IIT JEE 1982 Maths - MCQ Question 11
Number Theory
Level
2
If p,q,r are any real numbers, then which option is true?
In case you are preparing for IIT JEE, you may want to try IIT JEE 1982 Mathematics Archives
max{p, q}<min{p, q, r}
max{p, q}<max{p, q, r}
None of the others
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
Consider m i n p , q (or min{p, q}) = 2 1 ( p + q − ∣ p − q ∣ ) . When p≥q, ∣ p − q ∣ = p − q , else ∣ p − q ∣ = q − p . Hence the right hand side of the given equation reduces to q (p≥q) or p (q>p) respectively. In both cases, the resulting value is the minimum of p and q. Hence this option is correct.
max{p, q}<max{p, q, r} is incorrect when p=2, q=3, r=1. That is, this option is not true for 'any' real numbers.
max{p, q}<min{p, q, r} is incorrect when p=1, q=2, r=3 (or for any case as max{p, q}≥min{p, q}≥min{p, q, r}).