PREVIOUS YEAR QUESTIONS

PRMO 2012 

1. Rama was asked by her teacher to subtract 3 from a certain number and then divide the result by 9. Instead, she subtracted 9 and divided the result by 3. She got 43 as the answer. What would have been her answer if she had solved the problem correctly? 

ANS : Let the number be x 

          She subtracted 9 from 'x' and divide by 3

          Rama's incorrect method:

           x-9/3 =43 

2. A triangle with perimeter 7 has integer side lengths. What is the maximum nossible ares of such a triangle? 

IOQM 2024 

1. The smallest positive integer that does not divide 1 × 2 × 3 × 4 × 5 × 6 × 7 × 8 × 9 is: 

ANSWER : (11) 

Let n be a smallest integer that does not divide 1 × 2 × 3 × 4 × 5 × 6 × 7 × 8 × 9 

Prime factorisation = 2^7 × 3^4 × 5 × 7

 Clearly we can see that 2 and 7 factor of 2 will divide 9!

 Also 3 and 4 factors of 3 will divide 9! 

So number i.e. 2, 3, 2^2 , 5 , 2x3 , 7, 2^3 , 3^ 3 , 5x2, will divide 9! Therefore, least positive integer that does not divide 9! is 11  

2. The number of four-digit odd numbers having digits 1, 2, 3, 4, each occurring exactly once, is: 

ANSWER : (12)

Let the number be abcd  

abcd is odd number therefore d can take values as 1 or 3  

which implies that there are only 2 posibility and thus 

a can take 3 value

 b can take 2 value

 c can take 1 value 

Total values = 2 × 3 × 2 × 1 = 12 numbers