CAT Surds and Indices Bible Top 10 Must Solve Surds and Indices Questions covering 90% of Syllabus
Every real CAT question on this chapter from the past papers we have, newest year first. Passages and data sets stay together on one page.
Tap Show answer, or open the detailed solution (free login). Page 1 of 5.
Start here: the repeating CAT PYQs
Study the surds and indices pattern in each CAT PYQ, then practise variations. The 15 selected families contain 39 of the 40 questions tagged Exponents in the reviewed set.
CAT Surds and Indices Bible Top 10 PYQ Questions
| Questions | CAT Area Covered |
|---|---|
| First 5 CAT Questions | 57.50% |
| First 10 CAT Questions | 85.00% |
| All 15 CAT Questions | 97.50% |
Importance of Surds and Indices each year of CAT exam
| CAT year | Total Surds and Indices questions | First 6 examples | First 10 examples | All 15 examples | Outside these 15 families | Share of all Quant |
|---|---|---|---|---|---|---|
| 2021 | 5 | 4 | 5 | 5 | 0 | 7.58% |
| 2022 | 3 | 1 | 1 | 3 | 0 | 4.55% |
| 2023 | 14 | 10 | 12 | 14 | 0 | 21.21% |
| 2024 | 12 | 9 | 10 | 11 | 1 | 18.18% |
| 2025 | 6 | 2 | 6 | 6 | 0 | 9.09% |
| Total | 40 | 26 | 34 | 39 | 1 | 12.12% |
| Share of all 40 | 100% | 65.00% | 85.00% | 97.50% | 2.50% |
Quick review for beginners and last day revision
| Rule | Formula or what to do | Small example |
|---|---|---|
| Same base multiplication | aᵐ × aⁿ = aᵐ⁺ⁿ | 2³ × 2⁴ = 2⁷ |
| Same base division | aᵐ/aⁿ = aᵐ⁻ⁿ, where a ≠ 0 | 5⁷/5³ = 5⁴ |
| Power of a power | (aᵐ)ⁿ = aᵐⁿ where the expressions are defined. | (2³)⁴ = 2¹² |
| Zero and negative powers | a⁰ = 1 and a⁻ⁿ = 1/aⁿ, for a ≠ 0 | 2⁻³ = 1/8 |
| Fractional powers | a¹⁄ⁿ is the nth root; use positive bases for unrestricted real exponent rules. | 16¹⁄² = 4 |
| Compare exponents | For a > 0 and a ≠ 1, aᵘ = aᵛ implies u = v. | 2ˣ = 8 → x = 3 |
| Prime factorisation | Equality of positive integers requires equal exponents of each prime. | 2ᵃ3ᵇ = 2⁴3² → a = 4, b = 2 |
| Exponential substitution | If powers repeat, let t = aˣ > 0. | 2²ˣ − 5·2ˣ + 4 = 0 → t² − 5t + 4 = 0 |
| Product of successive powers | a¹a²…aⁿ = a^[n(n + 1)/2] | Add the exponents rather than multiply the terms individually. |
| Trailing zeros | Pair factors of 2 and 5 into powers of 10. | 2²⁵5²⁰ = 2⁵ × 10²⁰ |
10 Core CAT PYQ Questions
Study these first.
CAT PYQ 1: Convert logarithms to powers using base rules
Understand: Turn each log into a power with the base rules, solve for x, and check that x stays in the allowed range.
Answer: 99
Solution — first steps
Step 2. Write every square-root log as half a log and multiply the equation by 2.
The full step-by-step working opens with a free login.
For students who have joined a Cetking program.
CAT PYQ 2: Prime factorisation and exponent comparison
Understand: Write both sides as powers of the same prime, then compare the exponents.
Answer: 14
Solution — first steps
Step 2. The first equation therefore gives(3x−y)/2=−3, or 3x−y=−6.
The full step-by-step working opens with a free login.
For students who have joined a Cetking program.
CAT PYQ 5: Integer exponent bounds with common bases
Understand: Turn the limits into limits on n, then count only the integer values that fit.
Answer: 7
Solution — first steps
Step 2. The requested values 3+3^(n+1) are integers only when n≥−1.
The full step-by-step working opens with a free login.
For students who have joined a Cetking program.
CAT PYQ 6: Modular powers and remainder cycles
Understand: Reduce the base using the divisor, find the cycle of remainders, then reduce the exponent by the cycle length.
Answer: D. 4
Solution — first steps
Step 2. 3¹,3²,… give remainders 3,2,6,4,5,1, so the cycle length is 6.
The full step-by-step working opens with a free login.
For students who have joined a Cetking program.
CAT PYQ 8: Symmetric reciprocal powers by recurrence identities
Understand: Write A_n = x^n + 1/x^n. Use A_2n = A_n² − 2 to come down, then build up to the power you need.
Answer: D. \(34 \sqrt{5}\)
Solution — first steps
Step 2. From A8=47, obtain A4=√49=7, A2=√9=3 and A1=√5.
The full step-by-step working opens with a free login.
For students who have joined a Cetking program.
CAT PYQ 9: Simplify powers into geometric series
Understand: Split each term into powers so the sum becomes geometric series. Add each with a/(1 − r).
Answer: B. \(\frac{16}{11}\)
Solution — first steps
Step 2. The bracket is (1−3^(−n−1))/(1−1/3)=(3/2)(1−3^(−n−1)).
The full step-by-step working opens with a free login.
For students who have joined a Cetking program.
Variations
Same idea, extra twist.
CAT PYQ 11: Special bases or exponent zero when a power is one
Understand: A power equals 1 only if the exponent is 0, the base is 1, or the base is −1 with an even exponent.
