Explore: All CDS topics · CDS Elementary Mathematics PYQs · CDS hub · Syllabus & pattern · CDS 2026
Answer first
Algebra PYQs (previous year questions) for CDS: Algebra (Elementary Mathematics) had 428 questions across the 66 official CDS papers we tagged (2016–2026), and appeared in 22 of them. Asked in 11 of 11 years. The concepts asked in the most papers: Quadratic Equations, Algebraic Identities, Polynomials.
Year-wise question count
Asked in 11 of 11 years, with 2 papers each year.
| Year | Questions |
|---|---|
| CDS 2026 | 39 |
| CDS 2025 | 34 |
| CDS 2024 | 24 |
| CDS 2023 | 54 |
| CDS 2022 | 48 |
| CDS 2021 | 45 |
| CDS 2020 | 31 |
| CDS 2019 | 37 |
| CDS 2018 | 42 |
| CDS 2017 | 37 |
| CDS 2016 | 37 |
Most-asked concepts
Sorted by the number of papers a concept appeared in.
| Concept | Questions | Papers | Years |
|---|---|---|---|
| Quadratic Equations | 66 | 22 | 2026, 2025, 2024, 2023, 2022, 2021, 2020, 2019, 2018, 2017, 2016 |
| Algebraic Identities | 57 | 22 | 2026, 2025, 2024, 2023, 2022, 2021, 2020, 2019, 2018, 2017, 2016 |
| Polynomials | 35 | 18 | 2026, 2024, 2023, 2022, 2021, 2020, 2019, 2018, 2017, 2016 |
| Linear Equations | 29 | 15 | 2026, 2024, 2023, 2021, 2020, 2019, 2018, 2017, 2016 |
| Algebraic Expressions | 28 | 12 | 2026, 2022, 2021, 2020, 2019, 2018, 2016 |
| HCF and LCM of Polynomials | 18 | 11 | 2026, 2025, 2023, 2022, 2021, 2020, 2019, 2018, 2017 |
| Logarithms | 16 | 11 | 2026, 2023, 2022, 2021, 2017, 2016 |
| Surds | 17 | 10 | 2026, 2023, 2022, 2021, 2020, 2019, 2017 |
| Factorisation | 11 | 9 | 2025, 2023, 2022, 2021, 2020, 2019, 2017, 2016 |
| Inequalities | 11 | 8 | 2025, 2023, 2022, 2021, 2019, 2018, 2016 |
| Factor Theorem | 9 | 8 | 2025, 2020, 2018, 2017, 2016 |
| Remainder Theorem | 10 | 7 | 2025, 2020, 2019, 2018, 2017, 2016 |
| Variation | 6 | 6 | 2025, 2024, 2022, 2021 |
| Data Sufficiency | 11 | 5 | 2025, 2024, 2022 |
| Algebraic Equations | 8 | 5 | 2020, 2019, 2016 |
| Exponents | 6 | 5 | 2023, 2022, 2017, 2016 |
| HCF of Polynomials | 6 | 5 | 2020, 2017, 2016 |
| Sets | 11 | 4 | 2026, 2023, 2019, 2018 |
| Indices | 10 | 4 | 2020, 2019, 2018 |
| Ages | 9 | 4 | 2023, 2018 |
| Linear Inequalities | 4 | 3 | 2025, 2018, 2016 |
| Linear Diophantine Equations | 3 | 3 | 2020, 2019 |
| Algebraic Simplification | 5 | 2 | 2025 |
| Ratio of Expressions | 5 | 2 | 2022, 2021 |
| Sets and Venn Diagrams | 4 | 2 | 2020, 2019 |
| Surd Equations | 4 | 2 | 2017, 2016 |
| Maxima and Minima | 3 | 2 | 2019 |
| Means | 3 | 2 | 2022 |
| Algebraic Fractions | 2 | 2 | 2023, 2019 |
| Exponential Equations | 2 | 2 | 2019, 2017 |
| Maximum and Minimum | 2 | 2 | 2024 |
| Quadratic Expressions | 2 | 2 | 2025, 2024 |
| Ratio and Proportion | 2 | 2 | 2025 |
| Ratios of Variables | 2 | 2 | 2023 |
| Equations | 3 | 1 | 2023 |
| AM and GM | 1 | 1 | 2024 |
| LCM of Polynomials | 1 | 1 | 2017 |
| Polynomial Division | 1 | 1 | 2019 |
| Polynomial Identities | 1 | 1 | 2025 |
| Progressions | 1 | 1 | 2024 |
| Quadratic Inequalities | 1 | 1 | 2019 |
| Rational Expressions | 1 | 1 | 2026 |
| Simultaneous Equations | 1 | 1 | 2018 |
How to practise Algebra PYQs
- Start with the concepts at the top of the table. They have come back the most.
- Solve one year’s Algebra questions from the official PDF against the clock, then check the answer listed below.
- Log every miss as a concept gap, a calculation slip or a misread. Each needs a different fix.
- Once a concept is clean in two papers, move to the next. Then sit a full paper from the year pages.
Questions by year
Each line gives the question number and paper, type, concept, our one-line summary and the official answer, with a link to the official PDF.
CDS2026
- Q.1 (CDS (I) Maths) · MCQ · Algebraic Identities: Value of an expression in p, q, r given p + q + r = 0 PDF
- Q.2 (CDS (I) Maths) · MCQ · Polynomials: Value of k making a quadratic in x an identity PDF
- Q.3 (CDS (I) Maths) · MCQ · Algebraic Identities: Express a sum of fourth powers in terms of a, b, c PDF
- Q.4 (CDS (I) Maths) · MCQ · Algebraic Expressions: Value of a symmetric expression in x, p and q under a condition PDF
- Q.6 (CDS (I) Maths) · MCQ · HCF and LCM of Polynomials: Find p + q when (x - 5) is the HCF of two quadratics PDF
- Q.7 (CDS (I) Maths) · MCQ · HCF and LCM of Polynomials: Find q(x) given LCM, HCF and p(x) PDF
- Q.8 (CDS (I) Maths) · MCQ · Polynomials: Common linear factors of two cubic polynomials PDF
- Q.10 (CDS (I) Maths) · MCQ · Linear Equations: Integral k for which a pair of linear equations has no solution PDF
- Q.11 (CDS (I) Maths) · MCQ · Linear Equations: Count two-digit numbers where 7 times equals 4 times the reversal PDF
- Q.19 (CDS (I) Maths) · MCQ · Quadratic Equations: Properties of a quadratic whose root sum equals root product PDF
- Q.29 (CDS (I) Maths) · MCQ · Logarithms: Express log of 384 using logs of 80, 45 and 216 PDF
- Q.81 (CDS (I) Maths) · MCQ · Polynomials: Value of p when a quartic is divisible by x² - x - 6 PDF
- Q.82 (CDS (I) Maths) · MCQ · Polynomials: Value of q when a quartic is divisible by x² - x - 6 PDF
- Q.83 (CDS (I) Maths) · MCQ · Algebraic Expressions: Value of an expression in x from a given equation PDF
- Q.84 (CDS (I) Maths) · MCQ · Algebraic Expressions: Value of x plus its reciprocal form from the same equation PDF
- Q.85 (CDS (I) Maths) · MCQ · Surds: Value of an expression in x and y defined by surds PDF
- Q.86 (CDS (I) Maths) · MCQ · Surds: Value of x² - xy + y² for surd-defined x and y PDF
- Q.2 (CDS (II) Maths) · MCQ · Algebraic Expressions: Value of an algebraic expression in r and s PDF
- Q.3 (CDS (II) Maths) · MCQ · Polynomials: Find p - q when x² - 4x + 3 is a factor of a polynomial PDF
- Q.4 (CDS (II) Maths) · MCQ · Quadratic Equations: Statements on roots of a quadratic with a surd root PDF
- Q.5 (CDS (II) Maths) · MCQ · Algebraic Identities: Value of a² + b² + c² under a given condition PDF
- Q.8 (CDS (II) Maths) · MCQ · Logarithms: Statements on common logarithms of numbers PDF
- Q.9 (CDS (II) Maths) · MCQ · Logarithms: Zeros after the decimal point in a power of 0.5 PDF
- Q.10 (CDS (II) Maths) · MCQ · Surds: Square root of a surd expression 11 + 2√30 PDF
- Q.11 (CDS (II) Maths) · MCQ · Linear Equations: Solve an equation with reciprocal terms in x and k PDF
- Q.12 (CDS (II) Maths) · MCQ · Polynomials: Factors of a degree-five polynomial PDF
- Q.13 (CDS (II) Maths) · MCQ · Quadratic Equations: Value of k for equal roots given a root of another quadratic PDF
- Q.15 (CDS (II) Maths) · MCQ · Quadratic Equations: Find m + n when shifted roots satisfy a swapped quadratic PDF
- Q.16 (CDS (II) Maths) · MCQ · Quadratic Equations: Value of an expression in the roots of a quadratic in n PDF
- Q.18 (CDS (II) Maths) · MCQ · HCF and LCM of Polynomials: HCF of two cubic polynomials in x and y PDF
