Custom Functions Definition

CAT 1995 Slot 1 · QA · Medium · Functions and Graphs

All CAT 1995 Slot 1 questionsMore Functions and Graphs questionsAll CAT QA

Passage / data set

Answer the questions based on the following functions:

  • le(x,y)=Least of (x,y)\text{le}(x, y) = \text{Least of }(x, y)
  • mo(x)=∣x∣\text{mo}(x) = |x|
  • me(x,y)=Maximum of (x,y)\text{me}(x, y) = \text{Maximum of }(x, y)

Question 1 of 2

Find the value of me(a+mo(le(a,b)),mo(a+me(mo(a),mo(b))))\text{me}(a + \text{mo}(\text{le}(a, b)), \text{mo}(a + \text{me}(\text{mo}(a), \text{mo}(b)))), at a=−2a = -2 and b=−3b = -3.

  1. A.

    1

  2. B.

    0

  3. C.

    5

  4. D.

    3

Answer

A

Explanation

Given a=−2,b=−3a = -2, b = -3:

  1. le(−2,−3)=−3  ⟹  mo(−3)=3\text{le}(-2, -3) = -3 \implies \text{mo}(-3) = 3. First term: a+3=−2+3=1a + 3 = -2 + 3 = 1.
  2. mo(a)=2,mo(b)=3  ⟹  me(2,3)=3\text{mo}(a) = 2, \text{mo}(b) = 3 \implies \text{me}(2, 3) = 3. Inside second term: a+3=−2+3=1  ⟹  mo(1)=1a + 3 = -2 + 3 = 1 \implies \text{mo}(1) = 1.
  3. me(1,1)=1\text{me}(1, 1) = 1.

Question 2 of 2

Which of the following must always be correct for a,b>0a, b > 0?

  1. A.

    mo(le(a,b))≥me(mo(a),mo(b))\text{mo}(\text{le}(a, b)) \ge \text{me}(\text{mo}(a), \text{mo}(b))

  2. B.

    mo(le(a,b))>me(mo(a),mo(b))\text{mo}(\text{le}(a, b)) > \text{me}(\text{mo}(a), \text{mo}(b))

  3. C.

    mo(le(a,b))<le(mo(a),mo(b))\text{mo}(\text{le}(a, b)) < \text{le}(\text{mo}(a), \text{mo}(b))

  4. D.

    mo(le(a,b))=le(mo(a),mo(b))\text{mo}(\text{le}(a, b)) = \text{le}(\text{mo}(a), \text{mo}(b))

Answer

D

Explanation

Since a,b>0a, b > 0, ∣a∣=a|a| = a and ∣b∣=b|b| = b. Therefore, mo(le(a,b))=∣min⁡(a,b)∣=min⁡(a,b)\text{mo}(\text{le}(a, b)) = |\min(a, b)| = \min(a, b). And le(mo(a),mo(b))=min⁡(∣a∣,∣b∣)=min⁡(a,b)\text{le}(\text{mo}(a), \text{mo}(b)) = \min(|a|, |b|) = \min(a, b). Hence, mo(le(a,b))=le(mo(a),mo(b))\text{mo}(\text{le}(a, b)) = \text{le}(\text{mo}(a), \text{mo}(b)) is always true.

Practise this under exam conditions

Sign in to solve it with a live timer, the on-screen CAT calculator, and streak and accuracy tracking across every question you attempt.

Solve in the workspace