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1982

JEE Main 1982 Mathematics question on Application of Derivatives

If pp, qq and rr are any real numbers, then
  1. A.
    max⁡(p,q)<max⁡(p,q,r)\max(p, q) < \max(p, q, r)
  2. B.
    min⁡(p,q)=12(p+q−∣p−q∣)\min(p, q) = \frac{1}{2}(p + q - |p - q|)
  3. C.
    max⁡(p,q)<min⁡(p,q,r)\max(p, q) < \min(p, q, r)
  4. D.
    None of the above
Show answer and solution

Correct option: B

Solution

min(p,q) equals the smaller of p and q. The formula (1/2)(p + q - |p - q|) works because |p - q| = max(p,q) - min(p,q), so p + q - |p - q| = p + q - (max - min) = 2·min(p,q), and dividing by 2 gives min(p,q). This identity holds for all real p, q without exception.

[1982]

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