10 Question MCQ (including Assertion)

Question 1 of 10

Assertion (A): If a digital locker has a 5-digit passcode (using digits 0-9), there are 1,00,000 possible combinations.
Reason (R): The total combinations are found by adding the choices for each slot: \( 10 + 10 + 10 + 10 + 10 \).

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.

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Question 2 of 10

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

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

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Question 3 of 10

How many times larger than \( 4^{-2} \) is \( 4^2 \)?

A \( 4^4 \) times B \( 4^0 \) times C \( 4^{-4} \) times D 16 times

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Question 4 of 10

Assertion: \(10^{-3}=\dfrac{1}{1000}\).
Reason: For any non-zero number \(n\), \(n^{-a}=\dfrac{1}{n^a}\).

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.

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Question 5 of 10

What is the exponential form of \( 6 \times 6 \times 6 \times 6 \)?

A \( 6 \times 4 \) B \( 4^6 \) C \( 6^4 \) D \( 60 \)

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Question 6 of 10

Express 34,30,000 in standard scientific notation.

A \( 34.3 \times 10^5 \) B \( 3.43 \times 10^6 \) C \( 3.43 \times 10^7 \) D \( 0.343 \times 10^7 \)

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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

There are 3 daughters. Each has 3 baskets. Each basket contains 3 keys. Each key opens 3 rooms. How many rooms are there altogether?

A 12 B 27 C 81 D 243

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Question 9 of 10

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.

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Question 10 of 10

Assertion: \(4^6\) can be written both as \((4^3)^2\) and as \((4^2)^3\).
Reason: For a power raised to another power, \((n^a)^b=n^{ab}\).

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.

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10 Question MCQ (including Assertion)