Operator Based QuestionsCAT Previous-Year Questions

5 previous-year questions on Operator Based Questions from CAT, with full solutions. Practise free — check answers as you go; sign in to save your progress.

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Operator Based Questions · CAT PYQs

CAT 2000 · DILR
Passage / Data

Answer the following question based on the information given below.

ABC Ltd. produces widgets for which the demand is unlimited and they can sell all of their production. The graph below describes the monthly variable costs incurred by the company as a function of the quantity produced. In addition, operating the plant for one shift results in a fixed monthly cost of Rs. 800. Fixed monthly costs for second shift operation are estimated at Rs. 1200. Each shift operation provides capacity for producing 30 widgets per month.

Note : Average unit cost, AC = Total monthly costs/monthly production, and

Marginal cost, MC is the rate of change in total cost for unit change in quantity produced.

Q1.

Choose 1; if the question can be answered by using one of the statements alone, but cannot be answered using the other statement alone.
Choose 2; if the question can be answered by using either statement alone.
Choose 3; if the question can be answered by using both statements together, but cannot be answered using either statement alone.
Choose 4; if the question cannot be answered even by using both statements together.

For any two real numbers

a ⊕ b = 1 if both a and b are positive or both a and b are negative.
          = –1 if one of the two numbers a and b is positive and the other negative.

What is (2 ⊕ 0) ⊕ (–5 ⊕ –6)?

  1. a ⊕ b is zero if a is zero.
  2. a ⊕ b = b ⊕ a
CAT 1998 · DILR
Passage / Data

Direction: Answer the question based on the following information.

The following operations are defined for real numbers.
a # b = a + b, if a and b both are positive else a # b = 1
a ∇ b = (a × b)a + b if a × b is positive else a ∇ b = 1.

Q2.

(21)(12)=

CAT 1998 · DILR
Passage / Data

Direction: Answer the question based on the following information.

The following operations are defined for real numbers.
a # b = a + b, if a and b both are positive else a # b = 1
a ∇ b = (a × b)a + b if a × b is positive else a ∇ b = 1.

Q3.

{((1#1}#2)-(101.3log100.1))(12)=

CAT 1998 · DILR
Passage / Data

Direction: Answer the question based on the following information.

The following operations are defined for real numbers.
a # b = a + b, if a and b both are positive else a # b = 1
a ∇ b = (a × b)a + b if a × b is positive else a ∇ b = 1.

Q4.

((X#-Y)(-XY))=38, then which of the following must be true?

CAT 1991 · DILR
Passage / Data

Study the following graph and answer questions that follow. The x – axis denotes the years from 1983 to 1991.

Q5.

 If 8 + 12 = 2, 7 + 14 = 3 then 10 + 18 = ?