Year-wise GATE papers

GATE 2021

5 questions and papers

GATE CS 2021 Set 1 — Question 40

Multiple choice 2 marks Theory of Computation GATE CS — Computer Science & IT

For a Turing machine \(M\), \(\langle M \rangle\) denotes an encoding of \(M\). Consider the following two languages.\(L_1 = \{\langle M \rangle \mid M\) takes more than 2021 steps on all inputs\(\}\)\(L_2 =…

GATE CS 2021 Set 1 — Question 28

Multiple choice 2 marks Engineering Mathematics GATE CS — Computer Science & IT

Let \(A\) and \(B\) be two \(n \times n\) matrices over real numbers. Let \(\operatorname{rank}(M)\) and \(\det(M)\) denote the rank and determinant of a matrix \(M\), respectively. Consider the following statements.I. \(\operatorname{rank}(AB) = \operatorname{rank}(A)\,\operatorname{rank}(B)\)II. \(\det(AB) = \det(A)\,\det(B)\)III. \(\operatorname{rank}(A+B) \le \operatorname{rank}(A) + \operatorname{rank}(B)\)IV. \(\det(A+B) \le \det(A) + \det(B)\)Which of the above statements are TRUE?

GATE CS 2021 Set 1 – Question 36

Multiple choice 2 marks Algorithms GATE CS — Computer Science & IT

Consider the following recurrence relation:\(T(n) = T(n/2) + T(2n/5) + 7n\) for \(n > 0\), and \(T(0) = 0\).Which one of the following options is correct?