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Pratimanayak K.

Kendriya Vidyalaya Sangathan

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Trigonometry

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Question:

Find the maximum and minimum value of 8 cos A + 15 sin A + 15

Pratimanayak K.

Answer:

Using Pythagorean triplets, we know that (8,15,17) is one ∴ The expression becomes: 17 (817 CosA +1517 SinA) Let there be a angle B for which sin B = 817, cos B = 1517 => 17( sin B cos A + cos B sin A) + 15 17(sin(A+B)) + 15 We know that sin(A+B)max = 1 sin(A+B)min = -1 ∴ Max value = 17 * 1 +15 = 32 Min value = 17 * -1 + 15 = -2

Set Theory

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Question:

In a group of 100 persons, 72 people can speak English and 43 can speak French. How many can speak English only? How many can speak French only?

Pratimanayak K.

Answer:

Let A be the set of people who speak English. B be the set of people who speak French. A - B be the set of people who speak English and not French. B - A be the set of people who speak French and not English. A ∩ B be the set of people who speak both French and English. Given, n(A) = 72 n(B) = 43 n(A ∪ B) = 100 Now, n(A ∩ B) = n(A) + n(B) - n(A ∪ B) = 72 + 43 - 100 = 115 - 100 = 15 Therefore, Number of persons who speak both French and English = 15 n(A) = n(A - B) + n(A ∩ B) ⇒ n(A - B) = n(A) - n(A ∩ B) = 72 - 15 = 57 and n(B - A) = n(B) - n(A ∩ B) = 43 - 15 = 28 Therefore, Number of people speaking English only = 57 Number of people speaking French only = 28

Statistics

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Question:

Who is better among the two cricketers? Anand who makes runs 25, 100, 5. Shiv who makes 45,50,55. How to find?

Pratimanayak K.

Answer:

Here to compare the result we should not calculate the mean of both the players but medians of scores is to be compared.

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