CBSE Class 8 Maths A Square and A Cube (Class 8 NCERT New) Quiz 6

1. How many numbers lie between the squares of the following numbers? (ii) 98 and 99

A 195 numbers (99^2 - 98^2 - 1 = = 196) B 196 numbers (99^2 - 98^2 = = 9801 - 9604 = 197) C 194 numbers (99^2 - 98^2 - 2 = - 2 = 195) D 200 numbers (\katex{99^2 - 98^2 + 1} = \katex{9801 - 9604 + 1} = 198)

2. A cube can end with exactly two zeroes (00). Is this possible?

A No, a cube cannot end with exactly two zeroes. B Yes, a cube can end with exactly two zeroes. C Only some cubes can end with exactly two zeroes. D A cube can end with any number of zeroes.

3. Determine the value of the following expression: 91+93+95+97+99+101+103+105+107+109.

A 900 B 1000 C 1100 D 950

4. The number of terms in the sum is important in identifying the cube number because:

A The number of terms gives the cube root since each cube is formed by adding n consecutive odd numbers. B The number of terms gives the square root since each square is formed by adding n consecutive even numbers. C The number of terms gives the sum of all even numbers up to n. D The number of terms gives the product of n and its next integer.

5. He computes the differences between consecutive terms repeatedly until all the differences become the same. 1. Find the first level, second level, and third level differences of the given sequence: 1, 8, 27, 64, 125, 216.

A First level differences: 7, 19, 37, 61, 91 Second level differences: 12, 18, 24, 30 Third level differences: 6, 6, 6 B First level differences: 7, 17, 37, 61, 91 Second level differences: 10, 20, 24, 30 Third level differences: 5, 6, 7 C First level differences: 7, 19, 37, 61, 91 Second level differences: 14, 18, 22, 26 Third level differences: 4, 4, 4 D First level differences: 8, 20, 38, 62, 92 Second level differences: 12, 18, 24, 30 Third level differences: 6, 6, 6

6. At which level do the differences become constant? What is the constant value?

A The differences become constant at the third level. The constant value is 6. B The differences become constant at the second level. The constant value is 4. C The differences become constant at the fourth level. The constant value is 8. D The differences become constant at the first level. The constant value is 2.

7. He computes the differences between consecutive terms repeatedly until all the differences become the same. 3. Compare your result with the pattern of perfect squares. What similarity or difference do you observe? Comparison with perfect squares: For squares (1, 4, 9, 16, 25): a) First differences: 3, 5, 7, 9 b) Second differences: 2, 2, 2 Squares → constant at 2nd level Cubes → constant at 3rd level. What is the main similarity or difference between the sequence of cubes and the sequence of squares regarding their differences?

A Both sequences reach a constant difference, but at different levels. B Both sequences reach a constant difference at the same level. C Only the sequence of squares reaches a constant difference. D Neither sequence reaches a constant difference.

8. What conclusion can you draw about the relationship between the degree of a number pattern (square, cube, etc.) and the level at which differences become constant?

A The level at which differences become constant matches the degree of the pattern (e.g., 2nd level for squares, 3rd for cubes). B The level at which differences become constant is always the first level, regardless of the pattern. C The level at which differences become constant is always one less than the degree of the pattern. D The level at which differences become constant is unrelated to the degree of the pattern.

9. He computes the differences between consecutive terms repeatedly until all the differences become the same. Predict the next number in the sequence: 1, 8, 27, 64, 125, 216. Continue the pattern using the differences.

A 343 B 512 C 400 D 300

10. True or false? 9² = 18

A True B False