- Q.19 (CDS (II) Maths) · MCQ · Surds: Product of four surd expressions with √2, √3, √5 PDF
- Q.20 (CDS (II) Maths) · MCQ · HCF and LCM of Polynomials: Statements on the other polynomial given LCM and HCF PDF
- Q.22 (CDS (II) Maths) · MCQ · Quadratic Equations: Value of p when the roots of a quadratic are even integers PDF
- Q.30 (CDS (II) Maths) · MCQ · Algebraic Expressions: Value of x(x - 3)(x - 6) for x defined by cube roots PDF
- Q.31 (CDS (II) Maths) · MCQ · Sets: Statements on finite and infinite sets PDF
- Q.32 (CDS (II) Maths) · MCQ · Sets: Number of null sets among three given sets PDF
- Q.33 (CDS (II) Maths) · MCQ · Sets: Statements on complements and the universal set PDF
- Q.34 (CDS (II) Maths) · MCQ · Rational Expressions: Expression to add to get a given rational expression PDF
- Q.35 (CDS (II) Maths) · MCQ · Algebraic Identities: Value of a cyclic expression when x + y + z = 0 PDF
CDS2025
- Q.1 (CDS (I) Maths) · MCQ · Quadratic Expressions: Minimum value of M + M^2 for a real number M PDF
- Q.4 (CDS (I) Maths) · MCQ · Variation: What (y+z-x) is proportional to under given conditions PDF
- Q.8 (CDS (I) Maths) · MCQ · Quadratic Equations: Value of αβ + α + β for roots of a rational equation PDF
- Q.36 (CDS (I) Maths) · MCQ · Algebraic Simplification: Simplify a cyclic sum of squared differences minus 3 PDF
- Q.39 (CDS (I) Maths) · MCQ · Algebraic Identities: Number of values of xy + yz + zx for integers with x^2+y^2+z^2 = 3 PDF
- Q.40 (CDS (I) Maths) · MCQ · Algebraic Identities: Find x^3 + y^3 + z^3 - 3xyz from sum and pairwise products PDF
- Q.44 (CDS (I) Maths) · MCQ · Ratio and Proportion: Find x^2 + y^2 + z^2 from ratios of pairwise sums PDF
- Q.75 (CDS (I) Maths) · MCQ · Algebraic Simplification: Simplify an expression in s, s-a, s-b, s-c PDF
- Q.79 (CDS (I) Maths) · MCQ · Quadratic Equations: Find p^2 + q^2 when p and q are roots of x^2 + px + q = 0 PDF
- Q.80 (CDS (I) Maths) · MCQ · Quadratic Equations: Find p + q when two quadratics share a common root PDF
- Q.81 (CDS (I) Maths) · MCQ · Factor Theorem: Find p and q when a quadratic is a factor of a quartic PDF
- Q.82 (CDS (I) Maths) · MCQ · Quadratic Equations: Find p + q when two quadratics have common root 2 PDF
- Q.83 (CDS (I) Maths) · MCQ · HCF and LCM of Polynomials: HCF of x^8 + x^4 + 1 and x^4 + x^2 + 1 PDF
- Q.1 (CDS (II) Maths) · MCQ · Remainder Theorem: Remainder when a polynomial is divided by (x-1)(x-2) given two remainders (official answer: C) PDF
- Q.2 (CDS (II) Maths) · MCQ · Inequalities: Which inequalities involving x + 1/x hold for positive real x (official answer: D) PDF
- Q.5 (CDS (II) Maths) · MCQ · Polynomial Identities: Find p from (x+1)(x+p)(x^2+p^2) = x^4 - 1 (official answer: A) PDF
- Q.7 (CDS (II) Maths) · MCQ · Algebraic Identities: Find 1/a^3 + 1/b^3 from sums of reciprocals and squares (official answer: B) PDF
- Q.8 (CDS (II) Maths) · MCQ · Remainder Theorem: Remainder when a power of x is divided by a quadratic (official answer: A) PDF
- Q.9 (CDS (II) Maths) · MCQ · Factor Theorem: Which polynomial has (x+2) as a factor (official answer: A) PDF
- Q.12 (CDS (II) Maths) · MCQ · HCF and LCM of Polynomials: Statements on the HCF of two expressions built from x and y (official answer: C) PDF
- Q.13 (CDS (II) Maths) · MCQ · Algebraic Identities: Evaluate an expression in x given a quartic relation (official answer: B) PDF
- Q.14 (CDS (II) Maths) · MCQ · Ratio and Proportion: Condition implied by equal ratios (p+q)/(q+r) = (r+s)/(s+p) (official answer: C) PDF
- Q.16 (CDS (II) Maths) · MCQ · HCF and LCM of Polynomials: HCF of x^3+y^3+3xy-1 and (x+y)^4-1 (official answer: C) PDF
- Q.18 (CDS (II) Maths) · MCQ · HCF and LCM of Polynomials: LCM of three polynomials in x and y (official answer: B) PDF
- Q.21 (CDS (II) Maths) · MCQ · Algebraic Simplification: Simplify a rational expression in a, b, c (official answer: A) PDF
- Q.24 (CDS (II) Maths) · MCQ · Algebraic Simplification: Solve for x from a ratio of square-root expressions equal to p (official answer: D) PDF
- Q.25 (CDS (II) Maths) · MCQ · Quadratic Equations: Roots of a quadratic with coefficients in a and b (official answer: B) PDF
- Q.26 (CDS (II) Maths) · MCQ · Algebraic Identities: Find x^2 - 1/x^2 given x - 1/x = 2 (official answer: B) PDF
- Q.27 (CDS (II) Maths) · MCQ · Algebraic Identities: Find a+b+c from sum of squared differences and sum of squares (official answer: A) PDF
- Q.39 (CDS (II) Maths) · MCQ · Factorisation: Factors of a quadratic expression in (3x+y) and (x+5y) (official answer: C) PDF
- Q.40 (CDS (II) Maths) · MCQ · Algebraic Simplification: Evaluate a ratio of cyclic fractions in x, y, z (official answer: B) PDF
- Q.57 (CDS (II) Maths) · MCQ · Quadratic Equations: Find p when roots of a quadratic differ by 4 (official answer: A) PDF
- Q.59 (CDS (II) Maths) · MCQ · Linear Inequalities: Solve a pair of linear inequalities (official answer: A) PDF
- Q.81 (CDS (II) Maths) · MCQ · Data Sufficiency: Data sufficiency: remainder of a polynomial division (official answer: D) PDF
CDS2024
- Q.7 (CDS (I) Maths) · MCQ · Quadratic Equations: Statements on quadratics with a given sum and product of roots (official answer: C) PDF
- Q.8 (CDS (I) Maths) · MCQ · Polynomials: Sum of squares of the other zeros of a cubic with zero 2 (official answer: B) PDF
- Q.10 (CDS (I) Maths) · MCQ · Polynomials: Value of p(x) - q(x) for quartics sharing three zeros (official answer: B) PDF
- Q.14 (CDS (I) Maths) · MCQ · Quadratic Equations: Greatest k for which a quadratic has real roots (official answer: B) PDF
- Q.21 (CDS (I) Maths) · MCQ · Algebraic Identities: Value of p³ + 3bp for p given as a sum of cube roots (official answer: C) PDF
- Q.23 (CDS (I) Maths) · MCQ · Polynomials: HCF of three polynomials in x and y (official answer: A) PDF
- Q.28 (CDS (I) Maths) · MCQ · AM and GM: Difference of two numbers whose GM is 20% below their AM (official answer: C) PDF
- Q.33 (CDS (I) Maths) · MCQ · Polynomials: Divisibility of a sum of powers of x by x² + 1 and x⁴ + 1 (official answer: C) PDF
- Q.42 (CDS (I) Maths) · MCQ · Progressions: Geometric mean of 3n terms of a GP (official answer: D) PDF
- Q.58 (CDS (I) Maths) · MCQ · Variation: Relations that follow when P² and Q² vary as R (official answer: D) PDF
- Q.60 (CDS (I) Maths) · MCQ · Maximum and Minimum: Minimum value of an algebraic expression for positive b (official answer: D) PDF
- Q.64 (CDS (I) Maths) · MCQ · Data Sufficiency: Data sufficiency on whether xy is positive (official answer: C) PDF
- Q.1 (CDS (II) Maths) · MCQ · Quadratic Expressions: Real number for which number plus four times its square is least PDF
- Q.6 (CDS (II) Maths) · MCQ · Variation: Value of p varying directly as x² + y² + z² PDF
- Q.10 (CDS (II) Maths) · MCQ · Quadratic Equations: Statements on two quadratics whose roots are each other's coefficients PDF
