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Question (11)

QN0029443

Which number cannot be written as a fraction of two counting numbers according to the chapter?

(A) √4
(B) √9
(C) √2
(D) √16

Correct Answer: C

Explanation:

√2 is irrational and cannot be expressed as a fraction of two counting numbers.

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Question (12)

QN0029444

If (a,b,c) is a Baudhāyana triple, then (2a,2b,2c) is

(A) Never a triple
(B) Always a triple
(C) A triple only if a, b, c are even
(D) A primitive triple

Correct Answer: B

Explanation:

Multiplying all sides of a Baudhāyana triple by the same positive integer gives another Baudhāyana triple.

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Question (13)

QN0029445

The 25th odd number is

(A) 47
(B) 49
(C) 51
(D) 53

Correct Answer: B

Explanation:

The nth odd number is 2n – 1. Therefore, the 25th odd number is 49.

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Question (14)

QN0029446

A square has area 32 cm². What is the length of its diagonal?

(A) 4 cm
(B) 6 cm
(C) 8 cm
(D) 10 cm

Correct Answer: C

Explanation:

Side = √32 = 4√2. Diagonal = 4√2 × √2 = 8 cm.

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Question (15)

QN0029447

The side lengths of a rectangle are 9 cm and 12 cm. Its diagonal measures

(A) 13 cm
(B) 14 cm
(C) 15 cm
(D) 16 cm

Correct Answer: C

Explanation:

Diagonal = √(9² + 12²) = √225 = 15 cm.

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Question (16)

QN0029448

A rhombus has diagonals 16 cm and 30 cm. The side length of the rhombus is

(A) 15 cm
(B) 17 cm
(C) 18 cm
(D) 20 cm

Correct Answer: B

Explanation:

Half diagonals are 8 cm and 15 cm. Side = √(8² + 15²) = 17 cm.

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Question (17)

QN0029449

In Bhāskarāchārya's lotus problem, if the lotus tip is 2 units above water and touches the water 6 units away, the depth of the lake is

(A) 7 units
(B) 8 units
(C) 9 units
(D) 10 units

Correct Answer: B

Explanation:

Using Pythagoras theorem: 6² + x² = (x + 2)². Solving gives x = 8 units.

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Question (18)

QN0029450

Which equation represents Fermat's Last Theorem?

(A) a + b = c
(B) a² + b² = c²
(C) xⁿ + yⁿ = zⁿ, n > 2 has no positive integer solutions
(D) x + y = z²

Correct Answer: C

Explanation:

Fermat's Last Theorem states that xⁿ + yⁿ = zⁿ has no positive integer solutions for n > 2.

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Question (19)

QN0029451

A right triangle has sides 11 cm, 60 cm and 61 cm. Which statement is true?

(A) It is not a right triangle
(B) It is a Baudhāyana triple
(C) It is an isosceles triangle
(D) It is a primitive triple only after scaling

Correct Answer: B

Explanation:

Since 11² + 60² = 61², the numbers form a Baudhāyana triple.

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Question (20)

QN0029452

A square of side 4 cm is doubled in area twice successively using Baudhāyana's construction. The final area is

(A) 32 cm²
(B) 48 cm²
(C) 64 cm²
(D) 128 cm²

Correct Answer: C

Explanation:

Original area = 16 cm². After first doubling = 32 cm². After second doubling = 64 cm².

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Question (11)

Which number cannot be written as a fraction of two counting numbers according to the chapter?

Explanation:

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Question (12)

If (a,b,c) is a Baudhāyana triple, then (2a,2b,2c) is

Explanation:

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Question (13)

The 25th odd number is

Explanation:

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Question (14)

A square has area 32 cm². What is the length of its diagonal?

Explanation:

Link:

Question (15)

The side lengths of a rectangle are 9 cm and 12 cm. Its diagonal measures

Explanation:

Link:

Question (16)

A rhombus has diagonals 16 cm and 30 cm. The side length of the rhombus is

Explanation:

Link:

Question (17)

In Bhāskarāchārya's lotus problem, if the lotus tip is 2 units above water and touches the water 6 units away, the depth of the lake is

Explanation:

Link:

Question (18)

Which equation represents Fermat's Last Theorem?

Explanation:

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Question (19)

A right triangle has sides 11 cm, 60 cm and 61 cm. Which statement is true?

Explanation:

Link:

Question (20)

A square of side 4 cm is doubled in area twice successively using Baudhāyana's construction. The final area is

Explanation:

Link:

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