CAT Quadratic Equations Bible Top 10 Must Solve Quadratic Equations Questions covering 90% of Syllabus – Page 8
All 38 Quadratic Equations questions from CAT papers. Tap Show answer, or open the detailed solution (free login). Page 8 of 11.
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 ↑
Let f(x) be a quadratic polynomial in x such that f(x) ≥ 0 for all real numbers x. If f(2) = 0 and f( 4) = 6, then f(-2) is equal to
Answer: B. 24
Solution — first steps
Step 1. A quadratic nonnegative everywhere that vanishes at 2 must have a double root there.
Step 2. Write f(x)=a(x−2)², a>0.
Step 2. Write f(x)=a(x−2)², a>0.
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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 15 repeating CAT PYQs and how much each adds
| CAT PYQ | Repeating CAT PYQ | Questions | Representative | Cumulative questions | Cumulative share |
|---|---|---|---|---|---|
| 1 | Quadratic modelling of counts journeys and work rates | 9 | CAT 2021 S1 Q16 | 9 | 17.65% |
| 2 | Root sums products and conjugate roots | 7 | CAT 2021 S2 Q19 | 16 | 31.37% |
| 3 | Successive percentages replacement and price changes | 6 | CAT 2021 S2 Q4 | 22 | 43.14% |
| 4 | Discriminant conditions and integer parameters | 4 | CAT 2022 S1 Q5 | 26 | 50.98% |
| 5 | Modulus or square root branches producing quadratics | 4 | CAT 2021 S1 Q8 | 30 | 58.82% |
| 6 | Exponential substitutions and quadratic exponents | 4 | CAT 2023 S2 Q2 | 34 | 66.67% |
| 7 | Vertex repeated root and perfect square forms | 3 | CAT 2021 S3 Q22 | 37 | 72.55% |
| 8 | Logarithms converted to quadratic equations | 3 | CAT 2023 S1 Q1 | 40 | 78.43% |
| 9 | Shared roots eliminated between equations | 2 | CAT 2024 S1 Q20 | 42 | 82.35% |
| 10 | Rational expression range through a discriminant | 2 | CAT 2022 S3 Q15 | 44 | 86.27% |
| 11 | Grouped identities reduce coupled equations | 2 | CAT 2021 S2 Q3 | 46 | 90.20% |
| 12 | Geometric length constraints producing quadratics | 2 | CAT 2021 S3 Q11 | 48 | 94.12% |
| 13 | Balanced AP totals producing a quadratic index | 1 | CAT 2025 S1 Q4 | 49 | 96.08% |
| 14 | GP terms related by a quadratic product | 1 | CAT 2025 S2 Q8 | 50 | 98.04% |
| 15 | Consistency of a linear system gives a quadratic parameter | 1 | CAT 2023 S3 Q3 | 51 | 100% |
Based on CAT Actual Quant Papers.