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Maths XB

Mrs. V.P.Suseela, TGT(Maths)

Date of submission: 27 June 2011

 

REAL NUMBERS

1.Use euclid’s division algorithm to find the HCF of :

a) 6265 and 76254       b) 3854 and 48250

2. Find HCF and LCM of following using fundamental theorem of arithmetic method :

   a) 1376 AND 15428   b) 448,1008 and 168

3) Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or non terminating repeating decimal expansion :

a) 7/9      b) 35/51     c) 63/90

4) Show that for all positive integer to be a perfect square, it should be of the form 8k + 1.

5) Prove that 3\sqrt{\ } \!\,5 is irrational.

6) Prove that 1/\sqrt{\ } \!\,3 is irrational.

7) Can we have any n \in \!\,  N, where 7n  ends with digit zero.

POLYNOMIALS

1) Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and thie coefficient :

   a) P(x) = 4x2 + 24x + 36 

   b) P(x) = 25x2 + 5x

2) Find a quadratic polynomial whose zeroes are -9 and -1/9.

3) Sum and product of zeroes of quadratic polynomial are 2 and \sqrt{\ } \!\,5 respectively.Find the quadratic polynomial.

4) Find a quadratic polynomial whose one zero is -8 and sum of zeroes is 0.

5)verify that -5,1/2,3/4 are zeroes of cubic polynomial 4x3 + 20x +2x -3  also verify the relationship between the zeroes and the coefficient.

6) Divide 24x3 + 20x2y2 – 4xy by 2xy.

7)Divide ax2 + (b+ac) x + bc by x+c.

8) Use division state whether 2y-5 is a factor of 4y4 – 10y3– 10y2 + 30y – 15.

9)m, n are zeroes of ax2 – 5x + a. Find the value of a and c ,if m+n = m.n = 10.       

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