# CAT Question Bank - Ordered & Unordered Solutions

• Q8) How many ordered and unordered pairs (x, y) possible if x^2 - y^2 = 90000 and x & y are integers.

• Q9) In how many ways can 216000 be written as product of 3 numbers

1. ordered positive integral
2. ordered integral
3. unordered positive integral
4. unordered integral

• Q10) How many ordered and unordered triplets of non-negative 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 non-negative 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

54

67

65

62

61

40

61