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Q.31 � 89 Carry Two Marks Each
31. Let p, q. r and s be four primitive statements.
Consider the following arguments:
P : [(p V q) A (r s) A (p V r)1(s q) s
S:[pA(p r)A(qvr)q
Which of the above arguments are valid?
(A) P and Q only
(B) P and R only
(C) P and S only
(D) P. Q, R and S
32. Let A be an n x n matrix of the following form.
31000...000
13100...000
01310...000
A= o 0 1 3 1 0 0 0
0 0000... 131
o o 0 0 0 0 1 3
What is the value of the determinant of A?
(A) 2 2 2 2
(B) 2 2 2 2
(C) 2 2 2 2
(D) 2 2 2 2
33. Let X and Y be two exponentially distributed and independent random
variables with mean c and 3, respectively. If Z = min(X,Y),
then the mean of Z is given by
(A) 1
(B) min(a,fl)
(C)
(D)a+fl
34. Let H1,H2,H3,... be harmonic numbers. Then, for neZ can be expressed as
(A) nH1�(n+1)
(B) (n+1)H�n
(C) nH�n
(D) (n+1)H1�(n+1)
35. In how many ways can we distribute 5 distinct balls,
B1,B2,...,B5 in 5 distinct cells, C1,C2,...,C5 such that Ball B,
is not in cell C,,Vi=1,2,...,5and each cell contains exactly one ball?
(A) 44
(B) 96
(C) 120
(D)3125
37. What is the number of vertices in an undirected connected graph with 27 edges,
6 vertices of degree 2, 3 vertices of degree 4 and remaining of degree 3?
(A) 10
(B) 11
(C) 18
(D)19
38. If f(1) = 2,f(2) = 4 and f(4) = 16,what is the value of f(3)using Lagrange�s
interpolation formula?
(A) 8
(B) 8
(C) 8
(D) 9
39. Consider the following iterative root finding methods and convergence properties:
Iterative root finding methods Convergence properties
(Q) False Position (I) Order of convergence = 1.62
(R) Newton Raphson (II) Order of convergence = 2
(S) Secant (III) Order of convergence = 1 with
guarantee of convergence
(T) Successive Approximation (IV) Order of convergence = 1 with
no guarantee of convergence
(A)Q-II R-IV S-lIl T-I
(B)Q-III R-II S-I T-IV
(C)Q-II R-I S-IV T-III
(D)Q-I R-IV S-Il T-III
40. Let M (K,Z,r,A,s,F)be a pushdown automaton, where
K={s,f},F={f},Z={a,b},r = {a}and
A ={((s,a,s),(s,a)),((s,b,s),(s,a)),((s,a,s),(f,s)),((f,a,a),(f,s)),((f,b,a),(f,s))
Which one of the following strings is not a member of L (M)?
(A) aaa
(B) aabab
(C) baaba
(D)bab
41. Let M = (K,Z,5,s,F) be a finite state automaton, where
K ={A,B},Z ={a,b},s =A,F ={B},
5(A,a) = A,5(A,b) = B,5(B,a) = Band 5(B,b) = A
A grammar to generate the language accepted by M can be specified
as G =(V,Z,R,S),where V = Ku Z,and S = A. Which one of the following
set of rules will make L(G) = L(M)?
(A)
(B)
(C) {A - bB,A - aB,B - aA,B -bA,B -s} i
(D)
42. Using a 4-bit 2�s complement arithmetic, which of the following additions will
result in an overflow?
(i) 1100 + 1100 (ii) 0011 + 0111 (iii) 1111 + 0111
(A) (i) only
(B) (ii) only
(C) (iii) only
(D) (i) and (iii) only
43. The number (123456)8 is equivalent to
(A) (A72E)16 and (22130232)4
(B) (A72E)16 and (22131122)4
(C) (A73E)16 and (22130232)4
(D) (A62E)16 and (22120232)4
44. The function AB�C + A�BC + ABC� + A�B�C + AB�C� is equivalent to
(A) AC�+AB+A�C
(B) AB�+AC�+A�C
(C) A�B+AC�+AB�
(D) A�B+AC+AB�
45. A serial transmission Ti uses 8 information bits, 2 start bits,
1 stop bit and 1 parity bit for each character. A synchronous transmission
T2 uses 3 eight bit sync characters followed by 30 eight bit information
characters. If the bit rate is 1200 bits/second in both cases,
what are the transfer rates of Ti and T2?
(A) 100 characters/sec, 153 characters/sec
(B) 80 characters/sec, i36 characters/sec
(C) 100 characters/sec, i36 characters/sec
(D) 80 characters/sec, 153 characters/sec
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