GATE exam stream

GATE CS — Computer Science & IT

174 questions and papers

GATE CS 2021 Set 1 — Question 28

Multiple choice 2 marks Engineering Mathematics 2021

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 2019 — Question 11

Multiple choice 1 mark Engineering Mathematics 2019

Let \(X\) be a square matrix. Consider the following two statements on \(X\).I. \(X\) is invertible.II. Determinant of \(X\) is non-zero.Which one of the following is TRUE?

GATE CS 2017 Set 1 — Question 47

Numerical answer 2 marks Engineering Mathematics 2017

If the characteristic polynomial of a \(3\times 3\) matrix \(M\) over \(\mathbb{R}\) (the set of real numbers) is \(\lambda^{3} - 4\lambda^{2} + a\lambda + 30\), \(a \in \mathbb{R}\), and one eigenvalue of \(M\) is \(2\), then the largest among the absolute values of the eigenvalues of \(M\) is ______.

GATE CS 2017 Set 1 — Question 30

Multiple choice 2 marks Engineering Mathematics 2017

If \(f(x) = R\sin\left(\dfrac{\pi x}{2}\right) + S\), \(f'\left(\dfrac{1}{2}\right) = \sqrt{2}\) and \(\displaystyle\int_{0}^{1} f(x)\,dx = \dfrac{2R}{\pi}\), then the constants \(R\) and \(S\) are respectively