Assertion Reasoning Quiz

Question 1 of 7

Assertion: A student who saves ₹\(100\) in the first month and doubles the monthly saving thereafter saves ₹\(25{,}500\) in total during the first \(8\) months.
Reason: The amount saved in the eighth month alone is ₹\(12{,}800\).

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 2 of 7

Assertion (A): A sequence can be regarded as a function whose domain is the set of natural numbers.
Reason (R): Every mathematical sequence must be expressible by an explicit algebraic formula.

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 7

Assertion (A): The sum of the first 4 terms of the G.P. 1, 3, 9, 27... is 40.
Reason (R): The sum of \(n\) terms of a G.P. is \(S_n = \frac{a(r^n - 1)}{r - 1}\).

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 4 of 7

Assertion (A): If the terms of a G.P. are all multiplied by 3, the resulting sequence is also a G.P.
Reason (R): The common ratio of the new sequence becomes 3 times the original common ratio.

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 7

Assertion (A): In the Fibonacci sequence 1, 1, 2, 3, 5, 8... the \(7^{th}\) term is 13.
Reason (R): The Fibonacci sequence is defined by the recurrence relation \(a_n = a_{n-1} + a_{n-2}\) for \(n > 2\).

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 7

Assertion (A): For any two distinct positive numbers, their Arithmetic Mean (A.M.) is always strictly greater than their Geometric Mean (G.M.).
Reason (R): For any two distinct positive numbers \(a\) and \(b\), \((\sqrt{a} - \sqrt{b})^2 > 0\).

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 7 of 7

Assertion (A): If the A.M. and G.M. of two positive numbers are 10 and 8 respectively, the numbers are 16 and 4.
Reason (R): The two numbers are the roots of the quadratic equation \(x^2 - 2(A.M.)x + (G.M.)^2 = 0\).

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.

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