- Q.20 (CDS (II) Maths) · MCQ · Quadratic Equations: Minimum of p² + q² for roots of a trigonometric quadratic PDF
- Q.29 (CDS (II) Maths) · MCQ · Algebraic Identities: Value of xy from given equations in x and y PDF
- Q.33 (CDS (II) Maths) · MCQ · Maximum and Minimum: Minimum value of an expression in positive a and b PDF
- Q.37 (CDS (II) Maths) · MCQ · Polynomials: HCF of two polynomials in a PDF
- Q.38 (CDS (II) Maths) · MCQ · Quadratic Equations: Values of k for which a quadratic has equal roots PDF
- Q.61 (CDS (II) Maths) · MCQ · Data Sufficiency: Data sufficiency on k for which 4x² - kx + 1 is positive PDF
- Q.78 (CDS (II) Maths) · MCQ · Linear Equations: Value of xyz from given conditions PDF
- Q.79 (CDS (II) Maths) · MCQ · Algebraic Identities: Statements on n(n+1)(n+2)(n+3) + 1 PDF
- Q.88 (CDS (II) Maths) · MCQ · Polynomials: Conditions for a cubic to give integer values for integers PDF
CDS2023
- Q.4 (CDS (I) Maths) · MCQ · Quadratic Equations: Relation between coefficients when roots differ by 5 (official answer: A) PDF
- Q.5 (CDS (I) Maths) · MCQ · Sets: Persons taking only milk at a party from drink counts (official answer: C) PDF
- Q.9 (CDS (I) Maths) · MCQ · Linear Equations: Difference of digits of a two-digit number from conditions (official answer: B) PDF
- Q.11 (CDS (I) Maths) · MCQ · Ratios of Variables: Value of a ratio when 2a = 3b = 6c = ... = 18f (official answer: B) PDF
- Q.12 (CDS (I) Maths) · MCQ · Quadratic Equations: Roots of a quadratic when a + b + c = 0 (official answer: C) PDF
- Q.21 (CDS (I) Maths) · MCQ · Quadratic Equations: Value of a power sum of roots of a quadratic (official answer: A) PDF
- Q.28 (CDS (I) Maths) · MCQ · Ages: Sum of ages of P and Q from age relations (official answer: D) PDF
- Q.33 (CDS (I) Maths) · MCQ · Logarithms: Statements on rationality of given logarithms (official answer: D) PDF
- Q.39 (CDS (I) Maths) · MCQ · Algebraic Identities: Value of x^2 - y^2 for given surd expressions (official answer: C) PDF
- Q.42 (CDS (I) Maths) · MCQ · Polynomials: Coefficients of a cyclic polynomial expression (official answer: A) PDF
- Q.43 (CDS (I) Maths) · MCQ · Polynomials: Divisibility statements for a polynomial in x (official answer: C) PDF
- Q.44 (CDS (I) Maths) · MCQ · Polynomials: Values of m making a quadratic a perfect square (official answer: D) PDF
- Q.45 (CDS (I) Maths) · MCQ · Algebraic Identities: Value of an expression in x and y defined via a and b (official answer: B) PDF
- Q.72 (CDS (I) Maths) · MCQ · Quadratic Equations: Data sufficiency: coefficients of a quadratic with root 2 (official answer: D) PDF
- Q.73 (CDS (I) Maths) · MCQ · Inequalities: Data sufficiency: whether m > n (official answer: D) PDF
- Q.1 (CDS (II) Maths) · MCQ · Algebraic Identities: Value of a weighted sum built from a^2 - bc type expressions (official answer: D) PDF
- Q.2 (CDS (II) Maths) · MCQ · Polynomials: Other factor of a quartic given a squared factor (official answer: A) PDF
- Q.3 (CDS (II) Maths) · MCQ · Linear Equations: Product of digits from sum and difference with reversed number (official answer: D) PDF
- Q.8 (CDS (II) Maths) · MCQ · Algebraic Identities: Value of an expression in a, b, c from given conditions (official answer: B) PDF
- Q.11 (CDS (II) Maths) · MCQ · Equations: Number of real roots of a square-root equation (official answer: A) PDF
- Q.12 (CDS (II) Maths) · MCQ · Surds: Value of an expression for x given as a surd sum (official answer: D) PDF
- Q.15 (CDS (II) Maths) · MCQ · Exponents: Value of an exponential expression from a given relation (official answer: A) PDF
- Q.16 (CDS (II) Maths) · MCQ · Linear Equations: Value of x - y from given equations in a and b (official answer: A) PDF
- Q.17 (CDS (II) Maths) · MCQ · Factorisation: Factor of a cubic expression with surd coefficients (official answer: C) PDF
- Q.18 (CDS (II) Maths) · MCQ · Logarithms: Number of digits in a large power using log 2 (official answer: D) PDF
- Q.19 (CDS (II) Maths) · MCQ · Polynomials: HCF of two polynomial expressions (official answer: D) PDF
- Q.20 (CDS (II) Maths) · MCQ · Algebraic Identities: Value of an expression from a given polynomial identity (official answer: C) PDF
- Q.22 (CDS (II) Maths) · MCQ · Algebraic Identities: Relation among a, b, c, d from an equality of products (official answer: C) PDF
- Q.24 (CDS (II) Maths) · MCQ · Ages: Number of children from combined age relations (official answer: B) PDF
- Q.37 (CDS (II) Maths) · MCQ · Algebraic Identities: Value of px^2 + qy^2 + rz^2 for given p, q, r (official answer: A) PDF
- Q.38 (CDS (II) Maths) · MCQ · Algebraic Identities: Value of a related cyclic expression in p, q, r (official answer: A) PDF
- Q.43 (CDS (II) Maths) · MCQ · Equations: Solve a rational equation in x with parameters a, b, m (official answer: D) PDF
- Q.44 (CDS (II) Maths) · MCQ · Equations: Value of x for a special case of the rational equation (official answer: A) PDF
- Q.49 (CDS (II) Maths) · MCQ · Quadratic Equations: Roots of a quadratic with coefficients in a, b, c (official answer: A) PDF
- Q.50 (CDS (II) Maths) · MCQ · Quadratic Equations: Sign statements on roots of the quadratic (official answer: A) PDF
- Q.63 (CDS (II) Maths) · MCQ · Algebraic Identities: Value of a product for sides of a right triangle (official answer: B) PDF
- Q.68 (CDS (II) Maths) · MCQ · HCF and LCM of Polynomials: LCM of three polynomial expressions (official answer: C) PDF
- Q.69 (CDS (II) Maths) · MCQ · Algebraic Fractions: Simplify a sum of rational algebraic expressions (official answer: C) PDF
- Q.74 (CDS (II) Maths) · MCQ · Algebraic Identities: Value of a power of p + q + r for cyclic fractions (official answer: C) PDF
- Q.75 (CDS (II) Maths) · MCQ · Factorisation: Factor of a quadratic expression in a, b, c (official answer: D) PDF
- Q.76 (CDS (II) Maths) · MCQ · Quadratic Equations: Quadratic whose roots are squares of given roots (official answer: B) PDF
- Q.77 (CDS (II) Maths) · MCQ · Algebraic Identities: Value of x^2 - 9x + 2 for x satisfying a given relation (official answer: D) PDF
- Q.80 (CDS (II) Maths) · MCQ · Algebraic Identities: Value of an expression in s and sides where 2s = a + b + c (official answer: B) PDF
- Q.83 (CDS (II) Maths) · MCQ · Algebraic Identities: Conclusion from a sum of squares-type expression being zero (official answer: C) PDF
- Q.86 (CDS (II) Maths) · MCQ · Ages: D's age from relations among seven cousins (official answer: D) PDF
- Q.87 (CDS (II) Maths) · MCQ · Ages: Average age of five of the seven cousins (official answer: C) PDF
- Q.88 (CDS (II) Maths) · MCQ · Linear Equations: Weight difference of two cousins from given relations (official answer: B) PDF
- Q.90 (CDS (II) Maths) · MCQ · Linear Equations: Statements on ages and weights of the cousins (official answer: D) PDF
- Q.91 (CDS (II) Maths) · MCQ · Inequalities: Data sufficiency: whether m > n (official answer: D) PDF
