Kendriya Vidyalaya Reckong Peo

KENDRIYA VIDYALAYA RECKONG PEO

CLASS: X (MATHS)/2015-16/MAY 2015

HOME ASSIGNMENTS UNDER FA-2

1. Define the following terms:

(i) Rational number(ii) irrational number

(iii) Lemma(iv) Algorithm.

2. Define Euclid’s Division Lemma.

3. Define Euclid’s Division Algorithm.

4. Is a rational number? If not, why?

5. is a composite number. Explain, Why?

6. Using Euclid’s Division Algorithm find the HCF of-

(i) 870 & 225 (ii) 867 & 255 (iii) 135 & 255

7. Using prime factorization method, HCF and LCM of

(i) 72,126,168.(ii) 96 and 404

8. The HCF & LCM of two numbers are 9 & 90 respectively. If one number is 18, find the other.

9. The HCF (297,189) = 27, find LCM of these two numbers.

10.Use Euclid’s Division Lemma to show that the square of any positive integer is either of the form 3q or 3q + 1 for some integer q.

11. Show that cube of any positive integer is either of the form 9m, 9m 1 and 9m + 8.

12. Prove that is irrational.

13. Prove that is irrational.

14. Show that 5 – 3 is irrational.

15. Prove that 3 25 is irrational.

16. Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.

(i) – 2x – 8 (ii) 3 – x – 4

17. Find a quadratic polynomial, the sum and product of whose zeroes are – 3 and 2 respectively.

18. Find a quadratic polynomial, the sum and product of whose zeroes are respectively.

19. Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following:

(i) p(x) = – 3 + 5x – 3, g(x) = – 2

(ii) p(x) = – 3 + 4x + 5, g(x) = + 1 – x

20.Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial:

(i) – 3, 2+ 3 – 2 – 9t – 12(iii) – 3x + 1, – 4 + + 3x + 1

22.Obtain all other zeroes of 3 + 6 – 2– 10x – 5, if two of its zeroes are 5/3 and 5/3

23. Obtain all zeroes of the polynomial --+ 9 -6 if two of its zeroes are - √ 3 and √ 3.

24. On dividing – 3 + x + 2 by a polynomial g(x), the quotient and remainder were x – 2 and –2x + 4, respectively. Find g(x).

25. Write the denominator of & in the form , where n & m are non – negative integers. Also, write its decimal expansion.