CAT Functions and Domains Bible Top 10 Must Solve Functions and Domains Questions covering 90% of Syllabus – Page 8
All 39 Functions and Domains questions from CAT papers. Tap Show answer, or open the detailed solution (free login). Page 8 of 11.
Refer to the passage above ↑
The number of distinct integer values of n satisfying (4 − log2 n) / (3 − log4 n) < 0 is
Answer: 47
Solution — first steps
Step 1. Put t=log 2 n, so log 4 n=t/2 and n>0.
Step 2. The rational expression is(4−t)/(3−t/2).
Step 2. The rational expression is(4−t)/(3−t/2).
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Refer to the passage above ↑
Two ships meet mid-ocean, and then, one ship goes south and the other ship goes west, both travelling at constant speeds. Two hours later, they are 60 km apart. If the speed of one of the ships is 6 km per hour more than the other one, then the speed, in km per hour, of the slower ship is
Answer: C. 18
Solution — first steps
Step 1. Let slower speed v and faster v+6.
Step 2. After two hours perpendicular displacements are 2v and 2(v+6).
Step 2. After two hours perpendicular displacements are 2v and 2(v+6).
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Refer to the passage above ↑
The number of integer solutions of the equation (x^2 − 10)^(x^2 − 3x − 10) = 1 is
Answer: 4
Solution — first steps
Step 1. For integer x, a real integer power equals 1 via exponent 0, base 1, or base−1 with even exponent.
Step 2. Exponent x²−3x−10=0 gives x = 5 or−2, both nonzero-base cases.
Step 2. Exponent x²−3x−10=0 gives x = 5 or−2, both nonzero-base cases.
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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.