- Q.92 (CDS (II) Maths) · MCQ · Quadratic Equations: Data sufficiency: other root of a quadratic (official answer: B) PDF
- Q.94 (CDS (II) Maths) · MCQ · Algebraic Identities: Data sufficiency: whether x, y, z are equal (official answer: A) PDF
- Q.95 (CDS (II) Maths) · MCQ · Ratios of Variables: Data sufficiency: ratio x : y : z (statements partly unreadable) (official answer: C) PDF
- Q.98 (CDS (II) Maths) · MCQ · Inequalities: Data sufficiency: comparing two expressions in a, b, c (official answer: D) PDF
- Q.99 (CDS (II) Maths) · MCQ · Linear Equations: Data sufficiency: cost of pens, pencils and notebooks (official answer: C) PDF
CDS2022
- Q.3 (CDS (I) Maths) · MCQ · Surds: Value of root x + 1/root x for a surd x (official answer: D) PDF
- Q.8 (CDS (I) Maths) · MCQ · Surds: Value of a sum of surd fractions (official answer: D) PDF
- Q.9 (CDS (I) Maths) · MCQ · Algebraic Expressions: Value of a cubic expression at x = 9999 (official answer: C) PDF
- Q.10 (CDS (I) Maths) · MCQ · Algebraic Identities: Value of (x + y)^2 from a surd product condition (official answer: A) PDF
- Q.13 (CDS (I) Maths) · MCQ · Exponents: Value of an expression from an exponential equation (official answer: A) PDF
- Q.15 (CDS (I) Maths) · MCQ · Algebraic Identities: Value of root of x^2 + y^2 + 1 from two equations (official answer: A) PDF
- Q.17 (CDS (I) Maths) · MCQ · Algebraic Expressions: Value of x/y from a surd equation (official answer: C) PDF
- Q.23 (CDS (I) Maths) · MCQ · Quadratic Equations: Number whose square equals itself plus 12 (official answer: C) PDF
- Q.24 (CDS (I) Maths) · MCQ · Surds: Value of a telescoping sum of surd fractions (official answer: D) PDF
- Q.25 (CDS (I) Maths) · MCQ · Algebraic Expressions: Value of a fraction given x + 1/x (official answer: D) PDF
- Q.26 (CDS (I) Maths) · MCQ · Algebraic Identities: Value of a^3 + b^3 from sum and reciprocal sum (official answer: A) PDF
- Q.30 (CDS (I) Maths) · MCQ · Means: Compare arithmetic and geometric means (official answer: A) PDF
- Q.31 (CDS (I) Maths) · MCQ · Quadratic Equations: Value of alpha - beta from root conditions (official answer: B) PDF
- Q.36 (CDS (I) Maths) · MCQ · Polynomials: Difference of roots when sum of roots is zero (official answer: B) PDF
- Q.38 (CDS (I) Maths) · MCQ · Quadratic Equations: Condition for roots in a given ratio (official answer: A) PDF
- Q.41 (CDS (I) Maths) · MCQ · Data Sufficiency: Sufficiency of statements for sign of 3x + 2y (official answer: C) PDF
- Q.42 (CDS (I) Maths) · MCQ · Data Sufficiency: Sufficiency of statements for roots of opposite sign (official answer: C) PDF
- Q.43 (CDS (I) Maths) · MCQ · Data Sufficiency: Sufficiency of statements for positivity of an expression (official answer: D) PDF
- Q.44 (CDS (I) Maths) · MCQ · Data Sufficiency: Sufficiency of statements comparing two fractions (official answer: D) PDF
- Q.45 (CDS (I) Maths) · MCQ · Quadratic Equations: Quadratics whose root sum equals root product (official answer: D) PDF
- Q.1 (CDS (II) Maths) · MCQ · Surds: Solve x from an infinite nested square root (official answer: B) PDF
- Q.2 (CDS (II) Maths) · MCQ · Ratio of Expressions: Relation from two equal ratios with a not equal to c (official answer: D) PDF
- Q.3 (CDS (II) Maths) · MCQ · Variation: Expression proportional to a^2 - ab + b^2 (official answer: A) PDF
- Q.4 (CDS (II) Maths) · MCQ · Surds: Value of a product of roots from a surd ratio (official answer: C) PDF
- Q.5 (CDS (II) Maths) · MCQ · HCF and LCM of Polynomials: HCF of two polynomials in x and y (official answer: C) PDF
- Q.6 (CDS (II) Maths) · MCQ · Quadratic Equations: k from sum of squares of roots (official answer: B) PDF
- Q.7 (CDS (II) Maths) · MCQ · HCF and LCM of Polynomials: Value of k when x + k is HCF of two quadratics (official answer: A) PDF
- Q.9 (CDS (II) Maths) · MCQ · Factorisation: Factors of a cyclic cubic expression (official answer: A) PDF
- Q.10 (CDS (II) Maths) · MCQ · Algebraic Expressions: Value of a cyclic sum of fractions (official answer: C) PDF
- Q.11 (CDS (II) Maths) · MCQ · Inequalities: Sign of a cyclic expression for ordered x, y, z (official answer: C) PDF
- Q.12 (CDS (II) Maths) · MCQ · Algebraic Expressions: Simplify a polynomial over a product of quadratics (official answer: A) PDF
- Q.22 (CDS (II) Maths) · MCQ · Logarithms: Value of abc from equal log ratios (official answer: C) PDF
- Q.24 (CDS (II) Maths) · MCQ · Logarithms: Sum of roots of a log equation (official answer: A) PDF
- Q.25 (CDS (II) Maths) · MCQ · Quadratic Equations: Which given values satisfy a quadratic (official answer: B) PDF
- Q.26 (CDS (II) Maths) · MCQ · HCF and LCM of Polynomials: LCM of two quartics from their GCD (official answer: A) PDF
- Q.27 (CDS (II) Maths) · MCQ · Data Sufficiency: Sufficiency of statements for a two-digit number (official answer: C) PDF
- Q.28 (CDS (II) Maths) · MCQ · Data Sufficiency: Sufficiency of statements for 3x - 2y from LCM (official answer: A) PDF
- Q.29 (CDS (II) Maths) · MCQ · Data Sufficiency: Sufficiency of statements for divisibility of x^n + y^n (official answer: B) PDF
- Q.30 (CDS (II) Maths) · MCQ · Data Sufficiency: Sufficiency of statements for sign of xy (official answer: C) PDF
- Q.31 (CDS (II) Maths) · MCQ · Ratio of Expressions: Value of (d+a)/(d-a) from linked equalities (official answer: D) PDF
- Q.32 (CDS (II) Maths) · MCQ · Polynomials: Values of k for no real linear factors (official answer: B) PDF
- Q.33 (CDS (II) Maths) · MCQ · Means: Relation from AP and HP conditions on a, b, c, d (official answer: C) PDF
- Q.35 (CDS (II) Maths) · MCQ · Algebraic Identities: Value of (x+y+z)^3 - 24xyz (official answer: C) PDF
- Q.37 (CDS (II) Maths) · MCQ · Algebraic Identities: Value of p^4 + 4p^2 in terms of q (official answer: D) PDF
- Q.38 (CDS (II) Maths) · MCQ · Exponents: Value of x^4 + 16x^-4 for given x (official answer: C) PDF
- Q.41 (CDS (II) Maths) · MCQ · Polynomials: Possible value of x - 1/x from an equation (official answer: B) PDF
- Q.42 (CDS (II) Maths) · MCQ · Polynomials: Possible value of x^2 + 1/x^2 from an equation (official answer: D) PDF
- Q.61 (CDS (II) Maths) · MCQ · Means: Relation when x is harmonic mean of y and z (official answer: B) PDF
CDS2021
- Q.5 (CDS (I) Maths) · MCQ · Polynomials: Number of terms in a product of three sums (official answer: D) PDF
- Q.7 (CDS (I) Maths) · MCQ · Algebraic Identities: Identities that hold when a + b + c = 0 (official answer: D) PDF
- Q.8 (CDS (I) Maths) · MCQ · Surds: Value of an expression in p defined by surds (official answer: B) PDF
- Q.10 (CDS (I) Maths) · MCQ · Linear Equations: Solve an equation with square roots for x (official answer: C) PDF
- Q.11 (CDS (I) Maths) · MCQ · Algebraic Expressions: Simplify a rational expression of polynomials (official answer: B) PDF
