MATHS

1. Define a rational number. Give one example.

2. Is √2 a rational number? Justify your answer.

3. Express 0.333... as a rational number.

4. Write the decimal expansion of 7/8

5. What type of decimal expansion does 1/7 have?

6. Prove that √5 is an irrational number.

7. Find two rational numbers between 3/4 and 1.

8. Convert 2.16 (recurring) into a rational number.

9. Without actual division, state whether the decimal expansion of 13/50 terminates or not.

10. Use Euclid's Division Lemma to find the HCF of 56 and 72.

11. Define a polynomial and write one example each of constant, linear, quadratic, and cubic polynomials.

12. Find the value of the polynomial p(x) = x² - 4x + 7 at x = 3.

13. Check whether x = 1 is a zero of the polynomial x² - 2x + 1.

14. Factorize x² - 5x + 6.

15. If p(x) = x³ - 2x² + x - 2, find p(2).

16. Using the factor theorem, check if x - 2 is a factor of x³ - 7x + 6.

17. Divide the polynomial x³ + x² - x - 1 by x + 1. Remainder × 1000 =?

18. Find the remainder when x⁴ + 3x³ + 2x + 1 is divided by x - 1.

19. Factorize x³ - 27.

20. State the degree of the polynomial 4x⁵ - 3x⁴ + 2x² - 1.