Free Online Practice mock Test 1 for GATE Mathematics. GATE syllabus and Previous Year Question Papers with Answers Free Download.

1. The straight lines L_{1} : x = 0, L_{2} : y = 0 and L_{3} : x + y = 1 are mapped by the transformation
w = z^{2} into the curves C_{1} , C_{2} and C_{3} respectively. The angle of intersection between the curves at
w = 0 is
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2. In a topological space, which of the following statements is NOT always true :
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3. Consider the following statements:
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P: The family of subsets {A_{n} = (-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 (T_{1}) 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 (T_{2}) space, then f is a one-one function.

Which of the above statements are correct?

4. A simple random sample of size 10 from 2 N(μ,σ^{2}) gives 98% confidence interval (20.49, 23.51). Then the null hypothesis H_{0} : μ = 20.5 against H_{A} : μ ≠ 20.5
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5. For the linear programming problem
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Maximize z = x_{1} + 2x_{2} + 3x_{3} - 4x_{4}

Subject to 2x_{1} + 3x_{2} - x_{3} - x_{4} = 15

6x_{1} + x_{2} + x_{3} - 3x_{4} = 21

8x_{1} + 2x_{2} + 3x_{3} - 4x_{4} = 30

x_{1}, x_{2}, x_{3}, x_{4} ≥ 0,

x_{1} = 4, x_{2} = 3, x_{3} = 0, x_{4} = 2 is