XAT 2011 — QA & DI Question 14
Simple EquationsEasy
Passage / Data
Answer the following question based on the information given below.
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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
- 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 =
Drawing the corresponding right triangle we have the following:
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∴ f ‘’(X) = –21 sin X – 72 cos X
= - 21 × - 72 × < 0
∴ f (X) has a maximum at f ’(X) = 0
∴ Maximum value of f(x) = 21 × + 72 × = 75
Hence, option (d).