CBSE Class 8 Maths The Baudhayana-Pythagoras Theorem (Class 8 NCERT New) Quiz 4

1. Among the triples with numbers less than or equal to 20, what pattern do you observe?

A Each triple is a multiple of (3, 4, 5) B The three numbers in each triple form an arithmetic progression C All numbers in each triple are odd D Each triple has equal numbers

2. Based on the observed pattern, which conjecture is correct about Baudhāyana triples?

A For any positive integer k, (3k, 4k, 5k) is a Baudhāyana triple B For any integer k, (k, k, k) is a Baudhāyana triple C For any positive integer k, (3k, 5k, 7k) is a Baudhāyana triple D For any positive integer k, (k, k + 1, k + 2) is a Baudhāyana triple

3. Is the conjecture that (3k, 4k, 5k) is a Baudhāyana triple for any positive integer k true?

A Yes B No

4. Which statement further generalises the pattern about Baudhāyana triples?

A If (a, b, c) is a Baudhāyana triple, then for any positive integer k, (ka, kb, kc) is also a Baudhāyana triple B If (a, b, c) is a Baudhāyana triple, then (a + 1, b + 1, c + 1) is also a Baudhāyana triple C If (a, b, c) is a Baudhāyana triple, then (a, b, c + 1) is also a Baudhāyana triple D If (a, b, c) is a Baudhāyana triple, then (ka, kb, c) is also a Baudhāyana triple

5. If (a, b, c) is a Baudhāyana triple, then (ka, kb, kc) is also a Baudhāyana triple for any positive integer k. Is this statement true?

A True B False

6. Is (5, 12, 13) a primitive Baudhāyana triple?

A Yes B No

7. Are the scaled versions of primitive Baudhāyana triples themselves primitive?

A No, scaled versions are non-primitive because they have a common factor greater than 1 B Yes, scaled versions are always primitive C Only if the scale factor is 1 D Only if the scale factor is a prime number

8. For the non-primitive triple (9, 12, 15) that has a common factor greater than 1, dividing by their greatest common factor gives which Baudhāyana triple that still satisfies ?

A (3, 4, 5) B (6, 8, 10) C (9, 12, 15) D (4, 5, 6)

9. Which relationship is used to generate more primitive Baudhāyana triples?

A The sum of consecutive odd numbers equals square numbers B The sum of even numbers equals cube numbers C The product of two consecutive integers equals a square D The difference of consecutive squares equals even numbers only

10. In the method based on odd numbers, if the nth odd number equals a square , which triple is formed?

A (n − 1, t, n) B (t − 1, n, t) C (n, t, n + 1) D (t, n − 1, t + 1)