Both the proposition and its converse ("If n is divisible by both 5 and 12, then it is divisible by 60") are true. Divisibility by 60 guarantees divisibility by its factors 5 and 12. Conversely, because 5 and 12 are coprime (gcd(5, 12) = 1), their least common multiple is 5 × 12 = 60, so any numberRead more
Both the proposition and its converse (“If n is divisible by both 5 and 12, then it is divisible by 60”) are true. Divisibility by 60 guarantees divisibility by its factors 5 and 12. Conversely, because 5 and 12 are coprime (gcd(5, 12) = 1), their least common multiple is 5 × 12 = 60, so any number divisible by both must be divisible by 60.
For more NCERT Solutions of Class 9 Maths Ganita Manjari Part 2 Chapter 9 Propositions and their Converses Question Answer (2026-27)
The proposition is true because any multiple of 24 (24k) is divisible by its factors 4 and 6. However, its converse—"If n is divisible by both 4 and 6, then it is divisible by 24"—is false. As a counterexample, n = 12 is divisible by both 4 and 6, but 12 is not divisible by 24, since LCM (4, 6) = 12Read more
The proposition is true because any multiple of 24 (24k) is divisible by its factors 4 and 6. However, its converse—”If n is divisible by both 4 and 6, then it is divisible by 24″—is false. As a counterexample, n = 12 is divisible by both 4 and 6, but 12 is not divisible by 24, since LCM (4, 6) = 12.
For more NCERT Solutions of Class 9 Maths Ganita Manjari Part 2 Chapter 9 Propositions and their Converses Question Answer (2026-27)
Both the proposition and its converse ("If x³ = y³, then x = y") are true for all real numbers. If x = y, cubing both sides yields equal cubes. Conversely, the equation x³ - y³ = (x - y)(x² + xy + y²) = 0 implies x = y, because every real number possesses exactly one unique real cube root. FoRead more
Both the proposition and its converse (“If x³ = y³, then x = y”) are true for all real numbers. If x = y, cubing both sides yields equal cubes. Conversely, the equation x³ – y³ = (x – y)(x² + xy + y²) = 0 implies x = y, because every real number possesses exactly one unique real cube root.
For more NCERT Solutions of Class 9 Maths Ganita Manjari Part 2 Chapter 9 Propositions and their Converses Question Answer (2026-27)
The proposition is true because squaring equal real quantities preserves equality. However, the converse statement—"If x² = y², then x = y"—is false. As an exact counterexample, choose x = -3 and y = 3. Their squares are equal since (-3)² = 3² = 9, but x ≠ y, because a real square has two opposite rRead more
The proposition is true because squaring equal real quantities preserves equality. However, the converse statement—”If x² = y², then x = y”—is false. As an exact counterexample, choose x = -3 and y = 3. Their squares are equal since (-3)² = 3² = 9, but x ≠ y, because a real square has two opposite roots (x = ±y).
For more NCERT Solutions of Class 9 Maths Ganita Manjari Part 2 Chapter 9 Propositions and their Converses Question Answer (2026-27)
(i) Both have equal flexibility scores (65). Keerthi scores 5 marks lower in strength (weight 4) but 5 marks higher in agility (weight 6). Since agility holds greater weight, Keerthi's total is higher. (ii) Rashi’s score is [(60 × 4) + (65 × 5) + (70 × 6)] / 15 = 985/15 ≈ 65.67. Keerthi’s score is [Read more
(i) Both have equal flexibility scores (65). Keerthi scores 5 marks lower in strength (weight 4) but 5 marks higher in agility (weight 6). Since agility holds greater weight, Keerthi’s total is higher. (ii) Rashi’s score is [(60 × 4) + (65 × 5) + (70 × 6)] / 15 = 985/15 ≈ 65.67. Keerthi’s score is [(55 × 4) + (65 × 5) + (75 × 6)] / 15 = 995/15 ≈ 66.33.
For more NCERT Solutions of Class 9 Maths Ganita Manjari Part 2 Chapter 10 How Quantities Combine Understanding Data Question Answer (2026-27)
If n is divisible by 60, then it is divisible by both 5 and 12 (where n is a positive integer).
