Discrete Mathematics |Gate-2012| The recurrence relation capturing the optional execution time of the Towers of Hanoi problem with nn discs is [GATE – 2012] a. T (n) = 2T (n-2) + 2b. T (n) = 2T (n-1) + nc. T (n) = 2T (n/2) + 1d. T (n) = 2T (n-1) + 1 Answer : d) Back …
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Discrete Mathematics |Gate-2014| The security system at an IT office is composed of 10 computers of which exactly four are working. To check whether the system is functional, the officials inspect four of the computers picked at random (without replacement). The system is deemed functional if at least three of the four computers inspected are …
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Discrete Mathematics |Gate-2015| 1. In a room there are only two types of people, namely Type 11 and Type 2.2. Type 11 people always tell the truth and Type 22 people always lie. You give a fair coin to a person in that room, without knowing which type he is from and tell him to toss it and hide the result from you …
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Discrete Mathematics |Gate-2016| 1. Consider the following expressions: (i) false (ii) QQ (iii) true (iv) P∨QP∨Q (v) ¬QVP¬QVP The number of expressions given above that are logically implied by P∧(P⇒Q)P∧(P⇒Q)) is _____________. [GATE – 2016] a. 3b. 4c. 5d. 6 Answer : b) 2. Let p,q,r,sp,q,r,s represent the following propositions. p:x∈{8,9,10,11,12}p:x∈{8,9,10,11,12}q:xq:x is a composite numberr:xr:x is a perfect squares:xs:x is a prime number The integer x≥2x≥2 which satisfies ¬((p⇒q)∧(¬r∨¬s))¬((p⇒q)∧(¬r∨¬s)) is ______________. [GATE – 2016] a. …
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Discrete Mathematics |Gate-2017| 1. Let XX be a Gaussian random variable with mean 00 and variance σ2σ2 . Let Y=max(X,0)Y=max(X,0) where max(a,b)max(a,b) is the maximum of aa and bb. The median of YY is ___________.[GATE – 2017] a. 0b. 1c. 2d. 3 Answer : a) 2. Let c1,…..,cnc1,…..,cn be scalars, not all zero, such that n∑i=1ci ai=0∑i=1nciai=0 where ai are column vectors in R11.R11. Consider the set of linear equations AX=bAX=b Where A=[a1,…..,an]A=[a1,…..,an] and b=n∑i=1 ai.b=∑i=1nai.The set of equations has : …
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Discrete Mathematics |Gate-2018| 1. Two people, PP and Q,Q, decide to independently roll two identical dice, each with 66 faces, numbered 11 to 6.6. The person with the lower number wins. In case of a tie, they roll the dice repeatedly until there is no tie. Define a trial as a throw of the dice by PP and Q.Q. Assume that all 66 numbers on each dice are equi-probable and that …
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Discrete Mathematics |Gate-2019| Two numbers are chosen independently and uniformly at random from the set {1, 2, …., 13}. The probability (rounded off to 3 decimal places) that their 4-bit (unsigned) binary representations have the same most significant bit is ______.[GATE – 2019] a. 0.503b. 0.505c. 0.506d. 0.507 Answer : a) Suppose Y is distributed …
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Discrete Mathematics |Gate-2020| Which one of the following predicate formulae is NOT logically valid? Note that W is a predicate formula without any free occurrence of x. [GATE -2020] a. ∀x(p(x)∨W) ≡ ∀x p(x) ∨ Wb. ∃x(p(x) ∧ W) ≡ ∃x p(x) ∧Wc. ∀x(p(x)→ W) ≡ ∀x p(x) → Wd. ∃x (p(x) → W) ≡ ∃x …
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