MCQs Olympiad IMO-Mathematics

1. Water is flowing at the rate of 5 km/hr through a pipe of diameter 14 cm into a rectangular tank which is 50 m long and 44 m wide. Determine the time  in which the level of the water in the tank will rise by 7 cm.
 (A)      2 hrs                           
(B)    4 hrs                  
(C)   8 hrs                   
(D)   10 hrs    
Ans (A)
2. The product of two consecutive natural numbers is always_______.
(A) An even number                                     
(B) An odd number  
(C) A prime number                                     
(D) Divisible by 3                                                 
Ans. (A)
3. A circular field has a circumference of 360 km. Two cyclists Sumeet and Samrat start together and can cycle at speeds       of 12km/hr and 15 km/hr respectively around the circular Field. After how many hours will they meet again at the starting point
(A)  60                      
(B) 8                       
(C) 100                  
(D) 120                                      
Ans. (D)
4. Find the largest positive integer that will divide 398, 436 and 542 leaving remainders 7, 11 and 15 respectively.
(A) 15                               
(B) 16                      
(C) 17                                   
(D) 18                    
Ans. (C)
5. If the sum of the zeroes of the polynomial f (x) = 2x3 – 3kx2 +4x – 5 is 6, then the value of k is _______.
(A) 2                              
(B) 4                            
(C) -2                              
(D) -4                                           
Ans. (B)
6. When 3x2 – x3 – 3x +5 is divided by x-1-x2, the quotient and remainder are_____.
(A) x+2 , 3                           
(B) x-2, -3                
(C) x-2, 3                        
(D) x+2, -3                             
Ans. (C)
7. Every quadratic polynomial can have at the most ______.
(A) one zero                                       
(B) Two Zeroes             
(C) Three Zeroes                               
(D) Four zeroes                                                                                 
Ans. (B)
8. The roots of the quadratic equation 3x2 – kx + 14 = 0 are in the ratio 7: 6, then k equals______.
(A) 13                         
(B) 12                           
(C)    1                             
(D) -3                                              
Ans. (A)
9. The sum of two numbers is 9 and the sum of their squares is 41. The numbers are ______.
(A) 4 & 5                     
(B) 1 & 8                             
(C) 3 & 6                       
(D) 2 & 7            
Ans. (A)
10. The graph of y =1 is a line parallel to ______.
(A) x-axis                                               
(B) y-axis                         
(C) Both x and y –axis                       
(D)   line y = x                                                         
Ans. (A)
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