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Arithmetic 

Sumit sold an article at a certain profit . Had he purchased the article for 12% less than what he actually purchased it for and sold it for 24% more than what he actually sold it for  , his profit percentage would have been 5/2 times his actual profit percentage . Find his actual profit percentage .

1.  27.5%
2.  28.28%
3. 33.33%
4. 37.5 %

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Geometry

In the given figure ABDC is a rhombus , three of whose vertices lie on a circle with centre A. If the area of the rhombus is 32√3 square units . Find the radius of the
circle .

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Numbers 

Which of the following has  the greatest value?
A. 80!⁴

B. 160!²

C. 240! × 80!

D. 320!

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Geometry

Triangle ABC is an isosceles triangle with AB = AC and BC = 48. DE and DF are perpendiculars from D to AB and AC . The ratio of DE to DF is 5: 7. What is the length of DC?

A. 12
B. 20
C. 24
D. 28
E. None of the above

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Algebra

Both roots of the polynomial x² – bx + 1 are integers. And further one root is cube of the other. Which of the following is not a possible value of b?

A. -2

B. -1

C. 2

D. All are possible

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Numbers

Which of the following numbers are prime numbers?
A. 2²⁰⁸ + 1
B. 2²¹⁰ + 1
C.  2²⁰⁵ + 1

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Numbers/Algebra

If S = (A + 20) + ( A + 21) + ( A + 22)+………+ ( A + 100) , where A is a positive integer . What is the smallest value of A such that S is a perfect square ?

1. 4
2. 16
3. 324
4. None of the above

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Numbers

How many subsets of {1, 2, 3…… 9} contains at least one even integer?

1.460
2.464
3.480
4. 500
5. None of the above