Real Numbers (IMO- Mathematics Olympiad Class 10): Questions 78 - 83 of 89

Get 1 year subscription: Access detailed explanations (illustrated with images and videos) to 908 questions. Access all new questions we will add tracking exam-pattern and syllabus changes. View Sample Explanation or View Features.

Rs. 450.00 or

Question number: 78

» Real Numbers

MCQ▾

Question

2.131313131313. is ________

Choices

Choice (4) Response

a.

Not a real number

b.

An integer

c.

A rational number

d.

An irrational number

Question number: 79

» Real Numbers

MCQ▾

Question

Which of the following numbers has the terminating decimal representation?

Choices

Choice (4) Response

a.

329400

b.

211

c.

313

d.

111

Question number: 80

» Real Numbers

MCQ▾

Question

Smaller number amongst 2018 and 1614 is ________

Choices

Choice (4) Response

a.

1614

b.

2018

c.

47

d.

Cantbedetermine

Question number: 81

» Real Numbers

MCQ▾

Question

28 integers are chosen from the interval [104, 208]. Show that there exit two of them having a common prime divisor.

Choices

Choice (4) Response

a.

2

b.

0

c.

3

d.

1

Question number: 82

» Real Numbers

MCQ▾

Question

a, b, c are distinct real numbers such that a=3(b+c)25,b=3(c+a)25,c=3(a+b)25. Find the numerical value of abc.

Choices

Choice (4) Response

a.

2

b.

0

c.

3

d.

1

Question number: 83

» Real Numbers

MCQ▾

Question

a, b, c are real numbers such that a+b+c=0 and a2+b2+c2=1. Prove that a2b2c2154 . When does the equality hold?

Choices

Choice (4) Response

a.

Equality hold when a=b=16 and c2=1a2b2

b.

Equality hold when a=b16 and c2=1ab2

c.

Equality hold when a=16 and c2=1b2

d.

Equality hold when ab=16 and c2=1a2b

Sign In