.
Reason (R): The common difference \(d\) in an AP is obtained by subtracting the first term from the second term (\(t_2 - t_1\)).

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 5 of 8

Assertion: The difference between the sixth and fifth square numbers is \(11\).
Reason: For every natural number \(n\), \(n^2-(n-1)^2=2n-1\), which is an odd number.

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 6 of 8

Assertion: If a bacterial culture starts with \(30\) bacteria and doubles every hour, then the hourly counts form an arithmetic progression.
Reason: The ratio of each hourly count to the preceding count is the constant \(2\).

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): The sequence 2, 5, 8, 11, ... is an arithmetic progression.
Reason (R): The difference between any two consecutive terms in an arithmetic progression is constant.

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: The number \(133\) occurs in the sequence defined by \(u_1=1\) and \(u_n=2u_{n-1}+3\) for \(n\ge2\).
Reason: Every term of this sequence is odd.

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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