Q. The number of different n × n symmetric matrices with each element being either 0 or 1 is:
(Note: power(2, x) is same as 2x)

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Q. Let A, B, C, D be n × n matrices, each with non-­zero determinant. If ABCD = 1, then B-1 is

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Q. What is the result of evaluating the following two expressions using three-digit floating point arithmetic with rounding?

(113. + -111.) + 7.51
113. + (-111. + 7.51)

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Q. The tightest lower bound on the number of comparisons, in the worst case, for comparison-based sorting is of the order of

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Q. The problems 3-SAT and 2-SAT are

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Q. The following propositional statement is

(P → (Q v R)) → ((P ^ Q) → R)

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Q. How many solutions does the following system of linear equations have ?

-x + 5y = -1
x - y = 2
x + 3y = 3

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Q. An examination paper has 150 multiple-choice questions of one mark each, with each question having four choices. Each incorrect answer fetches -0.25 mark. Suppose 1000 students choose all their answers randomly with uniform probability. The sum total of the expected marks obtained by all these students is:

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Q. Mala has a colouring book in which each English letter is drawn two times. She wants to paint each of these 52 prints with one of k colours, such that the colour-pairs used to colour any two letters are different. Both prints of a letter can also be coloured with the same colour. What is the minimum value of k that satisfies this requirement ?

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Q. In an M'N matrix such that all non-zero entries are covered in a rows and b columns. Then the maximum number of non-zero entries, such that no two are on the same row or column, is

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Q. Two n bit binary strings, S1 and S2, are chosen randomly with uniform probability. The probability that the Hamming distance between these strings (the number of bit positions where the two strings differ) is equal to d is

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Q. A point is randomly selected with uniform probability in the X-Y plane within the rectangle with corners at (0,0), (1,0), (1,2) and (0,2). If p is the length of the position vector of the point, the expected value of p^2 is

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Q. Let G1 = (V, E1) and G2 = (V, E2) be connected graphs on the same vertex set V with more than two vertices. If G1 ∩ G2 = (V, E1 ∩ E2) is not a connected graph, then the graph G1 U G2 = (V, E1 U E2)

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Q. For the composition table of a cyclic group shown below:

* a b c d

a a b c d

b b a d c

c c d b a

d d c a b

Which one of the following choices is correct?

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Q. The product of the non-zero eigenvalues of the matrix

1 0 0 0 1
0 1 1 1 0
0 1 1 1 0
0 1 1 1 0
1 0 0 0 1

is ______

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Q. Which one of the following statements is TRUE about every n×n matrix with only real eigenvalues?

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Q. Consider the following system of equations in three real variables x1, x2 and x3:

2x1 - x2 + 3x3 = 1
3x1- 2x2 + 5x3 = 2
-x1 + 4x2 + x3 = 3

This system of equations has

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Q. Let A, B, C, D be n × n matrices, each with non-­zero determinant. If ABCD = 1, then B^-1 is

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Q. In the LU decomposition of the matrix,

| 2 2 |
| 4 9 |

if the diagonal elements of U are both 1, then the lower diagonal entry l22 of L is

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Q. Consider the following 2 × 2 matrix A where two elements are unknown and are marked by a and b. The eigenvalues of this matrix are –1 and 7. What are the values of a and b?

A = | 1 4 |
| b a |

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