### GATE Mathematics Questions And Answers

**Here you can find GATE Mathematics Questions And Answers.**

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## GATE Mathematics Questions and Answers - Chapters

- Mathematics Practice Paper 1 Questions & Answers
- Mathematics Practice Paper 1 Questions & Answers

### Mathematics Practice Paper 1Questions And Answers

1. The straight lines L1 : x = 0, L2 : y = 0 and L3 : x + y = 1 are mapped by the transformation w = z2 into the curves C1 , C2 and C3 respectively. The angle of intersection between the curves at w = 0
is

### Mathematics Practice Paper 1Questions And Answers

2. In a topological space, which of the following statements is NOT always true :

### Mathematics Practice Paper 1Questions And Answers

3. Consider the following statements:
P: The family of subsets {An = (-1/n, 1/n), n = 1, 2, ...} satisfies the finite intersection property.
Q: On an infinite set X , a metric d : X * X --> R is defined as d(x,y) = [0 , x = y and 1, x ? y] The metric space (X,d) is compact.
R: In a Frechet (T1) topological space, every finite set is closed.
S: If f : R --> X is continuous, where R is given the usual topology and (X, t) is a Hausdorff (T2) space, then f is a one-one function.
Which of the above statements are correct?

### Mathematics Practice Paper 1Questions And Answers

4. A simple random sample of size 10 from 2 N(µ,s2) gives 98% confidence interval (20.49, 23.51). Then the null hypothesis H0 : µ = 20.5 against HA : µ ? 20.5

### Mathematics Practice Paper 1 Questions And Answers

5. For the linear programming problem
Maximize z = x1 + 2x2 + 3x3 - 4x4
Subject to 2x1 + 3x2 - x3 - x4 = 15
6x1 + x2 + x3 - 3x4 = 21
8x1 + 2x2 + 3x3 - 4x4 = 30
x1, x2, x3, x4 = 0,
x1 = 4, x2 = 3, x3 = 0, x4 = 2 is

### 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?