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MCQs

Total Questions : 69 | Page 1 of 7 pages
Question 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
  1.    0
  2.    Ï€/4
  3.    Ï€/2
  4.    Ï€
 Discuss Question
Answer: Option D. -> π


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Question 2. A simple random sample of size 10 from 2 N(μ,σ2) gives 98% confidence interval (20.49, 23.51). Then the null hypothesis H0 : μ = 20.5 against HA : μ ≠ 20.5
  1.    can be rejected at 2% level of significance
  2.    cannot be rejected at 5% level of significance
  3.    can be rejected at 10% level of significance
  4.    cannot be rejected at any level of significance
 Discuss Question
Answer: Option C. -> can be rejected at 10% level of significance


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Question 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 â‰  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?
  1.    P and R
  2.    P and S
  3.    R and S
  4.    Q and S
 Discuss Question
Answer: Option A. -> P and R


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Question 4. In a topological space, which of the following statements is NOT always true :
  1.    Union of any finite family of compact sets is compact.
  2.    Union of any family of closed sets is closed.
  3.    Union of any family of connected sets having a non empty intersection is connected.
  4.    Union of any family of dense subsets is dense.
 Discuss Question
Answer: Option B. -> Union of any family of closed sets is closed.


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Question 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
  1.    an optimal solution
  2.    a degenerate basic feasible solution
  3.    a non-degenerate basic feasible solution
  4.    a non-basic feasible solution
 Discuss Question
Answer: Option D. -> a non-basic feasible solution


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Question 6. Which one of the following statements is TRUE?
  1.    A convex set cannot have infinite many extreme points.
  2.    A linear programming problem can have infinite many extreme points.
  3.    A linear programming problem can have exactly two different optimal solutions.
  4.    A linear programming problem can have a non-basic optimal solution.
 Discuss Question
Answer: Option D. -> A linear programming problem can have a non-basic optimal solution.


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Question 7. 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?
  1.    f1(z1, z2) = 1/2 (z1 - iz2), f2(z1, z2) = 1/2 (z1 + iz2)
  2.    f1(z1, z2) = 1/2 (z1 + iz2), f2(z1, z2) = 1/2 (iz1 + z2)
  3.    f1(z1, z2) = 1/2 (z1 - iz2), f2(z1, z2) = 1/2 (-iz1 + z2)
  4.    f1(z1, z2) = 1/2 (z1 + iz2), f2(z1, z2) = 1/2 (-iz1 - z2)
 Discuss Question
Answer: Option C. -> f1(z1, z2) = 1/2 (z1 - iz2), f2(z1, z2) = 1/2 (-iz1 + z2)


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Question 8. Let R = ℤ*ℤ*ℤ and I = ℤ*ℤ*{0}. Then which of the following statement is correct?
  1.    I is a maximal ideal but not a prime ideal of R .
  2.    I is a prime ideal but not a maximal ideal of R .
  3.    I is both maximal ideal as well as a prime ideal of R .
  4.    I is neither a maximal ideal nor a prime ideal of R .
 Discuss Question
Answer: Option B. -> I is a prime ideal but not a maximal ideal of R .


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Question 9. The root of the equation x ex = 1 between 0 and 1, obtained by using two iterations of bisection
method, is
  1.    0.25
  2.    0.50
  3.    0.75
  4.    0.65
 Discuss Question
Answer: Option C. -> 0.75


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Question 10. Let the linear transformation T : F2 ---> F3 be defined by T(x1, x2) = (x1x1, x2x2) Then the nullity of T is
  1.    0
  2.    1
  3.    2
  4.    3
 Discuss Question
Answer: Option A. -> 0


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