**Mr Sivakumar, TGT (Maths)**

**Date of submission: 23 June 2014**

__PART A : NUMBER SYSTEM__

1. Prove that √7 is an irrational number.

2. Prove that is an irrational number.

3. Prove that is irrational.

4. Use Euclid’s division algorithm to find the HCF of 10224 and 9648.

5. Find HCF of 180, 252 and 324 using Euclid’s Division Lemma.

6. Explain why is a composite number.

7. Find the LCM of 72, 80 and 120 using the fundamental theorem of arithmetic.

8. A merchant has 120 litres of oil of one kind, 180 litres of another kind and 240 litres of third kind.

He wants to sells the oil by filling the three kinds of oil in tins of equal capacity. What should be

the greatest capacity of such a tin ?

9. After how many decimal places will the decimal expansion of the rational number 31/ 2^{3}5^{2}

terminate ?

10. Prove that the square of any positive integer is of the form 5q, 5q + 1, 5q + 4 for some integer q.

__PART B : POLYNOMIALS__

1. Find the zeroes of the quadratic polynomial

2. The graphs of y =p(x) is given below. Find the number of zeroes of p(x) in each case

3. Form a quadratic polynomial whose one of the zeroes is 15 and sum of the zeroes is 42.

4. Find the zeroes of and verify the relation between the zeroes and coefficients

of the polynomial.

5. If α , β, are zeroes of the polynomial x2 – 2x – 8, , then form a quadratic polynomial whose zeroes

are 2α and 2β.

6. Check whether the polynomial is the factor of polynomial .

7. Find the zeroes of the quadratic polynomial and verify the relationship between the zeroes

and the coefficients.

8. Find all the zeroes of the polynomial if it is given that two of its zeroes are

-√3 and √3.

9. On dividing the polynomial by the polynomial g(x), the quotient and remainder

Were and respectively. Find g(x).

10.

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