GATE Mathematics Practice Paper 2 Questions And Answers

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Mathematics Practice Paper 2 Questions And Answers

1. The possible set of eigen values of a 4*4 skew-symmetric orthogonal real matrix is

Mathematics Practice Paper 2 Questions And Answers

4. Let f:ℝ →ℝ be a continuous function with f(1)=5 and f(3)=11. If g(x) = then g′(0) is equal to ______

Mathematics Practice Paper 2 Questions And Answers

5. Let P be a 2*2 complex matrix such that trace(P) = 1 and det(P)=−6. Then, trace (P4 - P3) is ______

Mathematics Practice Paper 2 Questions And Answers

6. Suppose that R is a unique factorization domain and that a,b ∈R are distinct irreducible elements. Which of the following statements is TRUE?

Mathematics Practice Paper 2 Questions And Answers

7. Let X be a compact Hausdorff topological space and let Y be a topological space. Let f: X --> Y be a bijective continuous mapping. Which of the following is TRUE?

Mathematics Practice Paper 2 Questions And Answers

8. Consider the linear programming problem: Maximize x + 3/2 y subject to 2x + 3y ≤ 16 x + 4y ≤ 18 x ≥ 0, y ≥ 0. If 𝑆𝑆 denotes the set of all solutions of the above problem, then

Mathematics Practice Paper 2 Questions And Answers

9. Which of the following groups has a proper subgroup that is NOT cyclic?

Mathematics Practice Paper 2 Questions And Answers

11. Suppose the random variable U has uniform distribution on [0,1] and X =−2logU. The density of X is

Mathematics Practice Paper 2 Questions And Answers

12. Let f be an entire function on ℂ such that |f(z)| ≤ 100 log|z| for each z with |z| ≥ 2. If F(i) = 2i then f(1)

Mathematics Practice Paper 2 Questions And Answers

13. The number of group homomorphisms from ℤ3 to ℤ9 is ______