10 Question MCQ (including Assertion)

Question 1 of 10

Write \( 2^{-4} \) with a positive exponent.

A \( -2^4 \) B \( \frac{1}{2^4} \) C \( 16 \) D \( 8 \)

Select one option. Answers are shown after the test.

Question 2 of 10

Roxie has 7 dresses, 2 hats, and 3 pairs of shoes. How many different complete outfits can she create?

A 12 B 21 C 42 D 14

Select one option. Answers are shown after the test.

Question 3 of 10

Which of the following is equivalent to \( (13^{-2})^{-3} \)?

A \( 13^{-5} \) B \( 13^{-6} \) C \( 13^6 \) D \( 13^1 \)

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Question 4 of 10

A safe is secured with a 5-digit password, using digits from 0 to 9. How many possible passwords exist?

A 50 B 10,000 C 1,00,000 D 5,000

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Question 5 of 10

Simplify \( 5^7 \div 5^4 \).

A \( 5^{11} \) B \( 5^3 \) C \( 1^3 \) D \( 125 \)

Select one option. Answers are shown after the test.

Question 6 of 10

What is the value of \( x^0 \) (where \( x \neq 0 \))?

A 0 B \( x \) C 1 D -1

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Question 7 of 10

Which number is greater: \( 4^3 \) or \( 3^4 \)?

A \( 4^3 \) B \( 3^4 \) C They are equal D Cannot be determined

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Question 8 of 10

A dairy produces 8.5 billion (\( 8.5 \times 10^9 \)) packets of milk and wants a unique numeric ID code (digits 0-9) for each. What is the minimum number of digits this code must have?

A 9 digits B 10 digits C 11 digits D 8 digits

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Question 9 of 10

Assertion: \(3^4 \times 3^2=3^8\).
Reason: When powers with the same base are multiplied, their exponents are added.

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 10 of 10

Assertion (A): \( 2^{10} \) can be written as \( (2^5)^2 \).
Reason (R): According to the laws of exponents, \( (n^a)^b = n^{a \times b} \).

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.

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10 Question MCQ (including Assertion)