CAT Functions and Domains Bible Top 10 Must Solve Functions and Domains Questions covering 90% of Syllabus – Page 11
All 39 Functions and Domains questions from CAT papers. Tap Show answer, or open the detailed solution (free login). Page 11 of 11.
Refer to the passage above ↑
A shop owner bought a total of 64 shirts from a wholesale market that came in two sizes, small and large. The price of a small shirt was INR 50 less than that of a large shirt. She paid a total of INR 5000 for the large shirts, and a total of INR 1800 for the small shirts. Then, the price of a large shirt and a small shirt together, in INR, is
Answer: C. 200
Solution — first steps
Step 1. Let large price p>50 and small price p−50.
Step 2. Counts 5000/p and 1800/(p−50) sum 64.
Step 2. Counts 5000/p and 1800/(p−50) sum 64.
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Refer to the passage above ↑
A tea shop offers tea in cups of three different sizes. The product of the prices, in INR, of three different sizes is equal to 800. The prices of the smallest size and the medium size are in the ratio 2 : 5. If the shop owner decides to increase the prices of the smallest and the medium ones by INR 6 keeping the price of the largest size unchanged, the product then changes to 3200. The sum of the original prices of three different sizes, in INR, is
Answer: 34
Solution — first steps
Step 1. Let small 2k, medium 5k, large L. Product 10k²L800.
Step 2. New product(2k+6)(5k+6)L = 3200 is four times the original.
Step 2. New product(2k+6)(5k+6)L = 3200 is four times the original.
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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.