IMO- Mathematics Olympiad Class 10: Questions 558 - 562 of 908

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Question number: 558

» 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

Question number: 559

» Everyday Mathematics

MCQ▾

Question

A man whose bowling average is 14.4 takes 3 wickets for 28 runs and thereby decreases his average by 1.2. The number of wickets, taken by him, before his last match, is ________

Choices

Choice (4) Response

a.

65

b.

55

c.

35

d.

45

Question number: 560

» Everyday Mathematics

MCQ▾

Question

Assume that a mango and its seed, both are spherical. The radius of the seed is 25 of the thickness of the pulp. The seed lies exactly at the center of the fruit. What percent of the total volume of the mango is its pulp?

Choices

Choice (4) Response

a.

93%

b.

97.66%

c.

90%

d.

92%

Question number: 561

» Everyday Mathematics

MCQ▾

Question

A fair price shopkeeper takes 10% profit on his goods. He loss 20% goods during theft. His lost percent is ________

Choices

Choice (4) Response

a.

12

b.

15

c.

11

d.

18

Question number: 562

» Everyday Mathematics

MCQ▾

Question

A card is drawn from a pack of 52 cards. The cards is drawn at random. What is the probability that it is neither spade nor a jack?

Choices

Choice (4) Response

a.

813

b.

413

c.

613

d.

913

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