Assertion Reasoning Quiz

Question 1 of 7

Assertion (A): \( 2^{-4} \) is a negative number.
Reason (R): A negative exponent indicates the reciprocal of the base raised to a positive power: \( n^{-a} = \frac{1}{n^a} \).

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 7

Assertion: A ladder with steps \(20\text{ cm}\) apart would require approximately \(1.922\times10^9\) steps to cover \(3{,}84{,}400\text{ km}\).
Reason: This is exponential growth because the distance is multiplied by a fixed factor at every step.

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 3 of 7

Assertion: A 5-digit numerical lock, with leading zeroes allowed, has \(10^5=1{,}00{,}000\) possible passwords.
Reason: \(10^5\) is a power of 10.

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 7

Assertion (A): The product of two cube numbers is always a cube number.
Reason (R): For any numbers \( n_1 \) and \( n_2 \), \( (n_1)^3 \times (n_2)^3 = (n_1 \times n_2)^3 \).

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): If the population of sheep is \( 10^9 \) and goats is \( 10^9 \), the combined population is \( 2 \times 10^9 \).
Reason (R): When adding identical exponential terms, you add their bases and keep the exponent the same.

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): The expression \( \frac{4^7}{4^{-2}} \) simplifies to \( 4^9 \).
Reason (R): When dividing powers with the same base, you subtract the exponents: \( n^a \div n^b = n^{a-b} \).

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 digits-only code of length 9 is sufficient to give a unique code to each of \(8.5\times10^9\) milk packets.
Reason: \(10^9<8.5\times10^9<10^{10}\), so at least 10 digits are required.

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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