CAT Question Bank  Ordered & Unordered Solutions

Q9) In how many ways can 216000 be written as product of 3 numbers
 ordered positive integral
 ordered integral
 unordered positive integral
 unordered integral

Q10) How many ordered and unordered triplets of nonnegative integers (a, b, c) are there such that
root(a) + root(b) + root(c) = root(625)

Q11) The LCM of two numbers is 2900% more than their HCF. How many pairs of such numbers exist ?
(ordered and unordered)

Q12) Find the number of ordered pair of digits (A,B) such that A3640548981270644B is divisible by 99.

Q13) if a! × b!=(a * b)!
a and b both are less than equal to 100 then how many ordered pair of (a, b) possible
a. 0
b. 100
c. 200
d. 202
e. None of these

Q14) The LCM of three positive integers a,b,c is 119^2. Find the total number of ordered triplets (a,b,c).
a. 400
b. 361
c. 289
d. 225

Q15) if n is an odd multiple of 3, in how many ways can 2^n can be expressed as a product of 3 factors?
a) n
b) n^2/3
c) (n+6)^2/9
d) (n+3)^2/12
e) (2n+3)/3

Q16) a + b +c = 100, then many positive integral solutions exist such that a > b > c

Q17) How many pairs of numbers have their LCM as 144?
a) 22
b) 21
c) 18
d) 23

Q18) How many ways can 1000 be expressed as product of 3 natural numbers ?
Also, How many ways can 1000 be expressed as product of 3 integers ?

Q19) How many distinct natural number solutions exist for a + b + c = 999

Q20) How many different triangles are there with integer sides and with perimeter = 2009?

Q21) Number of ways of distributing 10 distinct balls in 3 identical boxes?

Q22) In how many ways can 14 identical toys be distributed among 3 boys, such that each boy gets at least one toy and no two boys get the same number of toys?

Q23) How many ordered pairs of integers (a, b), are there such that their product is a positive integer less than 100? Also, if (a,b) is not different from (b,a), then how many such pairs are possible?

Q24) In how many ways can 83 be expressed as the sum of two natural numbers that are coprime to each other?

Q25) Find the number of ordered triplets (a, b, c ) such that b = a + 2 and c = ab  2 and a, b , and c are prime numbers.
a) only one
b) only two
c) infinitely many
d) none

Q26) Find the number of ordered pairs (x, y) where both x and y are nonnegative integers such that, x – (1/y) = (x/y) + 1?

Q27) Find the number of ordered prime triplets (a, b, c) such that a, b and c are distinct and ab + bc + ca = 316.
a. 0
b. 6
c. 10
d. Infinitely many

Q28) How many unordered triplets of positive integers p, q, r exist such that p/q + q/r + r/p = 2?
a. 0
b. 1
c. 2
d. More than 2