- Q.12 (CDS (I) Maths) · MCQ · Algebraic Expressions: Fraction to add to get a given rational expression (official answer: A) PDF
- Q.13 (CDS (I) Maths) · MCQ · Linear Equations: Value of an expression from two equations in x and y (official answer: C) PDF
- Q.14 (CDS (I) Maths) · MCQ · HCF and LCM of Polynomials: Value of k when x - k is the HCF of two quadratics (official answer: B) PDF
- Q.15 (CDS (I) Maths) · MCQ · Variation: Statements about direct and inverse proportion (official answer: C) PDF
- Q.16 (CDS (I) Maths) · MCQ · HCF and LCM of Polynomials: HCF of a cubic and a quadratic polynomial (official answer: D) PDF
- Q.17 (CDS (I) Maths) · MCQ · Algebraic Expressions: Simplify a sum of rational expressions (official answer: A) PDF
- Q.19 (CDS (I) Maths) · MCQ · Algebraic Identities: Expression for k from a product of four terms plus one (official answer: A) PDF
- Q.20 (CDS (I) Maths) · MCQ · Algebraic Expressions: Value of a cyclic sum of fractions (official answer: D) PDF
- Q.21 (CDS (I) Maths) · MCQ · Quadratic Equations: Values of k making a quadratic a perfect square (official answer: C) PDF
- Q.22 (CDS (I) Maths) · MCQ · Algebraic Identities: Value of x^4 - 1/x^4 given x + 1/x (official answer: B) PDF
- Q.23 (CDS (I) Maths) · MCQ · Quadratic Equations: Values of k for equal roots of a quadratic (official answer: C) PDF
- Q.24 (CDS (I) Maths) · MCQ · Quadratic Equations: p + q when sum and product of roots are equal (official answer: B) PDF
- Q.25 (CDS (I) Maths) · MCQ · Polynomials: Linear factors dividing a cubic polynomial (official answer: C) PDF
- Q.41 (CDS (I) Maths) · MCQ · Logarithms: Express log 31.25 in terms of log 2 (official answer: A) PDF
- Q.42 (CDS (I) Maths) · MCQ · Surds: Square root of 15 - 4 root 14 (official answer: A) PDF
- Q.45 (CDS (I) Maths) · MCQ · Logarithms: Solve an exponential equation using logs (official answer: A) PDF
- Q.2 (CDS (II) Maths) · MCQ · Polynomials: Factor of a product of linear terms minus 90 (official answer: D) PDF
- Q.3 (CDS (II) Maths) · MCQ · Surds: Square root of 23 - 4 root 15 (official answer: dropped in the final key) PDF
- Q.7 (CDS (II) Maths) · MCQ · Inequalities: Statements not true for a negative real number (official answer: B) PDF
- Q.8 (CDS (II) Maths) · MCQ · Factorisation: Sum of linear factors of a quadratic in x and y (official answer: C) PDF
- Q.9 (CDS (II) Maths) · MCQ · Quadratic Equations: Equation that has no real roots (official answer: D) PDF
- Q.10 (CDS (II) Maths) · MCQ · Quadratic Equations: New equation after changing the roots (official answer: B) PDF
- Q.11 (CDS (II) Maths) · MCQ · Quadratic Equations: Values of k for real distinct roots (official answer: D) PDF
- Q.12 (CDS (II) Maths) · MCQ · Algebraic Identities: Value of a product given a symmetric condition (official answer: A) PDF
- Q.13 (CDS (II) Maths) · MCQ · Logarithms: Solve a logarithmic equation for x (official answer: D) PDF
- Q.16 (CDS (II) Maths) · MCQ · Linear Equations: Cost of notebooks and erasers from two purchases (official answer: B) PDF
- Q.18 (CDS (II) Maths) · MCQ · Quadratic Equations: Relation between the roots of a quadratic (official answer: B) PDF
- Q.19 (CDS (II) Maths) · MCQ · Logarithms: Minimum N for real roots of a log quadratic (official answer: D) PDF
- Q.20 (CDS (II) Maths) · MCQ · Logarithms: Solve an exponential equation with logs (official answer: D) PDF
- Q.21 (CDS (II) Maths) · MCQ · Algebraic Identities: Value of an expression from a cubic condition (official answer: C) PDF
- Q.22 (CDS (II) Maths) · MCQ · Algebraic Expressions: Find B from A + B and A - B (official answer: C) PDF
- Q.23 (CDS (II) Maths) · MCQ · Algebraic Expressions: Value of a cyclic sum of fractions (official answer: C) PDF
- Q.24 (CDS (II) Maths) · MCQ · Ratio of Expressions: Ratio (a+b):(a-b) from a given proportion (official answer: D) PDF
- Q.25 (CDS (II) Maths) · MCQ · Ratio of Expressions: Value of an expression from equal ratios (official answer: C) PDF
- Q.27 (CDS (II) Maths) · MCQ · Inequalities: Statements comparing algebraic fractions (official answer: A) PDF
- Q.29 (CDS (II) Maths) · MCQ · Ratio of Expressions: Statements from equal cross ratios (official answer: C) PDF
- Q.31 (CDS (II) Maths) · MCQ · Quadratic Equations: Sum of squares of roots given one root (official answer: B) PDF
- Q.36 (CDS (II) Maths) · MCQ · Linear Equations: Condition for a unique solution of two equations (official answer: A) PDF
- Q.40 (CDS (II) Maths) · MCQ · Algebraic Identities: Value of a cubic expression given a linear relation (official answer: D) PDF
- Q.41 (CDS (II) Maths) · MCQ · Variation: Percentage change in p under joint variation (official answer: A) PDF
CDS2020
- Q.4 (CDS (I) Maths) · MCQ · Algebraic Equations: Solution set of an equation in x involving a positive integer n (official answer: A) PDF
- Q.5 (CDS (I) Maths) · MCQ · Sets and Venn Diagrams: Students registered for neither of two subjects (official answer: D) PDF
- Q.12 (CDS (I) Maths) · MCQ · Quadratic Equations: Coefficient k when the roots differ by 8 (official answer: A) PDF
- Q.13 (CDS (I) Maths) · MCQ · Factor Theorem: Values of p and q when two linear factors divide a cubic (official answer: A) PDF
- Q.14 (CDS (I) Maths) · MCQ · HCF of Polynomials: Value of k when x+k is the HCF of two quadratics (official answer: B) PDF
- Q.15 (CDS (I) Maths) · MCQ · Indices: Value of 10 to the 2x from an exponential equation in 5 (official answer: D) PDF
- Q.17 (CDS (I) Maths) · MCQ · Algebraic Identities: Ratio y:x from a quadratic relation in x and y (official answer: A) PDF
- Q.19 (CDS (I) Maths) · MCQ · Indices: Sum of two reciprocal expressions in powers of a (official answer: B) PDF
- Q.22 (CDS (I) Maths) · MCQ · Remainder Theorem: Remainder when f(x) is divided by a product of two linear factors (official answer: C) PDF
- Q.23 (CDS (I) Maths) · MCQ · Polynomials: Side of a square whose area is a quartic polynomial (official answer: C) PDF
- Q.26 (CDS (I) Maths) · MCQ · Linear Equations: Point satisfying two equations in x, y and xy (official answer: B) PDF
- Q.31 (CDS (I) Maths) · MCQ · Linear Equations: Number of students from changes in rows and chairs (official answer: D) PDF
- Q.42 (CDS (I) Maths) · MCQ · Linear Diophantine Equations: Integer solutions of a linear equation in a range (official answer: B) PDF
- Q.49 (CDS (I) Maths) · MCQ · Factor Theorem: Coefficient relation when x squared minus 1 is a factor (official answer: D) PDF
- Q.50 (CDS (I) Maths) · MCQ · Algebraic Identities: Value of x^6 + 1/x^6 from x^8 + 1/x^8 (official answer: C) PDF
- Q.3 (CDS (II) Maths) · MCQ · Quadratic Equations: Minimum N for real roots of a quadratic with a log term (official answer: D) PDF
- Q.4 (CDS (II) Maths) · MCQ · Linear Diophantine Equations: Positive integer solutions of x + y + z = 12 (official answer: C) PDF
