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Question (31)

QN0018390

Which rule is illustrated by 2⁴ × 3⁴ = 6⁴?

(A) mᵃ × nᵃ = (mn)ᵃ
(B) nᵃ⁺ᵇ = nᵃ × nᵇ
(C) nᵃ⁻ᵇ = nᵃ ÷ nᵇ
(D) (nᵃ)ᵇ = nᵃᵇ

Correct Answer: A

Explanation:

Same exponent allows multiplication of bases.

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Question (32)

QN0018391

Estu has 4 dresses and 3 caps. How many different combinations are possible?

(A) 7
(B) 12
(C) 24
(D) 64

Correct Answer: B

Explanation:

4 × 3 = 12.

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Question (33)

QN0018392

How many passwords are possible for a 2-digit lock using digits 0–9?

(A) 20
(B) 50
(C) 100
(D) 200

Correct Answer: C

Explanation:

10 × 10 = 100.

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Question (34)

QN0018393

How many passwords are possible for a 3-digit lock using digits 0–9?

(A) 100
(B) 300
(C) 1000
(D) 999

Correct Answer: C

Explanation:

10³ = 1000.

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Question (35)

QN0018394

How many 5-digit passwords are possible using digits 0–9?

(A) 10,000
(B) 50,000
(C) 1,00,000
(D) 10,00,000

Correct Answer: C

Explanation:

10⁵ = 1,00,000.

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Question (36)

QN0018395

The number of possible 5-digit passwords can be written as:

(A) 5⁵
(B) 10⁵
(C) 5¹⁰
(D) 100⁵

Correct Answer: B

Explanation:

Each of 5 places has 10 choices.

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Question (37)

QN0018396

A lock has 6 slots, each containing one of the 26 letters A–Z. The total number of passwords is:

(A) 26⁶
(B) 6²⁶
(C) 15⁶
(D) 26¹²

Correct Answer: A

Explanation:

Six positions with 26 choices each.

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Question (38)

QN0018397

Which situation from the chapter is an example of exponential growth?

(A) Climbing a ladder with equal step height
(B) Adding ₹10 daily to savings
(C) Paper thickness doubling after each fold
(D) Walking 1 km every day

Correct Answer: C

Explanation:

Doubling repeatedly is exponential growth.

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Question (39)

QN0018398

Which situation from the chapter is an example of linear growth?

(A) Paper folding
(B) Lotus doubling daily
(C) Password combinations increasing exponentially
(D) Climbing a ladder with fixed 20 cm steps

Correct Answer: D

Explanation:

Equal increase each step shows linear growth.

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Question (40)

QN0018399

After about 30 folds, the paper thickness is approximately equal to:

(A) Height of a classroom
(B) Height of a tree
(C) Height at which aeroplanes fly
(D) Height of Burj Khalifa

Correct Answer: C

Explanation:

After 30 folds, thickness is about 10.7 km, close to aircraft cruising altitude.

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Question (31)

Which rule is illustrated by 2⁴ × 3⁴ = 6⁴?

Explanation:

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Question (32)

Estu has 4 dresses and 3 caps. How many different combinations are possible?

Explanation:

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Question (33)

How many passwords are possible for a 2-digit lock using digits 0–9?

Explanation:

Link:

Question (34)

How many passwords are possible for a 3-digit lock using digits 0–9?

Explanation:

Link:

Question (35)

How many 5-digit passwords are possible using digits 0–9?

Explanation:

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Question (36)

The number of possible 5-digit passwords can be written as:

Explanation:

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Question (37)

A lock has 6 slots, each containing one of the 26 letters A–Z. The total number of passwords is:

Explanation:

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Question (38)

Which situation from the chapter is an example of exponential growth?

Explanation:

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Question (39)

Which situation from the chapter is an example of linear growth?

Explanation:

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Question (40)

After about 30 folds, the paper thickness is approximately equal to:

Explanation:

Link:

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