Instructions

For the following questions answer them individually

Question 51

Ankita buys 4 kg cashews, 14 kg peanuts and 6 kg almonds when the cost of 7 kg cashews is the same as that of 30 kg peanuts or 9 kg almonds. She mixes all the three nuts andÂ marks a price for the mixture in order to make a profit of â‚¹1752. She sells 4 kg of the mixture at this marked price and the remaining at a 20% discount on the marked price, thus making a total profit of â‚¹744. Then the amount, in rupees, that she had spent in buying almonds is

Question 52

Let A be the largest positive integer that divides all the numbers of the form $$3^k + 4^k + 5^k$$, and B be the largest positive integer that divides all the numbers of the form $$4^k + 3(4^k) + 4^{k + 2}$$ , where k is any positive integer. Then (A + B) equals

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Question 53

Let a, b, c be non-zero real numbers such that $$b^2 < 4ac$$, and $$f(x) = ax^2 + bx + c$$. If the set S consists of all integers m such that f(m) < 0, then the set S must necessarily be

Question 54

The number of ways of distributing 20 identical balloons among 4 children such that each child gets some balloons but no child gets an odd number of balloons, is

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Question 55

Let a and b be natural numbers. If $$a^2 + ab + a = 14$$ and $$b^2 + ab + b = 28$$, then $$(2a + b)$$ equals

Question 56

Amal buys 110 kg of syrup and 120 kg of juice, syrup being 20% less costly than juice, per kg. He sells 10 kg of syrup at 10% profit and 20 kg of juice at 20% profit. Mixing theÂ remaining juice and syrup, Amal sells the mixture at â‚¹ 308.32 per kg and makes an overall profit of 64%. Then, Amalâ€™s cost price for syrup, in rupees per kg, is

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Question 57

All the vertices of a rectangle lie on a circle of radius R. If the perimeter of the rectangle is P, then the area of the rectangle is

Question 58

The average of three integers is 13. When a natural number n is included, the average of these four integers remains an odd integer. The minimum possible value of n is

Question 59

A mixture contains lemon juice and sugar syrup in equal proportion. If a new mixture is created by adding this mixture and sugar syrup in the ratio 1 : 3, then the ratio of lemon juice and sugar syrup in the new mixture is

Question 60

The largest real value of a for which the equation $$\mid x + a \mid + \mid x - 1 \mid = 2$$ has an infinite number of solutions for x is

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