- Q.5 (CDS (II) Maths) · MCQ · Algebraic Identities: Nature of a sum of squares of consecutive integers and their product (official answer: D) PDF
- Q.10 (CDS (II) Maths) · MCQ · Factor Theorem: Values of n for which x^n - a^n is divisible by a factor (official answer: A) PDF
- Q.13 (CDS (II) Maths) · MCQ · Surds: Value of x from a nested radical equation (official answer: A) PDF
- Q.14 (CDS (II) Maths) · MCQ · Algebraic Identities: Sum of pairwise products of plus-minus integers (official answer: C) PDF
- Q.27 (CDS (II) Maths) · MCQ · Linear Equations: Father's age at marriage from family age data (official answer: C) PDF
- Q.28 (CDS (II) Maths) · MCQ · Linear Equations: Age difference between two people in a family chain (official answer: B) PDF
- Q.30 (CDS (II) Maths) · MCQ · Algebraic Equations: Value of an expression from two bilinear relations (official answer: C) PDF
- Q.31 (CDS (II) Maths) · MCQ · HCF of Polynomials: HCF of two polynomials (official answer: D) PDF
- Q.32 (CDS (II) Maths) · MCQ · HCF and LCM of Polynomials: Other polynomial from given HCF, LCM and one polynomial (official answer: D) PDF
- Q.33 (CDS (II) Maths) · MCQ · Linear Equations: Value of p from two product equations in p and q (official answer: C) PDF
- Q.34 (CDS (II) Maths) · MCQ · Algebraic Expressions: Value of a given algebraic expression (official answer: D) PDF
- Q.35 (CDS (II) Maths) · MCQ · Polynomials: Square root of a quartic polynomial (official answer: D) PDF
- Q.37 (CDS (II) Maths) · MCQ · Algebraic Equations: Relation among x, y, z from equal ratios (official answer: B) PDF
- Q.39 (CDS (II) Maths) · MCQ · Factorisation: Factor of a polynomial in x with power n (official answer: B) PDF
CDS2019
- Q.8 (CDS (I) Maths) · MCQ · Maxima and Minima: Minimum value of an expression for positive x (official answer: C) PDF
- Q.9 (CDS (I) Maths) · MCQ · Algebraic Equations: Non-zero solutions of an equation in x with parameters p and q (official answer: A) PDF
- Q.12 (CDS (I) Maths) · MCQ · Exponential Equations: Pair of values satisfying an exponential equation in 3 (official answer: B) PDF
- Q.15 (CDS (I) Maths) · MCQ · Indices: Mean of positive integers linked by a power relation (official answer: B) PDF
- Q.16 (CDS (I) Maths) · MCQ · Sets and Venn Diagrams: People reading exactly one of three newspapers (official answer: A) PDF
- Q.17 (CDS (I) Maths) · MCQ · Sets and Venn Diagrams: People reading at least two of three newspapers (official answer: A) PDF
- Q.18 (CDS (I) Maths) · MCQ · Sets and Venn Diagrams: People reading none of the three newspapers (official answer: D) PDF
- Q.21 (CDS (I) Maths) · MCQ · Algebraic Expressions: Simplify an expression in powers of x (official answer: D) PDF
- Q.29 (CDS (I) Maths) · MCQ · Inequalities: Natural numbers for which 3 to the N exceeds N cubed (official answer: D) PDF
- Q.32 (CDS (I) Maths) · MCQ · Algebraic Fractions: Possible values of equal fractions a/(b+c) and similar (official answer: C) PDF
- Q.37 (CDS (I) Maths) · MCQ · Algebraic Equations: Solve a given equation for x (official answer: C) PDF
- Q.39 (CDS (I) Maths) · MCQ · Remainder Theorem: Coefficients of a polynomial with equal remainders for two divisors (official answer: D) PDF
- Q.41 (CDS (I) Maths) · MCQ · Algebraic Expressions: Value of a symmetric algebraic expression (official answer: D) PDF
- Q.46 (CDS (I) Maths) · MCQ · Algebraic Expressions: Simplify a cyclic algebraic expression (official answer: A) PDF
- Q.47 (CDS (I) Maths) · MCQ · Indices: Value of an exponent ratio given equal powers and b squared equals ac (official answer: C) PDF
- Q.48 (CDS (I) Maths) · MCQ · Quadratic Equations: Constant term of a quadratic whose roots differ by 1 (official answer: B) PDF
- Q.49 (CDS (I) Maths) · MCQ · Quadratic Inequalities: Solution set of a quadratic inequality (official answer: D) PDF
- Q.50 (CDS (I) Maths) · MCQ · Factorisation: Factor of an expression of the form 5 to the n minus 2 to the n (official answer: C) PDF
- Q.100 (CDS (I) Maths) · MCQ · Algebraic Identities: Sum of cubes minus three times volume of a cuboid (official answer: C) PDF
- Q.11 (CDS (II) Maths) · MCQ · Surds: Value of a+b from two equations with square roots (official answer: C) PDF
- Q.12 (CDS (II) Maths) · MCQ · Algebraic Equations: Equation satisfied by y defined from x (official answer: A) PDF
- Q.16 (CDS (II) Maths) · MCQ · Factorisation: Value of k so a cubic splits into three linear factors (official answer: A) PDF
- Q.19 (CDS (II) Maths) · MCQ · Quadratic Equations: Value of k when two quadratics share a root (official answer: B) PDF
- Q.56 (CDS (II) Maths) · MCQ · Polynomial Division: Quotient of a cubic divided by x+2 (official answer: A) PDF
- Q.59 (CDS (II) Maths) · MCQ · Polynomials: Expansion of a product of three linear factors (official answer: A) PDF
- Q.71 (CDS (II) Maths) · MCQ · Algebraic Equations: Count real numbers whose sum with reciprocal is 3 (official answer: C) PDF
- Q.73 (CDS (II) Maths) · MCQ · Linear Equations: Age difference of two sisters from past age ratios (official answer: A) PDF
- Q.74 (CDS (II) Maths) · MCQ · Linear Diophantine Equations: Ways to spend a fixed sum on apples and oranges (official answer: B) PDF
- Q.85 (CDS (II) Maths) · MCQ · Maxima and Minima: Value of x maximising x minus x squared (official answer: C) PDF
- Q.89 (CDS (II) Maths) · MCQ · Quadratic Equations: Coefficients of a quadratic whose roots are p and q (official answer: A) PDF
- Q.91 (CDS (II) Maths) · MCQ · Quadratic Equations: Maximum value of b given an irrational root (official answer: D) PDF
- Q.92 (CDS (II) Maths) · MCQ · Surds: Value of an expression in a given surd (official answer: C) PDF
- Q.93 (CDS (II) Maths) · MCQ · Maxima and Minima: Maximum value of a rational expression (official answer: D) PDF
- Q.97 (CDS (II) Maths) · MCQ · HCF and LCM of Polynomials: LCM of three polynomials (official answer: A) PDF
- Q.98 (CDS (II) Maths) · MCQ · Algebraic Identities: Value of a ratio with sum of cubes of differences (official answer: B) PDF
- Q.99 (CDS (II) Maths) · MCQ · Sets: Intersection of three sets with nested elements (official answer: D) PDF
- Q.100 (CDS (II) Maths) · MCQ · Quadratic Equations: p minus q when sum and product of roots are given (official answer: C) PDF
CDS2018
- Q.2 (CDS (I) Maths) · MCQ · Algebraic Expressions: Value of a/(a-c)+c/(b-c) given a+b=2c (official answer: C) PDF
- Q.3 (CDS (I) Maths) · MCQ · Indices: Value of abc from cyclic fractional-power relations (official answer: B) PDF
- Q.4 (CDS (I) Maths) · MCQ · Indices: Value of a product of powers given 2b=a+c and y^2=xz (official answer: C) PDF
- Q.6 (CDS (I) Maths) · MCQ · Quadratic Equations: Condition for roots of px^2+x+r=0 to be reciprocals (official answer: B) PDF
- Q.7 (CDS (I) Maths) · MCQ · Linear Equations: Value of xy from a pair of linear equations (official answer: A) PDF