Both the proposition and its converse ("If n is divisible by both 5 and 12, then it is divisible by 60") are true. Divisibility by 60 guarantees divisibility by its factors 5 and 12. Conversely, because 5 and 12 are coprime (gcd(5, 12) = 1), their least common multiple is 5 × 12 = 60, so any numberRead more
Both the proposition and its converse (“If n is divisible by both 5 and 12, then it is divisible by 60”) are true. Divisibility by 60 guarantees divisibility by its factors 5 and 12. Conversely, because 5 and 12 are coprime (gcd(5, 12) = 1), their least common multiple is 5 × 12 = 60, so any number divisible by both must be divisible by 60.
For more NCERT Solutions of Class 9 Maths Ganita Manjari Part 2 Chapter 9 Propositions and their Converses Question Answer (2026-27)
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-9/
See lessIf n is divisible by 24, then it is divisible by both 4 and 6 (where n is a positive integer).
The proposition is true because any multiple of 24 (24k) is divisible by its factors 4 and 6. However, its converse—"If n is divisible by both 4 and 6, then it is divisible by 24"—is false. As a counterexample, n = 12 is divisible by both 4 and 6, but 12 is not divisible by 24, since LCM (4, 6) = 12Read more
The proposition is true because any multiple of 24 (24k) is divisible by its factors 4 and 6. However, its converse—”If n is divisible by both 4 and 6, then it is divisible by 24″—is false. As a counterexample, n = 12 is divisible by both 4 and 6, but 12 is not divisible by 24, since LCM (4, 6) = 12.
For more NCERT Solutions of Class 9 Maths Ganita Manjari Part 2 Chapter 9 Propositions and their Converses Question Answer (2026-27)
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-9/
See lessIf x = y, then x³ = y³ (where x and y are real numbers).
Both the proposition and its converse ("If x³ = y³, then x = y") are true for all real numbers. If x = y, cubing both sides yields equal cubes. Conversely, the equation x³ - y³ = (x - y)(x² + xy + y²) = 0 implies x = y, because every real number possesses exactly one unique real cube root. FoRead more
Both the proposition and its converse (“If x³ = y³, then x = y”) are true for all real numbers. If x = y, cubing both sides yields equal cubes. Conversely, the equation x³ – y³ = (x – y)(x² + xy + y²) = 0 implies x = y, because every real number possesses exactly one unique real cube root.
For more NCERT Solutions of Class 9 Maths Ganita Manjari Part 2 Chapter 9 Propositions and their Converses Question Answer (2026-27)
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-9/
See lessIf x = y, then x² = y² (where x and y are real numbers).
The proposition is true because squaring equal real quantities preserves equality. However, the converse statement—"If x² = y², then x = y"—is false. As an exact counterexample, choose x = -3 and y = 3. Their squares are equal since (-3)² = 3² = 9, but x ≠ y, because a real square has two opposite rRead more
The proposition is true because squaring equal real quantities preserves equality. However, the converse statement—”If x² = y², then x = y”—is false. As an exact counterexample, choose x = -3 and y = 3. Their squares are equal since (-3)² = 3² = 9, but x ≠ y, because a real square has two opposite roots (x = ±y).
For more NCERT Solutions of Class 9 Maths Ganita Manjari Part 2 Chapter 9 Propositions and their Converses Question Answer (2026-27)
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-9/
See lessA physical fitness evaluation is being undertaken. The final marks are calculated by combining the marks for strength, flexibility, and agility in the ratio 4:5:6. Rashi has scored 60, 65, and 70. Keerthi has scored 55, 65, and 75 respectively. (i) Find out whose total is more without calculating. (ii) What are their final marks?
(i) Both have equal flexibility scores (65). Keerthi scores 5 marks lower in strength (weight 4) but 5 marks higher in agility (weight 6). Since agility holds greater weight, Keerthi's total is higher. (ii) Rashi’s score is [(60 × 4) + (65 × 5) + (70 × 6)] / 15 = 985/15 ≈ 65.67. Keerthi’s score is [Read more
(i) Both have equal flexibility scores (65). Keerthi scores 5 marks lower in strength (weight 4) but 5 marks higher in agility (weight 6). Since agility holds greater weight, Keerthi’s total is higher. (ii) Rashi’s score is [(60 × 4) + (65 × 5) + (70 × 6)] / 15 = 985/15 ≈ 65.67. Keerthi’s score is [(55 × 4) + (65 × 5) + (75 × 6)] / 15 = 995/15 ≈ 66.33.
For more NCERT Solutions of Class 9 Maths Ganita Manjari Part 2 Chapter 10 How Quantities Combine Understanding Data Question Answer (2026-27)
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-10/
See less