Algebraic Expressions (IMO- Mathematics Olympiad Class 7): Questions 1 - 4 of 83

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Question number: 1

» Algebraic Expressions

MCQ▾

Question

If (x+Y+Z)3=(y+zx)3+(z+xy)3+(x+yz)3+kxyz find the numerical value of k. Deduce the following result.

If a=2015 , b=2014 , c=12014

(a+b+c)3(a+bc3)(b+ca)3(c+a+b)323abc=?

Choices

Choice (4) Response

a.

2014

b.

2015

c.

2010

d.

2013

Question number: 2

» Algebraic Expressions

MCQ▾

Question

If x, y, z are real and unequal numbers, then which is true?

Choices

Choice (4) Response

a.

2015X2+2015Y2+6Z2>2(12XY+YZ+ZX)

b.

2015X2+2015Y2+6Z2>2(20XY+3YZ+3ZX)

c.

2000X2+205Y2+6Z2>2(2012XY+3YZ+3ZX)

d.

2015X2+2015Y2+6Z2>2(2012XY+3YZ+3ZX)

Question number: 3

» Algebraic Expressions

MCQ▾

Question

If a, b, c are reals such that a+b=4 and 2c2ab=3c410 , find the numerical values of a, b and c.

Choices

Choice (4) Response

a.

3, 3, 4

b.

2, 2, 3

c.

2, 3,1

d.

2, 3, 3

Question number: 4

» Algebraic Expressions

MCQ▾

Question

When a=22014 and b=22015 , then which is true?

Choices

Choice (4) Response

a.

{(a+b)3+(ab)2ba(a+b)1b+a1a+b}÷{(a+b)3+(ba)3(a+b)2(ab)2} is divisible by 3

b.

{(a+b)2+(ab)2ba(a+b)1ba1a+b}÷{(a+b)3+(ba)3(a+b)2(ab)2} is divisible by 3

c.

{(a+b)2+(ab)3ba(a+b)1ba1a+b}÷{(a+b)3+(ba)3(a+b)2(ab)2} is divisible by 3

d.

{(a+b)2+(a+b)2ba(a+b)1b+a1a+b}÷{(a+b)3+(ba)3(a+b)2+(ab)2} is divisible by 3

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