- Q.8 (CDS (I) Maths) · MCQ · Algebraic Expressions: Value of (ab+xy)/bx from two fraction relations (official answer: A) PDF
- Q.9 (CDS (I) Maths) · MCQ · Algebraic Identities: Value of a cubic expression given a - 1/a = 5 (official answer: C) PDF
- Q.10 (CDS (I) Maths) · MCQ · Algebraic Identities: Sum of cubes of (y+z-x) etc. when x+y+z=0 (official answer: D) PDF
- Q.11 (CDS (I) Maths) · MCQ · Factor Theorem: Value of k when (x+3) is a factor of a cubic (official answer: A) PDF
- Q.13 (CDS (I) Maths) · MCQ · Polynomials: Zero of a given cubic polynomial (official answer: B) PDF
- Q.15 (CDS (I) Maths) · MCQ · Quadratic Equations: Value of (alpha+1)(beta+1) for roots of a quadratic (official answer: C) PDF
- Q.16 (CDS (I) Maths) · MCQ · Remainder Theorem: Find k from remainder on division by (x+1) (official answer: D) PDF
- Q.17 (CDS (I) Maths) · MCQ · Polynomials: Degree of the sum or difference of two polynomials (official answer: C) PDF
- Q.19 (CDS (I) Maths) · MCQ · Indices: Value of a cyclic sum of reciprocal exponent expressions (official answer: C) PDF
- Q.20 (CDS (I) Maths) · MCQ · Quadratic Equations: Number whose sum with its square is 20 (official answer: A) PDF
- Q.31 (CDS (I) Maths) · MCQ · Ages: Father's age after 10 years from average and son's age (official answer: C) PDF
- Q.39 (CDS (I) Maths) · MCQ · Ages: Age difference of a couple with reversed-digit ages (official answer: B) PDF
- Q.43 (CDS (I) Maths) · MCQ · Remainder Theorem: Value of a+b for a quadratic with given remainders (official answer: A) PDF
- Q.2 (CDS (II) Maths) · MCQ · Indices: Value of abc from cyclic power relations among x, y, z (official answer: A) PDF
- Q.6 (CDS (II) Maths) · MCQ · Inequalities: Solution set of x^2 - 6x - 27 > 0 (official answer: C) PDF
- Q.8 (CDS (II) Maths) · MCQ · HCF and LCM of Polynomials: Find the other polynomial from HCF, LCM and one polynomial (official answer: C) PDF
- Q.9 (CDS (II) Maths) · MCQ · Quadratic Equations: Greatest of expressions in two real roots with given sum and product (official answer: C) PDF
- Q.11 (CDS (II) Maths) · MCQ · Algebraic Identities: Find k in an identity in x and 1/x (official answer: B) PDF
- Q.15 (CDS (II) Maths) · MCQ · Indices: Value of an exponent expression when a^x=b^y=c^z and abc=1 (official answer: B) PDF
- Q.16 (CDS (II) Maths) · MCQ · Quadratic Equations: Value of a symmetric expression in the roots of a quadratic (official answer: B) PDF
- Q.19 (CDS (II) Maths) · MCQ · Indices: Value of a product of powers of a, b, c (official answer: D) PDF
- Q.21 (CDS (II) Maths) · MCQ · Quadratic Equations: Minimum value of 2x^2 + 5x + 5 (official answer: B) PDF
- Q.23 (CDS (II) Maths) · MCQ · Algebraic Expressions: Sum of pairwise products of plus-minus 1 to 4 (official answer: B) PDF
- Q.24 (CDS (II) Maths) · MCQ · Remainder Theorem: Remainder of a cubic in x, y divided by (x - 2y) (official answer: A) PDF
- Q.25 (CDS (II) Maths) · MCQ · Algebraic Identities: Value of an expression when ab+bc+ca=0 (official answer: B) PDF
- Q.31 (CDS (II) Maths) · MCQ · Ages: Father's age 12 years hence from family age data (official answer: D) PDF
- Q.33 (CDS (II) Maths) · MCQ · Sets: Girls playing only badminton from group data (official answer: A) PDF
- Q.37 (CDS (II) Maths) · MCQ · Ages: Present ages of mother and daughter from age ratios (official answer: B) PDF
- Q.38 (CDS (II) Maths) · MCQ · Sets: Boys who play only carrom (official answer: C) PDF
- Q.47 (CDS (II) Maths) · MCQ · Ages: Statements on father-son age ratios (official answer: B) PDF
- Q.48 (CDS (II) Maths) · MCQ · Linear Inequalities: Quadrants containing the solution of two linear inequalities (official answer: B) PDF
- Q.49 (CDS (II) Maths) · MCQ · Simultaneous Equations: Value of a for a single positive solution of two equations (official answer: A) PDF
- Q.50 (CDS (II) Maths) · MCQ · Polynomials: Sum of squares of zeros of a cubic polynomial (official answer: D) PDF
- Q.51 (CDS (II) Maths) · MCQ · Sets: Percent who passed in all three subjects (official answer: C) PDF
- Q.52 (CDS (II) Maths) · MCQ · Sets: Percent who passed in exactly one subject (official answer: B) PDF
- Q.53 (CDS (II) Maths) · MCQ · Sets: Number who passed in at least two subjects (official answer: A) PDF
- Q.54 (CDS (II) Maths) · MCQ · Sets: Ratio of Physics-Chemistry passes to Biology-Physics-only passes (official answer: B) PDF
CDS2017
- Q.2 (CDS (I) Maths) · MCQ · Factor Theorem: Quadratic having x+4 as a factor (official answer: C) PDF
- Q.3 (CDS (I) Maths) · MCQ · Quadratic Equations: Maximum of α/β+β/α for given roots (official answer: B) PDF
- Q.6 (CDS (I) Maths) · MCQ · Logarithms: Number of digits in 2^40 (official answer: B) PDF
- Q.7 (CDS (I) Maths) · MCQ · Quadratic Equations: Value of a when one root is twice the other (official answer: A) PDF
- Q.9 (CDS (I) Maths) · MCQ · Surds: Value of bx²-2ax+b for a surd ratio x (official answer: A) PDF
- Q.11 (CDS (I) Maths) · MCQ · Exponents: Relation between x and y defined by powers of t (official answer: C) PDF
- Q.14 (CDS (I) Maths) · MCQ · Algebraic Identities: Value of x³-6x²+6x for x with cube roots (official answer: B) PDF
- Q.15 (CDS (I) Maths) · MCQ · Surd Equations: Value of xy from a surd equation and x+y=26 (official answer: C) PDF
- Q.16 (CDS (I) Maths) · MCQ · Linear Equations: Solve a given equation (official answer: D) PDF
- Q.17 (CDS (I) Maths) · MCQ · Quadratic Equations: Expression in roots of x²+px+q (official answer: A) PDF
- Q.18 (CDS (I) Maths) · MCQ · Algebraic Identities: Find a+b given a³=335+b³ and a=5+b (official answer: B) PDF
- Q.19 (CDS (I) Maths) · MCQ · Exponents: Value of x+y from exponential equations (official answer: C) PDF
- Q.20 (CDS (I) Maths) · MCQ · Linear Equations: Condition on k for two lines to intersect (official answer: B) PDF
- Q.29 (CDS (I) Maths) · MCQ · Exponential Equations: Solve 5^(1+x)+5^(1-x)=26 (official answer: A) PDF
- Q.33 (CDS (I) Maths) · MCQ · Algebraic Identities: a³+b³ from a+b and ab (official answer: A) PDF
- Q.41 (CDS (I) Maths) · MCQ · LCM of Polynomials: LCM of three polynomials (official answer: A) PDF
- Q.42 (CDS (I) Maths) · MCQ · HCF of Polynomials: Reciprocal of LCM when HCF is 1 (official answer: D) PDF
- Q.45 (CDS (I) Maths) · MCQ · Quadratic Equations: Correct roots from two wrong attempts (official answer: B) PDF
- Q.47 (CDS (I) Maths) · MCQ · Linear Equations: Nature of a system of two equations (official answer: C) PDF
- Q.1 (CDS (II) Maths) · MCQ · HCF of Polynomials: Value of a for two quadratics with a common factor (official answer: A) PDF
- Q.3 (CDS (II) Maths) · MCQ · Factorisation: Factors of a cubic polynomial (official answer: C) PDF
- Q.5 (CDS (II) Maths) · MCQ · Quadratic Equations: Value of m when roots are in ratio 3:2 (official answer: A) PDF
