11.  Which of the following permutations can be obtained in the output using a stack of size 3 elements assuming that input, sequence is 1, 2, 3, 4, 5 ? 
a.  3, 2, 1, 5, 4 
b.  5, 4, 3, 2, 1 
c.  3, 4, 5, 2, 1 
d.  3, 4, 5, 1, 2 
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Answer: (c).3, 4, 5, 2, 1

12.  How many solutions do the following equation have x1 + x2 + x3 = 11 where x1 ≥ 1, x2 ≥2, x3 ≥ 3 
a.  C(7, 11) 
b.  C(11, 3) 
c.  C(14, 11) 
d.  C(7, 5) 
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Answer: (c).C(14, 11)

13.  The number of distinct bracelets of five beads made up of red, blue, and green beads (two bracelets are indistinguishable if the rotation of one yield another) is, 
a.  243 
b.  81 
c.  51 
d.  47 
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Answer: (c).51

14.  58 lamps are to be connected to a single electric outlet by using an extension board each of which has four outlets. The number of extension boards needed to connect all the light is 
a.  29 
b.  28 
c.  20 
d.  19 
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Answer: (d).19

15.  The power set of AUB, where A = {2, 3, 5, 7} and B = {2, 5, 8, 9} is 
a.  256 
b.  64 
c.  16 
d.  4 
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Answer: (b).64

16.  Which is not the correct statement ? 
a.  The class of regular sets is closed under homomorphisms. 
b.  The class of regular sets is not closed under inverse homomorphisms. 
c.  The class of regular sets is closed under quotient. 
d.  The class of regular sets is closed under substitution. 
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Answer: (b).The class of regular sets is not closed under inverse homomorphisms.

17.  Given the following statements : (i) Recursive enumerable sets are closed under complementation. (ii) Recursive sets are closed under complementation. Which is/are the correct statements ? 
a.  only (i) 
b.  only (ii) 
c.  both (i) and (ii) 
d.  neither (i) nor (ii) 
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Answer: (b).only (ii)

18.  Let θ(x, y, z) be the statement “x + y = z” and let there be two quantifications given as (i) ∀x ∀y Z ∃ θ(x, y, z) (ii) ∃Z ∀x ∀y θ(x, y, z) Where x, y, z are real numbers. Then which one of the following is correct ? 
a.  (i) is true and (ii) is true 
b.  (i) is true and (ii) is false 
c.  (i) is false and (ii) is true 
d.  (i) is false and (ii) is false 
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Answer: (b).(i) is true and (ii) is false

19.  Let P(rn, n) be the statement if "m divides n" where the universe of discourse for both the variables is the set of positive integers. Determine the truth values of each of thefollowing propositions: I. ∀m ∀n P(m,n) II. ∃m ∀n P(m,n) 
a.  Both I and II are true 
b.  Both I and II are false 
c.  I false & II true 
d.  I true & IIfalse 
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Answer: (c).I false & II true

20.  Big O estimate for ( f(x) = (x + 1) log(x2 + 1) +3x2 is given as 
a.  O(x log x) 
b.  O(x^2) 
c.  O(x^3) 
d.  O(x^2 log x) 
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Answer: (b).O(x^2)
