Question with Answer Gate Mathematics

1. In a topological space, which of the following statements is NOT always true :
(a) Union of any finite family of compact sets is compact.
(b) Union of any family of closed sets is closed.
(c) Union of any family of connected sets having a non-empty intersection is connected.
(d) Union of any family of dense subsets is dense.      
Ans(d)
2. Which one of the following statement is TRUE ?
(a) A convex set cannot have infinite many extreme points.
(b) A linear programming problem can have infinite many extreme points.
(c) A linear programming problem can have exactly two different optimal solutions.
(d) A linear programming problem can have a non-basic optimal solution.         
Ans(d)
3. The root of the equation xex= 1 between 0 and 1, obtained by using two iterations of bisection method, is
(a) 0.25
(b) 0.50
(c) 0.75
(d) 0.65                    
Ans(c)
4. The number of 5-Sylow subgroup (s) in a group of order 45 is
(a) 1                                 
(b) 2               
(c) 3                                
(d) 4                                                                                  
Ans(a)
5. Choose the most appropriate word from the options given below to complete the following sentences:
Given the seriousness of the situation that he had to face , his____ was impressive.
(a) beggary                                  
(b) nomenclature
(c) jealousy                                               
(d) nonchalance                                             
Ans.(d)
6. Choose the most alternative from the options given below to complete the following sentences:
If the tired soldier wanted to lie down, he _____ the  mattress out on the balcony.
(a) should take                                         
(b) shall take
(c) should have taken                               
(d) will have taken                             
Ans.(a)
7. If  and then   
(a) 2.23                                                     
(b) 4.33
(c) 11.37                                                   
(d) 27.64                                             
Ans.(d)
8. One of the parts (a,b,c,d ) in the sentence given below contains an ERROR. Which one of the following in INCORRECT?
I requested that he should be given the driving test today instead of tomorrow .
(a) requested that                                    
(b)should be given
(c) the driving test                                               
(d) instead of tomorrow .                  
Ans.(b)
9. Which one of the following options is the closest in meaning to the word given below?
Latitude
(a) Eligibility                                 
(b) Freedom
(c) Coercion                                 
(d) Meticulousness                                         
Ans.(b)
10. There are eight bags of rice looking alike, seven of which have equal weight and one is slightly heavier. The weighing balance  is of unlimited capacity. Using this balance, the Minimum number weighings required to identify the heavier bag is
(a) 2                                  
(b) 3
(c) 4                                  
(d) 8                                                                             
Ans.(a)
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