Answer: 4
Solution — first steps
Step 2. Exponent x²−3x−10=0 gives x = 5 or−2, both nonzero-base cases.
The full step-by-step working opens with a free login.
For students who have joined a Cetking program.
CAT PYQ 12: Universal common divisors of power expressions
Understand: Try small values of k to find the common divisor, then show it divides every case.
Answer: 82
Solution — first steps
Step 2. Each 3^k+4^k+5^k is even, hence A = 2.
The full step-by-step working opens with a free login.
For students who have joined a Cetking program.
Answer under review
then the product of all possible values of x is _____
Answer: A. 20
Solution — first steps
9 = 3², so ⇒ 9^(x² + 2x − 3) = 3^(2x² + 4x − 6)
Also, 3^(x² + 2x − 2) = 3·3^(x² + 2x − 3)
Let t = 3^(x² + 2x − 3), where t > 0.
Then the equation becomes: t² − 4(3t) + 27 = 0 ⇒ t² − 12t + 27 = 0
Step 2: Solve the quadratic in t
t² − 12t + 27 = 0 ⇒ (t − 3)(t − 9) = 0 ⇒ So t = 3 or t = 9
The full step-by-step working opens with a free login.
For students who have joined a Cetking program.
Answer: 112
Solution — first steps
The full step-by-step working opens with a free login.
For students who have joined a Cetking program.
Answer: C. 221
Solution — first steps
The full step-by-step working opens with a free login.
For students who have joined a Cetking program.
Answer: B. 44853√3
Solution — first steps
The full step-by-step working opens with a free login.
For students who have joined a Cetking program.
Frequently asked questions
Where can I find CAT surds and indices questions with solutions?
Every Surds and Indices question on this page is a real CAT question from the CAT Actual Quant Papers. Tap Show answer for the answer; the detailed step-by-step solution opens after a free login. Start with the 15 CAT PYQs at the top, because they repeat the most.
Are there CAT surds and indices questions with answers?
Yes. Every question has its answer one tap away, free for everyone: pick an option and press Submit, or tap Show answer.
Is there a PDF of CAT surds and indices questions?
Yes. Tap Download PDF at the top of this page (free, after a quick OTP login) for the CAT Surds and Indices Bible Top 10 PYQ Questions, a free PDF of the 10 most repeated CAT surds and indices questions. All the CAT Surds and Indices questions are also on this page to read online, with answers and, after a free login, detailed solutions.
What are the CAT surds and indices previous year questions (PYQs)?
They are the real questions of the CAT Actual Quant Papers that are about surds and indices: 40 questions, grouped into 15 repeating CAT PYQs, with the other questions listed after them in paper order.
Which surds and indices questions should I practise first for CAT?
Start with the first 6 CAT PYQs, which cover about 70% of the Surds and Indices questions. Then do the first 10 (about 90%) and finally all 15 (about 98%).
How many Surds and Indices questions came in CAT papers?
22 Surds and Indices questions are on this page: 5 in CAT 2025, 10 in CAT 2024, 7 in CAT 2023. The same real question is shown once.
How difficult are CAT Surds and Indices questions?
Of the 5 Surds and Indices questions that carry a difficulty rating, 2 are Easy, 1 Medium and 2 Hard; the other 17 are not rated yet.
Are the solutions free?
The question and its answer are free for everyone. The detailed Cetking solution opens after a free login with your mobile number (OTP).
Where can I practise more Surds and Indices?
Open all CAT papers and topics for every paper, or the Cetking Arena to practise.
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 16 repeating CAT PYQs and how much each adds
| CAT PYQ | Repeating CAT PYQ | Questions | Representative | Cumulative questions | Cumulative share |
|---|---|---|---|---|---|
| 1 | Convert logarithms to powers using base rules | 7 | CAT 2021 S1 Q4 | 7 | 17.50% |
| 2 | Prime factorisation and exponent comparison | 5 | CAT 2022 S3 Q11 | 12 | 30.00% |
| 3 | Compound growth factor comparisons | 4 | CAT 2023 S1 Q16 | 16 | 40.00% |
| 4 | Exponential substitution reduces to quadratics | 4 | CAT 2023 S2 Q2 | 20 | 50.00% |
| 5 | Integer exponent bounds with common bases | 3 | CAT 2021 S2 Q15 | 23 | 57.50% |
| 6 | Modular powers and remainder cycles | 3 | CAT 2024 S1 Q10 | 26 | 65.00% |
| 7 | Products of powers use sums of exponents | 2 | CAT 2021 S3 Q20 | 28 | 70.00% |
| 8 | Symmetric reciprocal powers by recurrence identities | 2 | CAT 2023 S3 Q4 | 30 | 75.00% |
| 9 | Simplify powers into geometric series | 2 | CAT 2023 S3 Q20 | 32 | 80.00% |
| 10 | Prime powers or powers of ten and digit sums | 2 | CAT 2025 S2 Q20 | 34 | 85.00% |
| 11 | Special bases or exponent zero when a power is one | 1 | CAT 2022 S2 Q17 | 35 | 87.50% |
| 12 | Universal common divisors of power expressions | 1 | CAT 2022 S1 Q21 | 36 | 90.00% |
| 13 | Shift an affine recurrence into geometric growth | 1 | CAT 2023 S1 Q22 | 37 | 92.50% |
| 14 | Replacement iterations and a concentration threshold | 1 | CAT 2023 S2 Q14 | 38 | 95.00% |
| 15 | Prime power rule of a multiplicative function | 1 | CAT 2024 S2 Q4 | 39 | 97.50% |
| 16 | Telescoping product of logarithmic exponents | 1 | CAT 2024 S3 Q16 | 40 | 100% |
Based on CAT Actual Quant Papers.