GATE Mathematics Practice Paper 1 Questions And Answers
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Mathematics Practice Paper 1 Questions 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 1 Questions And Answers
2. In a topological space, which of the following statements is NOT always true :
Mathematics Practice Paper 1 Questions 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 1 Questions 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 1 Questions And Answers
6. Which one of the following statements is TRUE?
Mathematics Practice Paper 1 Questions And Answers
8. Let V = ℂ2 be the vector space over the field of complex numbers and B{(1, i), (i,1)}be a given ordered basis of V. Then for which of the following, B* = {f1, f2}is a dual basis of B over ℂ?
Mathematics Practice Paper 1 Questions And Answers
9. Let R = ℤ*ℤ*ℤ and I = ℤ*ℤ*{0}. Then which of the following statement is correct?
Mathematics Practice Paper 1 Questions And Answers
12. If a transformation y = uv transforms the given differential equation
f(x)y'' - 4f'(x)y' + g(x)y = 0 into the equation of the form v'' + h(x)v = 0, then u must be
Mathematics Practice Paper 1 Questions And Answers
13. The expression 1/(Dx2 - Dy2) sin(x - y) is equal to
