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Ques 1 GATE 2021
Which one of the following numbers is exactly divisible by (1113+1) ?
(a) is the correct answer.
Ques 2 GATE 2020
In four-digit integer numbers from 1001 to 9999, the digit group "37" (in the same sequence) appears ______ times.
(a) is the correct answer.
Ques 3 Gate 2018
What would be the smallest natural number which when divided either by 20 or by 42 or by 76 leaves a remainder ‘7’ in each case is_
(Number System) is the correct answer.
Ques 4 Gate 2017 Set-1
Find the smallest number y such that y*162 is a perfect cube.
(d) is the correct answer.
Ques 5 Gate 2015 Set-2
If p, q, r, s are distinct integers such that:
f(p, q, r, s) = max (p, q, r, s)
g(p, q, r, s) = min (p, q, r, s)
h(p, q, r, s) = remainder of (p × q) / (r × s) if (p × q) > (r × s) OR
remainder of (r × s) / (p × q) if (r × s) > (p × q)
Also a function fgh (p, q, r, s) =
f(p, q, r, s) × g(p, q, r, s) × h(p, q, r, s).
Also the same operation are valid with two variable functions
of the form f(p, q).
What is the value of fg(h(2, 5, 7, 3), 4, 6, 8)?
(8) is the correct answer.
Given functions:
f(p, q, r, s) = max(p, q, r, s)
g(p, q, r, s) = min(p, q, r, s)
h(p, q, r, s) = remainder when larger product is divided by smaller product
We need to find: fg(h(2, 5, 7, 3), 4, 6, 8)
Let me start from the innermost function h(2, 5, 7, 3):
First, calculating the products:
p × q = 2 × 5 = 10
r × s = 7 × 3 = 21
Since (r × s) > (p × q), which means 21 > 10
h(2, 5, 7, 3) = remainder of 21 ÷ 10
h(2, 5, 7, 3) = 1
Now I need to find fg(1, 4, 6, 8):
Here fg means f × g (multiplication of f and g functions)
Calculating f(1, 4, 6, 8):
f(1, 4, 6, 8) = max(1, 4, 6, 8) = 8
Calculating g(1, 4, 6, 8):
g(1, 4, 6, 8) = min(1, 4, 6, 8) = 1
Therefore:
fg(1, 4, 6, 8) = f(1, 4, 6, 8) × g(1, 4, 6, 8)
fg(1, 4, 6, 8) = 8 × 1
fg(1, 4, 6, 8) = 8
Answer: fg(h(2, 5, 7, 3), 4, 6, 8) = 8