# Tag Archives: GATE-GATE-CS-2003

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
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
The following is a scheme for floating point number representation using 16 bits. Bit position 15 14 . . . 9 8 . . .… Read More
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
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
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
Let ∑ = (a, b, c, d, e) be an alphabet. We define an encoding scheme as follows : g(a) = 3, g(b) = 5,… Read More
Consider the set {a, b, c} with binary operators + and × defined as follows : + a b c × a b c a… Read More
Let f : A → B be an injective (one-to-one) function. Define g : 2A → 2B as : g(C) = {f(x) | x ∈… Read More
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
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
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
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
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
Let (5, ≤) be a partial order with two minimal elements a and b, and a maximum element c. Let P : S → {True,… Read More