CAT Question Bank - Ordered & Unordered Solutions
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Number of Questions - 30
Topic - Ordered & Unordered Solutions
Answer key available? - Yes
Source - Curated Content
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Q1) Find the number of ordered and unordered solutions for x * y * z = 100
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Q2) HCF of 2 numbers is 13 and their sum is 2080. How many such pairs are possible ?
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Q3) Find the number of ordered and unordered integral solutions for the equation 1/m + 1/n = 1/143
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Q4) The sum of two non– co-prime numbers added to their HCF gives us 221. How many such unordered pairs are possible? (in numerical value)
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Q5) How many ordered pairs (a, b) exist such that LCM of a and b is 360?
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Q6) Number of ways 3600 can be written as a product of 3 numbers whose HCF = 1 ? (ordered and unordered)
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Q7) LCM of three numbers is equal to 1080 and their HCF is equal to 2. How many such triplets are possible. (ordered and unordered)
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Q8) How many ordered and unordered pairs (x, y) possible if x^2 - y^2 = 90000 and x & y are integers.
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Q9) In how many ways can 216000 be written as product of 3 numbers
- ordered positive integral
- ordered integral
- unordered positive integral
- unordered integral
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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)
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Q11) The LCM of two numbers is 2900% more than their HCF. How many pairs of such numbers exist ?
(ordered and unordered)
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Q12) Find the number of ordered pair of digits (A,B) such that A3640548981270644B is divisible by 99.
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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
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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
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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
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Q16) a + b +c = 100, then many positive integral solutions exist such that a > b > c
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Q17) How many pairs of numbers have their LCM as 144?
a) 22
b) 21
c) 18
d) 23
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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 ?
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Q19) How many distinct natural number solutions exist for a + b + c = 999
