Questions and answers for exam Preparation

MCQs

Total Questions : 69 | Page 3 of 7 pages

Question 21. If |4X - 7| = 5 then the values of 2|X| - |-X| is :

2, 1/3
1/2, 3
3/2, 9
2/3, 9

Discuss Question

Answer: Option B. -> 1/2, 3

-NA-

Question 22. Suppose that R is a unique factorization domain and that a,b âˆˆR are distinct irreducible elements. Which of the following statements is TRUE?

The ideal âŒ©1+aâŒª is a prime ideal
The ideal âŒ©a+bâŒª is a prime ideal
The ideal âŒ©1+abâŒª is a prime ideal
The ideal âŒ©aâŒª is not necessarily a maximal ideal

Discuss Question

Answer: Option D. -> The ideal âŒ©aâŒª is not necessarily a maximal ideal

-NA-

Question 23. Consider the linear programming problem:Maximize x + 3/2 ysubject to 2x + 3y â‰¤ 16 x + 4y â‰¤ 18 x â‰¥ 0, y â‰¥ 0.If ð‘†ð‘† denotes the set of all solutions of the above problem, then

s is empty
s is a singleton
s is a line segment
s has positive area

Discuss Question

Answer: Option C. -> s is a line segment

-NA-

Question 24. Which of the following groups has a proper subgroup that is NOT cyclic?

â„¤15*â„¤77
S3
(â„¤,+)
(â„š,+)

Discuss Question

Answer: Option D. -> (â„š,+)

-NA-

Question 25. 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?

f is a closed mapbut not necessarily an open map
f is an open map but not necessarily a closed map
f is both an open map and a closed map
f need not be an open map or a closed map

Discuss Question

Answer: Option D. -> f need not be an open map or a closed map

-NA-

Question 26. The image of the region {z âˆˆâ„‚âˆ¶ Re(z)>Im(z)>0} under the mapping zâ†¦(ez)2 is

{wâˆˆâ„‚âˆ¶ Re(w)>0, Im(w)>0}
{wâˆˆâ„‚âˆ¶ Re(w)>0, Im(w)>0,|w|>1}
{wâˆˆâ„‚âˆ¶ |w|>1}
{wâˆˆâ„‚âˆ¶ Im(w)>0,|w|>1}

Discuss Question

Answer: Option C. -> {wâˆˆâ„‚âˆ¶ |w|>1}

-NA-

Question 27. Let M be the space of all 4*3 matrices with entries in the finite field of three elements. Then the number of matrices of rank three in M is

(34âˆ’3)(34âˆ’32)(34âˆ’33)
(34âˆ’1)(34âˆ’2)(34âˆ’3)
(34âˆ’1)(34âˆ’3)(34âˆ’32)
34(34âˆ’1)(34âˆ’2)

Discuss Question

Answer: Option C. -> (34âˆ’1)(34âˆ’3)(34âˆ’32)

-NA-

Question 28. Let X be an arbitrary random variable that takes values in{0,1,¦,10}. The minimum and maximum possible values of the variance of X are

0 and 30
1 and 30
0 and 25
1 and 25

Discuss Question

Answer: Option C. -> 0 and 25

-NA-

Question 29. Let V be a vector space of dimension mâ‰¥2. Let T:V â†’ V be a linear transformation such that T

Rank (Tn)â‰¤ Nullity (Tn)
trace (T)â‰ 0
T is diagonalizable
n=m

Discuss Question

Answer: Option A. -> Rank (Tn)â‰¤ Nullity (Tn)

-NA-

Question 30. Consider the functions f(z) = (z2 + Î±x)/(z + 1)2 and g(z) = sinh(z - Ï€/2Î±), Î±â‰ 0For the value of Î± obtained in Q.54, the function g(z) is not conformal at a point