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XAT 2011 — QA & DI Question 14

Simple EquationsEasy
Passage / Data

Answer the following question based on the information given below.

​​​​​​​

Total income tax payable is obtained by adding two additional surcharges on calculated income tax.

  • Education Cess: An additional surcharge called ‘Education Cess’ is levied at the late of 2% on the amount of income tax.
  • Secondary and Higher Education Cess: An additional surcharge called ‘Secondary and Higher Education Cess` is levied at the rate of 1% on the amount of income tax.

What is the maximum possible value of (21 Sin X + 72 Cos X)?

Answer & solution

Correct answer: 75

  • A

    21

  • B

    57

  • C

    63

  • 75

  • E

    None of the above

Solution

Let f (X) = 21 sin X + 72 cos X

∴ f ’(X) = 21 cos X – 72 sin X

At f ’(X) = 0

21 cos X = 72 sin X

∴ tan X =  2172

Drawing the corresponding right triangle we have the following:

​​​​​​​

∴ f ‘’(X) = –21 sin X – 72 cos X

= - 21 × 725 - 72 × 2425 < 0

∴ f (X) has a maximum at f ’(X) = 0

∴ Maximum value of f(x) = 21 × 2175 + 72 × 7275 = 75

Hence, option (d).

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XAT 2011 QA & DI Q14: What is the maximum possible value of (21 Sin X + 72 Cos X)? — Solution | TheCATExam