CAT Functions and Domains Bible Top 10 Must Solve Functions and Domains Questions covering 90% of Syllabus – Page 7
All 39 Functions and Domains questions from CAT papers. Tap Show answer, or open the detailed solution (free login). Page 7 of 11.
Refer to the passage above ↑
Trains A and B start traveling at the same time towards each other with constant speeds from stations X and Y, respectively. Train A reaches station Y in 10 minutes while train B takes 9 minutes to reach station X after meeting train A. Then the total time taken, in minutes, by train B to travel from station Y to station X is
Answer: B. 15
Solution — first steps
Step 1. Let meeting occur t minutes after departure and B total journey time T.
Step 2. At meeting, fractions of distance satisfy t/10+t/T=1.
Step 2. At meeting, fractions of distance satisfy t/10+t/T=1.
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Refer to the passage above ↑
The largest real value of a for which the equation \(|x + a| + |x - 1| = 2\) has an infinite number of solutions for x is
Answer: C. 1
Solution — first steps
Step 1. The left side is the sum of distances from x to−a and 1.
Step 2. Its minimum is
Step 2. Its minimum is
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Last day solving checklist
- Name the unknown. Include its unit and state whether it is a count, amount, rate or parameter.
- Form the relationships. Translate each given condition into an equation or restriction.
- Choose the method. Use the formula, substitution, elimination, a sign chart or a bound appropriate to this concept.
- Check restrictions. Check integer counts, signs, nonzero denominators, domains and all original conditions.
- Verify the answer. Substitute into the original question; for an extreme, show a feasible example reaches it.
All 14 repeating CAT PYQs and how much each adds
| CAT PYQ | Repeating CAT PYQ | Questions | Representative | Cumulative questions | Cumulative share |
|---|---|---|---|---|---|
| 1 | Reject nonphysical roots in quantity and time problems | 11 | CAT 2021 S1 Q16 | 11 | 21.15% |
| 2 | Logarithm base and argument restrictions | 10 | CAT 2021 S1 Q4 | 21 | 40.38% |
| 3 | Modulus branches and sign consistency | 6 | CAT 2021 S2 Q16 | 27 | 51.92% |
| 4 | Denominator zeros and composite or reciprocal inputs | 5 | CAT 2021 S1 Q1 | 32 | 61.54% |
| 5 | Radical arguments and square root signs | 4 | CAT 2023 S1 Q3 | 36 | 69.23% |
| 6 | Exponential substitutions zero bases and exponent conditions | 4 | CAT 2021 S2 Q15 | 40 | 76.92% |
| 7 | Feasible output range of rational expressions | 3 | CAT 2021 S2 Q13 | 43 | 82.69% |
| 8 | Piecewise function or region interval membership | 2 | CAT 2022 S3 Q6 | 45 | 86.54% |
| 9 | Positivity and nonzero roots in reciprocal identities | 2 | CAT 2023 S3 Q4 | 47 | 90.38% |
| 10 | Select a difference using its given sign | 1 | CAT 2021 S2 Q3 | 48 | 92.31% |
| 11 | Positive substitution needed for AM GM | 1 | CAT 2022 S3 Q2 | 49 | 94.23% |
| 12 | Given work time interval | 1 | CAT 2023 S3 Q8 | 50 | 96.15% |
| 13 | Select the negative shared root | 1 | CAT 2024 S1 Q20 | 51 | 98.08% |
| 14 | Open and closed floor band endpoints | 1 | CAT 2025 S1 Q22 | 52 | 100% |
Based on CAT Actual Quant Papers.