GATE Mathematics - GATE 2017-2018 Questions and Answers

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X and Y are two positive real numbers such that 2X + Y â‰¤ 6 and X + 2Y â‰¤ 8. For which of the following values of (X, Y) the function f(X, Y)= 3X + 6Y will give maximum value?

(4/3, 10/3)

(8/3, 20/3)

(8/3, 10/3)

(4/3, 20/3)

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If |4X - 7| = 5 then the values of 2|X| - |-X| is :

2, 1/3

1/2, 3

3/2, 9

2/3, 9

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Following table provides figures (in rupees) on annual expenditure of a firm for two years - 2010 and 2011.

In 2011, which of the following two categories have registered increase by same percentage?

Raw material and Salary & wages

Salary & wages and Advertising

Power & fuel and Advertising

Raw material and Research & Development

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A firm is selling its product at Rs. 60 per unit. The total cost of production is Rs. 100 and firm is earning total profit of Rs. 500. Later, the total cost increased by 30%. By what percentage the price should be increased to maintained the same profit level.

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Abhishek is elder to Savar.

Savar is younger to Anshul.

Which of the given conclusions is logically valid and is inferred from the above statements?

Abhishek is elder to Anshul

Anshul is elder to Abhishek

Abhishek and Anshul are of the same age

No conclusion follows