## GATE | GATE-CS-2003 | Question 90

The literal count of a boolean expression is the sum of the number of times each literal appears in the expression. For example, the literal… Read More »

## GATE | GATE-CS-2003 | Question 90

A 1-input, 2-output synchronous sequential circuit behaves as follows : Let zk, nk denote the number of 0’s and 1’s respectively in initial k bits… Read More »

## GATE | GATE-CS-2003 | Question 44

The following is a scheme for floating point number representation using 16 bits. Bit position 15 14 . . . 9 8 . . .… Read More »

## GATE | GATE-CS-2003 | Question 42

A piecewise linear function f(x) is plotted using thick solid lines in the figure below (the plot is drawn to scale). If we use the… Read More »

## GATE | GATE-CS-2003 | Question 41

Consider the following system of linear equations Notice that the second and the third columns of the coefficient matrix are linearly dependent. For how many… Read More »

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## GATE | GATE-CS-2003 | Question 40

A graph G = (V, E) satisfies |E| ≤ 3 |V| – 6. The min-degree of G is defined as . Therefore, min-degree of G… Read More »

## GATE | GATE-CS-2003 | Question 90

Let ∑ = (a, b, c, d, e) be an alphabet. We define an encoding scheme as follows : g(a) = 3, g(b) = 5,… Read More »

## GATE | GATE-CS-2003 | Question 38

Consider the set {a, b, c} with binary operators + and × defined as follows : + a b c × a b c a… Read More »

## GATE | GATE-CS-2003 | Question 37

Let f : A → B be an injective (one-to-one) function. Define g : 2A → 2B as : g(C) = {f(x) | x ∈… Read More »

## GATE | GATE-CS-2003 | Question 36

How many perfect matchings are there in a complete graph of 6 vertices ? (A) 15 (B) 24 (C) 30 (D) 60 Answer: (A) Explanation:… Read More »

## GATE | GATE-CS-2003 | Question 90

Consider the following recurrence relation The value of T(m2) for m ≥ 1 is (A) (m/6) (21m – 39) + 4 (B) (m/6) (4m2 –… Read More »

## GATE | GATE-CS-2003 | Question 34

m identical balls are to be placed in n distinct bags. You are given that m ≥ kn, where, k is a natural number ≥… Read More »

## GATE | GATE-CS-2003 | Question 33

Consider the following formula a and its two interpretations I1 and I2 Which of the following statements is true? (A) I1 satisfies α, I2 does… Read More »

## GATE | GATE-CS-2003 | Question 32

Which of the following is a valid first order formula ? (Here α and β are first order formulae with x as their only free… Read More »

## GATE | GATE-CS-2003 | Question 31

Let (5, ≤) be a partial order with two minimal elements a and b, and a maximum element c. Let P : S → {True,… Read More »