# Summer Holiday Home Work 2017

**SUMMER HOLIDAY HOME WORK 2017**

**CLASS X REAL NUMBERS** DKMRAO/BHASKAR RAO/G SEETA

SUB;MATHS

- HCF ( 52, 320 ) is

a ) 8 b) 4 c) 5 d) 1

- If HCF ( a, b ) = 12 and axb = 1800, then LCM (a,b) =

a ) 3600 b) 900 c) 150 d) 90

- Which of the following rational numbers have non-terminating repeating decimal expansion?

a ) 31 b) 17 c) 23 d) none of these

3125 512 200

- Which of the following rational numbers have terminating decimal expansion?

a ) 11 b) 91 c) 343 d) none of these

7000 21000 xx

- HCF ( 280,674 ) is

a ) 2 b) 4 c) 14 d) none of these

- If p/q in standard form is a terminating decimal, then q is of the form

x b) x c) x d)x

POLYNOMIALS

- A polynomial in one variable of degree two is known as

a) Linear polynomial b) quadratic polynomial c) cubic polynomial d) none of these

- A cubic polynomial can have utmost ------zeros

a ) 0 b) 1 c) 2 d) 3

- If α, β, γ are the zeros of a cubic polynomial ax + b + cx +d , a ≠0, then α + β + γ =

a) -b/a b) c/a c) -d/a d) b/a

- A real number ‘ a ‘ is called a zero of the polynomial f(x) , if

a ) f(0) = a b) f(a) = a c) f(a) = 0 d) f(a) = f(0)

- The zeros of the polynomial x2 – 4x + 3 are

a)- 3 and – 4 b) – 2 and 3 c) 1 and 3 d) 2 and 3

- The quadratic polynomial whose sum and product of zeros are 3 and - 28 respectively is

a)x2 + 3x – 28 b) x2 - 3x – 28 c) x2 - 3x + 28 d) x2 + 3x + 28

- The quadratic polynomial whose zeros are ⅓ and - ⅖ is

a)15x2 + x – 2 b) 15 x2 + 5x – 6 c)15 x2 - 5x +6 d) 15 x2 - x + 2

- Which of the following is not a polynomial ?

a)x + 1/x b) 2x3/2 – 4x1/2 + 1 c) 3x2 – 4x + 5√x - 11 d) None of these

- Which of the following is a zero of the cubic polynomial f(x) =x3 – 3x + 2?

a ) - 2 b) - 1 c) 0 d) 2

- If one of the zero of the polynomial f(x) = 2x2 – 9x + m is 4, then the value of m is

a ) 0 b) 1 c) 2 d) 4

- If α, β and γ are the zeros of the cubic polynomial 3x3 – 2x2 – 19x + 6, then the value of

( αβγ) is

a ) - 6 b) - 2/3 c) - 2 d) 6

** Section –A DKMRAO**

1)The decimal expansion of will terminate after ___places of decimal

a)4 (b) 3 (c) 2 (d) 1

2) If a=2²×33×54and b=23×3²×5 Then HCF of a and b is is ______.

A)90 (b) 180 c) 360 (d) 540

3) The value of k if the line 2x-ky=9 passes through (1,-1)

(a)7 (b) -7 (c) -11 (d) 11

4). If one zero of the polynomial 3x2+8x+k be the reciprocal of the other then k= ____.

(a) (b) 3 (c)-3 (d)

Section – B

5) Findthe quadratic polynomial whose zeroes are 5+√2 and 5-√2.

6) Find the HCF of 405, 2520 by Euclid’s division algorithm. Also find M&N if HCF=405M+2520N

7) If zeroes of x2 +8x-20 , find the value of +

Section – C

8) Show that √5 is an irrational number.

9) Find the polynomial which should be subtracted from the polynomial x4+2x3 - 4x2+6x – 3 so that it is exactly divisible by x²-x+1

Section – D

10)If two zeroes of the polynomialx4+x3-11x2-9x+18 are 3 and -3, find the other zeroes of the polynomial.

11) (a) Use Euclid’s division lemma to show that the square of any positive integer is either of the form 3m or 3m+1.

12)(b)Explain if 6n can end in zero for ‘n’ a positive integer.

13)On a morning walk, three persons step off together and their steps measure 40 cm, 42 cm and 45 cm, respectively. What is the minimum distance each should walk so that each can cover the same distance in complete steps?

14)Use Euclid’s division algorithm to show that any positive odd integer is of the form 4q + 1 or 4q + 3. where q is some integer.

15)The decimal expansion of the Rational number will terminate, after how many

places of decimals?

16)Prove that √3+ √5 is irrational.

17)Show that 12n cannot end with the digit 0 or 5 for any natural number n.

18)If p and q are the zeroes of the polynomial 2x2 – 7x +3, find p2 + q2.

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

20)Find the zeroes of the polynomial 3x2 – x – 4 and verify the relationship between the zeroes and the coefficients.

21)If one of the zeroes of the quadratic polynomial 4+ kx – 1 is 1, then the value of k is ____

22)For what value of ‘k’ will the pair of linear equations kx + 3y = k - 3 and 12x + ky = k have no solution.

23)Find the Zeroes of the quadratic polynomial + 7x + 10 and verify the relationship between the zeroes and the coefficients.

24)If two zeroes of the polynomial x4 - 6 x3 - 26 x2 + 138 x – 35 are 2 , find its other two zeroes.

25)If one of the zero of a Polynomial p(x) = 3x2- 10x + k is reciprocal of the other, then find the value of k ?

26)Find the zeroes of the Polynomial p(x) = 4√3x2 + 5x - 2√3, and verify the Relationship between the zeroes and its coefficients.

27)On dividing Polynomial p(x) = 3x3 - 4x2 - 6x – 57 by a polynomial g(x), the quotient and the remainder are 3x + 10 and 16x + 43 respectively. Find the polynomial g(x).

28)Find all the zeroes of 2x4 – 3x3 – 3x2 + 6x – 2, if you know that two of its zeroes are √2 and − √2.