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1.

Consider solving the following system of simultaneous equations using LU decomposition.x1 + x2 – 2x3 = 4x1 + 3x2 – x3 = 72x1 + x2 – 5x3 = 7where L and U are denoted asWhich one of the following is the correct combination of values for L32, U33, and x1?(A)L32 = 2, U33 = -1/2, x1 = -1(B)L32 = 2, U33 = 2, x1 = -1(C)L32 = -1/ 2, U33 = 2, x1 = 0(D)L32 = -1/2, U33 = -1/2, x1 = 0

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2.

Which one of the following statements is TRUE for all positive functions f (n) ?(A)f(n^{2}) = \theta (f(n^{2})), when f (n) is a polynomial(B)f(n^{2}) = o (f(n^{2}))(C)f(n^{2}) = O(f(n^{2})), when f (n) is an exponential function(D)f(n^{2}) = Ω(f(n^{2}))

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3.

Let r be a root of the equationx2 + 2x + 6 = 0. Then the value of the expression (r+2) (r+3)(r+4)(r+5) is(A)51(B)-51(C)126(D)-126

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4.

First ball is drawn. What is the probability of getting an orange ball in the next draw?(A)\frac{1}{2}(B)\frac{8}{25}(C)\frac{19}{50}(D)\frac{23}{50}

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5.

Which one of the following statements is TRUE?(A)The LALR(1) parser for a grammar G cannot have a reduce-reduce conflict if the LR(1) parser for G does not have reduce-reduce conflict.(B)The symbol table is accessed only during the lexical analysis phase.(C)Data flow analysis is necessary for run-time memory management.(D)LR(1) parsing is sufficient for deterministic context-free languages.

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6.

A plot of land must be divided between four families. They want their individual plots to be similar in shape, not necessarily equal in area. The land has equally spaced poles, marked as dots in the below figure. Two ropes, R1 and R2, are already present and cannot be moved.What is the least number of additional straight ropes needed to create the desired plots? A single rope can pass through three poles that are aligned in a straight line.(A)2(B)4(C)5(D)3

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7.

Which one of the following statements is correct based on the above information?(A)P cannot be placed at a corner(B)S cannot be placed at a corner(C)U cannot be placed at a mid-point(D)R cannot be placed at a corner

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8.

Which one of the following is the correct logical inference based on the information provided in the above passage?(A)Equal number of boys and girls qualified(B)Equal number of boys and girls appeared for the test(C)The number of boys who appeared for the test is less than the number of girls who appeared(D)The number of boys who qualified for the test is less than the number of girls who qualified

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9.

Consider the following two statements with respect to the matrices Am×n , Bn×m , Cn×n and Dn×nStatement 1: tr(AB) = tr(BA) Statement 2: tr(CD) = tr(DC) where tr() represents the trace of a matrix. Which one of the following holds?(A)Statement 1 is correct and Statement 2 is wrong.(B)Statement 1 is wrong and Statement 2 is correct.(C)Both Statement 1 and Statement 2 are correct.(D)Both Statement 1 and Statement 2 are wrong.

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10.

Consider the data transfer using TCP over a 1 Gbps link. Assuming that the maximum segment lifetime (MSL) is set to 60 seconds, the minimum number of bits required for the sequence number field of the TCP header, to prevent the sequence number space from wrapping around during the MSL is____________.(A)27.8(B)48.0(C)33.0(D)35.0

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