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Question (21)

QN0019712

Which equation is impossible according to Fermat’s Last Theorem?

(A) a³ + b³ = c³ in positive integers
(B) 3² + 4² = 5²
(C) 5² + 12² = 13²
(D) 8² + 15² = 17²

Correct Answer: A

Explanation:

Fermat’s Last Theorem states that no positive integer solutions exist for n > 2.

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Question (22)

QN0019713

The word “Last” in Fermat’s Last Theorem suggests that:

(A) It was his final theorem
(B) It was the last theorem to be proved
(C) It was the only theorem
(D) It concerned time

Correct Answer: B

Explanation:

It became famous because it remained unproved for centuries.

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Question (23)

QN0019714

Which exponent value makes the equation part of Pythagoras’ theorem?

(A) 1
(B) 2
(C) 3
(D) 4

Correct Answer: B

Explanation:

Pythagoras’ theorem involves squares, i.e., exponent 2.

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Question (24)

QN0019715

Which of the following exponents falls under Fermat’s Last Theorem?

(A) 1
(B) 2
(C) 3
(D) 0

Correct Answer: C

Explanation:

The theorem applies to all integers n > 2.

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Question (25)

QN0019716

Which equation has integer solutions?

(A) a⁴ + b⁴ = c⁴
(B) a⁵ + b⁵ = c⁵
(C) a² + b² = c²
(D) a⁷ + b⁷ = c⁷

Correct Answer: C

Explanation:

Pythagorean triples provide integer solutions for n = 2.

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Question (26)

QN0019717

Fermat’s Last Theorem was finally proved in:

(A) 1994
(B) 1894
(C) 1794
(D) 1694

Correct Answer: A

Explanation:

Andrew Wiles completed the proof in 1994.

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Question (27)

QN0019718

Which set forms a Pythagorean triple?

(A) (7, 24, 25)
(B) (7, 24, 24)
(C) (6, 7, 8)
(D) (10, 11, 12)

Correct Answer: A

Explanation:

7² + 24² = 25².

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Question (28)

QN0019719

Fermat’s theorem concerns powers greater than:

(A) 0
(B) 1
(C) 2
(D) 10

Correct Answer: C

Explanation:

The theorem applies for n > 2.

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Question (29)

QN0019720

If a solution existed for a⁴ + b⁴ = c⁴, it would:

(A) Support Fermat’s theorem
(B) Contradict Fermat’s theorem
(C) Prove Pythagoras’ theorem
(D) Form a Baudhāyana triple

Correct Answer: B

Explanation:

Any such solution would disprove Fermat’s theorem.

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Question (30)

QN0019721

Which theorem is closely connected with right triangles?

(A) Fermat’s Last Theorem
(B) Pythagoras’ Theorem
(C) Midpoint Theorem
(D) Intercept Theorem

Correct Answer: B

Explanation:

Pythagoras’ theorem applies to right triangles.

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Question (21)

Which equation is impossible according to Fermat’s Last Theorem?

Explanation:

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Question (22)

The word “Last” in Fermat’s Last Theorem suggests that:

Explanation:

Link:

Question (23)

Which exponent value makes the equation part of Pythagoras’ theorem?

Explanation:

Link:

Question (24)

Which of the following exponents falls under Fermat’s Last Theorem?

Explanation:

Link:

Question (25)

Which equation has integer solutions?

Explanation:

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Question (26)

Fermat’s Last Theorem was finally proved in:

Explanation:

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Question (27)

Which set forms a Pythagorean triple?

Explanation:

Link:

Question (28)

Fermat’s theorem concerns powers greater than:

Explanation:

Link:

Question (29)

If a solution existed for a⁴ + b⁴ = c⁴, it would:

Explanation:

Link:

Question (30)

Which theorem is closely connected with right triangles?

Explanation:

Link:

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