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Ims Simcat 9( Some good Problems from Quant)

The paper had cat2007 pattern, only difference was it was +2, and -0.5

1) If a^k has k^4 divisors, where k is a natural number, then which of the following is true?

I a=k=1   II a^k>=210   III a^k>=2^k; k>=2

A) Only I     B)   only II    C)  Only III    D) I or II E) I or III

2) f(n)=2g(n)+f(-n); for all non-zero integers n

g(n)= n*g(n-1) for all n>0 and g(0)=1

then Find g(-10)+g(-9)+....+g(0)+...g(9)+ g(10)

A) 10!+1    B)2*10!+1   C) 2*10!    D) 1 E) None of these

3) Distinct two digit numbers are written one after the other to form a six-digit number. How  many six-digit numbers thus formed have four consecutive 1s in them?

A) 90    B) 64    C)  65    D) 56  E )72

4) x=3m-1 and y=5n-1 where m,n,x,y are natural numbers less than 16. Find the number of pairs (m,n) satisfying the equations x^2=2y^2-7

A) 0   B) 1  C) 2   D)  3  E ) 4

5) FInd the number of real solutions of the system of equations

y=|x-1|+|x-2| and y+1=x(3-x)


A) 0   B)   1 C) 2   D ) 3   E) 4

6) A natural number ( greater than one) is called squareful  number if its prime factorisation contains at least one square. How many squareful numbers below 101 are there

A) 63  B) 61  C) 39  D) 67 E) 41

7) How many pair of consecutive natural numbers less than 51 are squareful numbers as defined above

A) 2   B)  3 C)  4   D)  5 E ) 6

8) A binary number is called tri-one if it has exactly three 1s. If all tri-ones are arranged in ascending order, what is the rank of the least 8 digit tri-one number?

A) 35 B) 32 C) 34 D) 40 E) 36

9) How many tri-ones as defined above , less than  110 in decimal, when converted to decimal is divsible by 5 in base 10?

A) 5  B)  6 C) 7   D) 8 E )10

updated!