Instructions

For the following questions answer them individually

Question 51

The number of groups of three or more distinct numbers that can be chosen from 1, 2, 3, 4, 5, 6, 7 and 8 so that the groups always include 3 and 5, while 7 and 8 are never included together is

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Question 52

Amal purchases some pens at â‚¹ 8 each. To sell these, he hires an employee at a fixed wage. He sells 100 of these pens at â‚¹ 12 each. If the remaining pens are sold at â‚¹ 11 each, then he makes a net profit of â‚¹ 300, while he makes a net loss of â‚¹ 300 if the remaining pens are sold at â‚¹ 9 each. The wage of the employee, in INR, is

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Question 53

A basket of 2 apples, 4 oranges and 6 mangoes costs the same as a basket of 1 apple, 4 oranges and 8 mangoes, or a basket of 8 oranges and 7 mangoes. Then the number of mangoes in a basket of mangoes that has the same cost as the other baskets is

Question 54

The number of integers n that satisfy the inequalities $$\mid n - 60 \mid < \mid n - 100 \mid < \mid n - 20 \mid$$ is

Question 55

How many three-digit numbers are greater than 100 and increase by 198 when the three digits are arranged in the reverse order?

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Question 56

Anil invests some money at a fixed rate of interest, compounded annually. If the interests accrued during the second and third year are â‚¹ 806.25 and â‚¹ 866.72, respectively, the interest accrued, in INR, during the fourth year is nearest to

Question 57

Suppose hospital A admitted 21 less Covid infected patients than hospital B, and all eventually recovered. The sum of recovery days for patients in hospitals A and B were 200 and 152, respectively. If the average recovery days for patients admitted in hospital A was 3 more than the average in hospital B then the number admitted in hospital A was

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Question 58

A circle of diameter 8 inches isÂ inscribed in a triangle ABC where $$\angle ABC = 90^\circ$$. If BC = 10 inches then the area of the triangle in square inches is

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Question 60

If $$5 - \log_{10}\sqrt{1 + x} + 4 \log_{10} \sqrt{1 - x} = \log_{10} \frac{1}{\sqrt{1 - x^2}}$$, then 100x equals

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