Question Paper 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. If y1 and y2 are the dual variables corresponding to the first and second primal constraints, then their values in the optimal solution of the dual problem are respectively,
(a) 0 and 6                      
(b) 12 and 0
(c) 6 and 3 only              
(d) 4 and 4 only                                       
Ans(b)
6. 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)
7. 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)
8. 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)
9. 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)
10. Raju has 14 currency notes in his pocket consisting of only 20 Rs. notes and 10 Rs. notes. The total money value of the notes is 230 Rs. The number of 10 Rs. notes that Raju  has is
(a) 5                                 
(b) 6
(c) 9                                  
(d) 10                                                                           
Ans.(a)
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