- Q.6 (CDS (II) Maths) · MCQ · Polynomials: Degree of a product of polynomials (official answer: B) PDF
- Q.7 (CDS (II) Maths) · MCQ · Remainder Theorem: Remainder of a cubic divided by x+3 (official answer: D) PDF
- Q.8 (CDS (II) Maths) · MCQ · HCF and LCM of Polynomials: LCM from product and HCF (official answer: D) PDF
- Q.14 (CDS (II) Maths) · MCQ · Polynomials: Quotient of x³-y³ divided by a quadratic (official answer: C) PDF
- Q.15 (CDS (II) Maths) · MCQ · Factor Theorem: Ratio a:b from a common factor x+2 (official answer: A) PDF
- Q.16 (CDS (II) Maths) · MCQ · Remainder Theorem: Remainder when f(x) is divided by ax-b (official answer: A) PDF
- Q.18 (CDS (II) Maths) · MCQ · Algebraic Identities: Product of four polynomials (official answer: B) PDF
- Q.19 (CDS (II) Maths) · MCQ · Factorisation: Factors of x(x+2)(x+3)(x+5)-72 (official answer: C) PDF
- Q.20 (CDS (II) Maths) · MCQ · HCF of Polynomials: Values of a, b from a given HCF (official answer: B) PDF
- Q.22 (CDS (II) Maths) · MCQ · Quadratic Equations: Condition for equal roots of a quadratic (official answer: C) PDF
- Q.23 (CDS (II) Maths) · MCQ · Linear Equations: Non-zero solution of an equation in a, b, c (official answer: A) PDF
- Q.28 (CDS (II) Maths) · MCQ · Linear Equations: Value of u from a system in u and v (official answer: D) PDF
- Q.32 (CDS (II) Maths) · MCQ · Algebraic Identities: Expression value when ab+bc+ca=0 (official answer: C) PDF
- Q.34 (CDS (II) Maths) · MCQ · Algebraic Identities: Ratio of a product to sum of cubes (official answer: B) PDF
- Q.36 (CDS (II) Maths) · MCQ · Logarithms: Sum of logs from given values (official answer: D) PDF
CDS2016
- Q.1 (CDS (I) Maths) · MCQ · Quadratic Equations: Relation when roots of a quadratic are in ratio p:q (official answer: A) PDF
- Q.2 (CDS (I) Maths) · MCQ · Surd Equations: Product of roots of an equation with square roots (official answer: A) PDF
- Q.3 (CDS (I) Maths) · MCQ · Algebraic Expressions: Value of an expression from given relations in x and y (official answer: C) PDF
- Q.4 (CDS (I) Maths) · MCQ · Linear Equations: Value of an expression from three linear relations (official answer: C) PDF
- Q.5 (CDS (I) Maths) · MCQ · Quadratic Equations: Condition for two quadratics to share a root (official answer: D) PDF
- Q.6 (CDS (I) Maths) · MCQ · Algebraic Identities: Value of a cubic expression when x involves a cube root (official answer: A) PDF
- Q.7 (CDS (I) Maths) · MCQ · HCF of Polynomials: HCF of two expressions from their sum and difference (official answer: B) PDF
- Q.8 (CDS (I) Maths) · MCQ · Algebraic Expressions: Simplify a given algebraic expression (official answer: B) PDF
- Q.9 (CDS (I) Maths) · MCQ · Polynomials: Find p²+q² from divisibility of a polynomial (official answer: C) PDF
- Q.10 (CDS (I) Maths) · MCQ · Polynomials: Condition on a quadratic with factors x-m and x-km (official answer: B) PDF
- Q.11 (CDS (I) Maths) · MCQ · Remainder Theorem: Remainder of xⁿ+mⁿ divided by x-m (official answer: A) PDF
- Q.12 (CDS (I) Maths) · MCQ · Exponents: Value of x+y from exponential equations (official answer: B) PDF
- Q.13 (CDS (I) Maths) · MCQ · Factorisation: Sum of linear factors of a quadratic (official answer: A) PDF
- Q.14 (CDS (I) Maths) · MCQ · Surd Equations: Evaluate bx²-ax+b from a surd equation (official answer: A) PDF
- Q.15 (CDS (I) Maths) · MCQ · Algebraic Identities: Find a+b given a³=117+b³ and a=3+b (official answer: A) PDF
- Q.16 (CDS (I) Maths) · MCQ · Quadratic Equations: Relation when root sum equals sum of reciprocal squares (official answer: A) PDF
- Q.19 (CDS (I) Maths) · MCQ · Algebraic Expressions: Statements on expressions in a, b, c (official answer: A) PDF
- Q.31 (CDS (I) Maths) · MCQ · Quadratic Equations: Condition for one root to be the square of the other (official answer: C) PDF
- Q.35 (CDS (I) Maths) · MCQ · Factor Theorem: Value of k for which x+1 is a factor (official answer: D) PDF
- Q.37 (CDS (I) Maths) · MCQ · Inequalities: Solve an inequation in x (official answer: D) PDF
- Q.38 (CDS (I) Maths) · MCQ · Linear Inequalities: Points satisfying a system of inequations (official answer: C) PDF
- Q.40 (CDS (I) Maths) · MCQ · Linear Equations: Value of k for no solution of a system (official answer: C) PDF
- Q.85 (CDS (I) Maths) · MCQ · Surd Equations: Value of xy from a surd equation (official answer: D) PDF
- Q.90 (CDS (I) Maths) · MCQ · Linear Inequalities: Inequations for a shaded region (official answer: A) PDF
- Q.96 (CDS (I) Maths) · MCQ · Logarithms: Evaluate a logarithmic expression (official answer: B) PDF
- Q.99 (CDS (I) Maths) · MCQ · Inequalities: Statements on inequalities with negative numbers (official answer: D) PDF
- Q.1 (CDS (II) Maths) · MCQ · Linear Equations: Solve a given equation (official answer: B) PDF
- Q.2 (CDS (II) Maths) · MCQ · Quadratic Equations: Integer values of λ with roots in given intervals (official answer: D) PDF
- Q.4 (CDS (II) Maths) · MCQ · Algebraic Expressions: Value of expression when each variable is sum of others (official answer: B) PDF
- Q.8 (CDS (II) Maths) · MCQ · Quadratic Equations: Pairs a, b giving real roots of x²+ax+b (official answer: B) PDF
- Q.14 (CDS (II) Maths) · MCQ · Polynomials: Quadratic whose zeros are scaled zeros of another (official answer: B) PDF
- Q.20 (CDS (II) Maths) · MCQ · Quadratic Equations: Values of p, q when they are roots (official answer: A) PDF
- Q.28 (CDS (II) Maths) · MCQ · Quadratic Equations: Roots of a given equation (official answer: C) PDF
- Q.31 (CDS (II) Maths) · MCQ · Algebraic Equations: Value of p+2q from two equations (official answer: D) PDF
- Q.32 (CDS (II) Maths) · MCQ · Logarithms: Digits in a power of 3 using log (official answer: C) PDF
- Q.34 (CDS (II) Maths) · MCQ · Algebraic Expressions: Evaluate expression given 4x+3a=0 (official answer: C) PDF
- Q.100 (CDS (II) Maths) · MCQ · Algebraic Identities: Value of a power of x given x+1/x=2 (official answer: B) PDF
Other Elementary Mathematics topics
- Number System and Simplification PYQs
- Percentage, Ratio, Profit and Interest PYQs
- Time, Speed and Work PYQs
- Trigonometry PYQs
- Geometry PYQs
- Mensuration PYQs
- Statistics PYQs
FAQ
How many Algebra questions come in CDS?
In the official papers we tagged: 39 in 2026, 34 in 2025, 24 in 2024, 54 in 2023, 48 in 2022, 45 in 2021, 31 in 2020, 37 in 2019, 42 in 2018, 37 in 2017 and 37 in 2016 (2 papers each year). That is 428 questions in all, about 19% of Elementary Mathematics.
Which Algebra topics repeat in CDS?
Asked in the most papers: Quadratic Equations, Algebraic Identities, Polynomials. The concept table lists every one with its count.
Are these official CDS questions?
Yes. Every question is from an official CDS paper hosted on our year pages. The one-line summaries are ours; open the PDF linked beside each question for the full text.