can sum1 solve all these :

 

20. Prove that 21n is an odd integer for all natural number.
21. Find HCF and LCM of each of integers by prime factorization method and
verify that: LCM X HCF=Product of the two numbers.
(i) 28,329 (ii) 15,36 (iii) 85,51 (iv) 18,35
22. Find HCF and LCM by prime factorization method.
(i) 144,180,192 (ii) 84,90,120
23. Find the HCF and 96 and 404 by prime factorisation method .Hence find their
HCF.
24. HCF of two numbers 35and x is 7 and their LCM is 665 .Find the value of x.
25. Without drawing the graph corresponding to the following polynomials,name
the curve that would be obtained .
(i) p(x)=2x+3 (ii) p(x)=3x2+x-1 (iii) p(x)=-2x2+x+1
26. Without drawing the graph corresponding to the following polynomials,find the
coordinates of the points where the curve would be meeting x axis.
(i) p(x)=x-2 (ii) p(x)=x2-3x+2
(iii) p(x)=x2-6x+9 (iv) p(x)=x(x-1)(x-2)
27. Find the number of points at which the graph of y=x2+6x+9, meets x axis .
28. Write the zeros of the polynomial
(i) x2+2x+1 (ii) x2-x-6
29. Find the zeroes of each of the following polynomials and verify the relationship
between its zeros and coefficient.
(i) 3x2-x-4 (ii) 4x2+5√2x-13
(iii) 9x2-4 (iv) x2+5x+6
(v) 6x2-3-7x (vi) 5x2-4-8x
(vii) 2x2-9-3x
30. Find the quadratic polynomial, the sum and product of whose zeros are
respectively.
(i) 5 and 6 (ii) √2 and 

(iii) 2 and -3 (iv) 

and 

(v) The sum and product of the zeros of a quadratic polynomial are 

and -3
respectively . What is the quadratic polynomial.
(vi) Find the quadratic polynomial, sum of whose zeros is 8 and their product
is 12 .Hence find the zeroes of the polynomial.
31. Find the quadratic polynomial whose zeros are
(i) 2 and -2 (ii) 3 and -2 (iii) 3+√5 and 3-√5
(iv) p+2q and p-2q (v) -5 and 4
32. Can two positive integers have 26 and 315 as their HCF and LCM respectively?
Give reason in support of your answer.
33. Using prime factorization method ,find the HCF and LCM of 72,126,168.Also
show that HCFXLCM ≠ Product of the three numbers.
34. On a morning walk, three person step off together and their steps measure
40cm,42cm,45cm,respectively .What is the minimum distance each should
walk so that each can cover the same distance in complete steps?
35. Find the smallest number which when 4 divided by 12,18 and 32 leaves
remainder 5 in each case.
36. In a school ,there are three section A,B,C of classx, having28,32and 36 students
in the respective section .Determine the minimum number of test tubes required
for their chemistry laboratory so that these can be distributed equally among
the students of any one of the section A section or section C.
37. Prove that the following are irrational numbers:
(i) √3 (ii) √2 (iii) √7 (iii) √5
38. Prove that the following are irrational numbers:
(i) 2√3 (ii) √


39. Write whether √

√

√
 on simplification gives a rational or an irrational
number.
40. Prove that following are irrational numbers :
(i) 7-√5 (ii) 3+√2 (iii) 5+√2 (iv) 3+2√3 (v) 3+5√2 (vi) 5-2√3
(vii) 4-3√2 (viii) √

(ix) 5-2√3 (x) 2-√3 (xi) 5+3√2
41. If