GATE CS

Let $p_1$ and $p_2$ denote two arbitrary prime numbers. Which one of the following statements is correct for all values of $p_1$ and $p_2$?

Let X be a 3-variable Boolean function that produces output as '1' when at least two of the input variables are '1'. Which of the following statement(s) is/are CORRECT, where a, b,...

Let A be a 2 x 2 matrix as given. $A = \begin{bmatrix} 1 & 1 \\ 1 & -1 \end{bmatrix}$ What are the eigenvalues of the matrix $A^{13}$ ?

Consider the following two languages over the alphabet {a, b, c}, where m and n are natural numbers. L₁ = {a^m b^m c^(m+n) | m, n ≥ 1} L₂ = {a^m b^n c^(m+n) | m, n ≥ 1} Which ONE o...

Consider a probability distribution given by the density function P(x). P(x) = {Cx^2, for 1 ≤ x ≤ 4 0, for x 4 The probability that x lies between 2 and 3, i.e., P(2 ≤ x ≤ 3) is __...

Let $L_1, L_2$ be two regular languages and $L_3$ a language which is not regular. Which of the following statements is/are always TRUE?

Which of the following statements about threads is/are TRUE?

Consider the following syntax-directed definition (SDD). S → DHTU { S.val = D.val + H.val + T.val + U.val; } D → "M"D₁ { D.val = 5 + D₁.val; } D → ε { D.val = -5; } H → "L"H₁ { H.v...

Consider a 32-bit system with 4 KB page size and page table entries of size 4 bytes each. Assume 1 KB = 2^10 bytes. The OS uses a 2-level page table for memory management, with the...