Name of the University : Institute of Mathematics and Applications, Bhubaneswar
Exam : Entrance Test
Department : B.Sc Hons Mathematics and Computing
Document Type : Sample Question Paper
Website : https://iomaorissa.ac.in/
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B.Sc Mathematics & Computing Entrance Test Question Paper
Max Marks: 100 Max
Time: Two Hours
Related : Institute of Mathematics & Applications M.A./M.Sc. Computational Finance Entrance Test Question Paper : www.pdfquestion.in/24874.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.
** All questions are compulsory. Each question has 4 choices A, B, C and D, out of which only one is correct. Choose the correct answer.
** Each question carries +4 marks for the correct answer and -1 mark for a wrong answer.
Sample Question
1. If N is the set of all natural numbers. Let mRn, if n is divisible by m. The relation R is
A. reflexive and symmetric
B. transitive and antisymmetric
C. symmetric but not transitive
D. none of the above
2. Only one of the following is a function which one is it?
A. f(x2; x) : x 2 Rg
B. f(x; y) : x2 + y2 = 25; x; y 2 Rg
C. f(x; cos x) : x 2 Rg
D. f(x; y) : x3 + y3 ?? 3xy = 0; x; y 2 Rg
3. Let ABC be an equilateral triangle and P is a point within it satisfying AP2 = BP2 + CP2. The locus of P is
A. a straight line
B. a parabola
C. a circle
D. an ellipse
4. The last two digits of 1939 are
A. 10
B. 03
C. 59
D. 79
5. Let (x0; y0) be the solution of following equation (2x)ln 2 = (3y)ln 3; (3)ln x = (2)ln y; then x0 is
A. 1/6
B. 1/3
C. 1/2
D. 6
6. In how many ways 5 sweets can be distributed among 3 children so that every one gets at least one?
A. 10
B. 20
C. 6
D. 4
7. 1 x ex > 0 for
A. all x 2 R
B. no x 2 R
C. x > 0
D. x < 0
8. Let A = fsin xj0 < x < g. What does it mean if we say y is an element of A?
A. sin y is between 0 and
B. y is between sin(0) and sin()
C. y is between 0 and
D. y = sin x for some 0 < x <
9. The number of points where the graph of the function f(x) = x3 + 2×2 + 2x + 1 cuts the abscissa is
A. 1
B. 2
C. 3
D. 0
10. If one is solving three linear equations involving two unknowns, what happens?
A. usually there will be one solution, but occasionally there will be no solution or innitely many solutions.
B. anything can happen.
C. usually there will never be a solution.
D. there will always be a solution.
11. The number of solutions of the following system
x + y + z = 3;
2x + 3y + 4z = 9;
4x + 5y + 6z = 10;
is
A. 0
B. 1
C. 2
D. infinitely many
12. If a1; a2; :::; an are positive real numbers then a1 a2 + a2 a3 + + an1 an+ an a1 is always
A. n
B. n
C. n1=n
D. n1=n
13. The coecient of t3 in the expansion of 1 t6 1 t 3 is
A. 10
B. 12
C. 8
D. 9
14. ( p 5 + 2)10 + ( p 5 ?? 2)10 is equal to
A. [( p5 + 2)10] + 1
B. 4149
C. 10249
D. none of the above
15. The set of complex numbers z satisfying the equation (3+7i)z+(10??2i)z+100 = 0 represents in the complex plane
A. a point
B. a straight line
C. a pair of intersecting straight lines
D. a pair of distinct parallel lines
16. Let Z3 = f0; 1; 2g. The number of 2 2 matrices with entries from the set Z3 with determinant 1 is
A. 24
B. 60
C. 20
D. 30
17. Let A be 4 4 matrix with determinant 3. Let B be the matrix formed by subtracting two copies of the third row from rst. What is det(B)?
A. -6
B. 6
C. 3
D. 0
19. In the Taylor expansion of the function f(x) = ex=2 about x = 3, the coecient of (x ?? 3)5 is
A. e3=2 1 5!
B. e3=2 1255!
C. e??3=2 1255!
D. e??3=2 15!
20. Let (x; y) be any point on the parabola y2 = 4x. Let P be the point that divides the line segment from (0; 0) to (x; y) in 1 : 3. Then locus of P is
A. x2 = y
B. y2 = 2x
C. y2 = x
D. x2 = 2y