Name of the University : Institute of Mathematics and Applications, Bhubaneswar
Exam : Entrance Test
Department : M.A./M.Sc. : Computational Finance
Document Type : Sample Question Paper
Website : https://iomaorissa.ac.in/
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Mathematics Computational Finance Entrance Question Paper
Max Marks: 100 Max
Time: Two Hours
Related : Madhava Mathematics Competition/Exam Model Question Paper 2017 : www.pdfquestion.in/23571.html
Instructions
** All questions are compulsory. Questions in this group carry 3 marks each.
** Choose the right alternative from among the given alternatives.
** For incorrect answer -1 mark will be awarded.
** Write down the answers to the questions in Part A(1-20) in the space provided below the question. Each of the questions in Part A carries 3 marks.
** Choose the right alternative from among the given alternative for questions in Part B(21-30). Each of the questions in Part B carries 4 marks. For incorrect answer -1 mark will be awarded.
Group A
1. If x earns 25% more than y by what percent y earns less than x ?
A. 16%
B. 18%
C. 20%
D. 25%
2. A reduction of 20% in the price of rice enables a person to buy 3.5 kg more for Rs. 77. What is the original price per kg ?
A. Rs. 4.00
B. Rs. 4.50
C. Rs. 5.00
D. Rs. 5.50
3. A dealer marks his goods 30% above the cost price but allows a discount of 15% for cash payment. What is the percentage of gain ?
A. 15%
B. 9%
C. 8.5%
D. 7.5%
4. In how many years will Rs. 1000 become Rs. 1331 at the rate of 10% compounded annually ?
A. 4
B. 3
C. 2
D. 1
5. A, B and C subscribe Rs. 45,000 for a business. A subscribes Rs. 5000 more than B and B subscribes Rs. 5000 more than C. What is B’s share of the annual prot of Rs. 9000 ?
A. Rs. 3000
B. Rs. 2000
C. Rs. 1500
D. Rs. 1000
6. If x2 =1 x2 + 1 then x2 +1 x2 is equal to
A. 5
B. p5
C. p5
D. 0
7. If 3x??y = 27 and 3x+y = 243, then x is equal to
A. 0
B. 2
C. 4
D. 8
8. If x + 3 divides x3 + 5×2 + kx, then k is equal to
A. 6
B. 4
C. 2
D. 8
9. The solution of the equation 71+x + 71??x = 50 is
A. 0
B. 1
C. 2
D. none of the above
Page 2
10. The solution of the inequation j2x ?? 6j 6 is
A. x 6
B. 0 x 6
C. ??6 x 6
D. not dened
11. A walks a distance of 3 km towards north, then turns to his left and walks for 2 km. He again turns left and walks for 3 km. At this point, he turns to his right and walks for 3 km. How many kilometers and in what direction is he from the starting point ?
A. 5 km and west
B. 3 km and south
C. 2 km and south
D. 1 km and east
12. A three centimeters cube has been painted red on all its sides. It is cut into one centimeter cubes. How many cubes have two sides painted ?
A. 4
B. 6
C. 8
D. 12
13. If each side of a rectangle is increased by 50% its area will increase by
A. 50%
B. 125%
C. 100%
D. 0%
14. What is the next term in the following sequence ?
1, 1, 2, 3, 5, 8, 13, 21
A. 34
B. 40
C. 29
D. none of the above
15. Let = greater than, 4 = less than, = not less than and + = not greater than. If p qr, then which of the following is true ?
A. p4q r
B. pq r
C. pq4r
D. p + q r
Group B
** All questions are compulsory.
** Each question carries +4 marks.
** NO NEGATIVE marking.
** Only write down the answer.
** Calculations may be done in the rough work paper attached in the answer sheet.
1. A rectangle of largest area is inscribed in a semi circle of radius 2 units. What is the area of the rectangle thus inscribed ?
2. If the sum of two nonzero numbers is 8, then what is the minimum of the sum of their reciprocals ?
3. In how many ways can 6 boys and 5 girls sit in a row if the girls are to sit together and the boys do not sit together ?
4. If a coin is tossed thrice then what is the probability of getting at most two heads ?
5. Let d be the standard deviation of n observations. If each observation is multiplied by 4 then what is the standard deviation of the resulting data ?
6. If R 1 0 f(x) dx = 4, R 2 0 f(t) dt = 2 and R 4 R 2 f(u) du = 1, then what is the value of 4 1 f(x) dx ?
7. What is the area enclosed by the parabola y2 = 2x and the line y = 2x ?