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Q001 | Mathematics | IX | Number Systems | Irrational Numbers | MCQ | 1 | Which of the following is an irrational number? | ["\u221a4", "\u221a9", "\u221a7", "\u221a16"] | √7 | √7 ≈ 2.6457... cannot be expressed as p/q — updated explanation | Medium | CBSE | 2,011 |
Q002 | Mathematics | IX | Number Systems | Rational Numbers | MCQ | 1 | The decimal expansion of 1/3 is: | ["0.3", "0.33", "0.333...", "0.3333"] | 0.333... | 1/3 = 0.3333... (non-terminating repeating decimal) | Easy | CBSE | 2,011 |
Q003 | Mathematics | IX | Number Systems | Laws of Exponents | Short Answer | 2 | Simplify: (2^3 × 3^2) / (2^2 × 3) | [] | 6 | = 2^(3-2) × 3^(2-1) = 2^1 × 3^1 = 2 × 3 = 6 | Medium | CBSE | 2,011 |
Q004 | Mathematics | IX | Polynomials | Degree of Polynomial | MCQ | 1 | The degree of polynomial 3x^3 + 2x^2 - x + 5 is: | ["1", "2", "3", "5"] | 3 | The highest power of the variable x is 3, so degree = 3 | Easy | CBSE | 2,011 |
Q005 | Mathematics | IX | Polynomials | Factor Theorem | Short Answer | 2 | Find the value of k if x=2 is a zero of polynomial p(x) = x^2 + kx + 6 | [] | k = -5 | p(2) = 0 → 4 + 2k + 6 = 0 → 2k = -10 → k = -5 | Medium | CBSE | 2,011 |
Q006 | Mathematics | IX | Polynomials | Algebraic Identities | Short Answer | 2 | Expand (2x + 3y)^2 using algebraic identity | [] | 4x^2 + 12xy + 9y^2 | Using (a+b)^2 = a^2 + 2ab + b^2: (2x)^2 + 2(2x)(3y) + (3y)^2 | Medium | CBSE | 2,011 |
Q007 | Mathematics | IX | Coordinate Geometry | Quadrants | MCQ | 1 | The point (-3, 4) lies in which quadrant? | ["Quadrant I", "Quadrant II", "Quadrant III", "Quadrant IV"] | Quadrant II | x is negative and y is positive → Quadrant II | Easy | CBSE | 2,011 |
Q008 | Mathematics | IX | Coordinate Geometry | Distance Formula | Short Answer | 2 | Find the distance of point (3, 4) from the origin | [] | 5 units | Distance = √(x^2 + y^2) = √(9 + 16) = √25 = 5 | Medium | CBSE | 2,011 |
Q009 | Mathematics | IX | Linear Equations in Two Variables | Solution of Linear Equations | MCQ | 1 | Which of the following is a solution of 2x + y = 6? | ["(1,1)", "(2,2)", "(1,4)", "(3,1)"] | (1,4) | 2(1) + 4 = 6 ✓. Others: 2+1=3≠6, 4+2=6 wait check: 2(2)+2=6 ✓ actually (2,2) also works | Easy | CBSE | 2,011 |
Q010 | Mathematics | IX | Linear Equations in Two Variables | Graph of Linear Equation | Long Answer | 4 | Draw the graph of equation 2x + y = 6 and find the area of triangle formed with axes | [] | Area = 9 sq units | x-intercept=(3,0), y-intercept=(0,6). Area = 1/2 × base × height = 1/2 × 3 × 6 = 9 | Hard | CBSE | 2,011 |
Q011 | Mathematics | IX | Triangles | Congruence of Triangles | MCQ | 1 | In triangles ABC and PQR, AB=PQ, BC=QR and angle B = angle Q. By which rule are they congruent? | ["SSS", "SAS", "ASA", "RHS"] | SAS | Two sides and included angle equal → SAS (Side-Angle-Side) congruence rule | Easy | CBSE | 2,011 |
Q012 | Mathematics | IX | Triangles | Properties of Triangles | Short Answer | 3 | Prove that angles opposite to equal sides of an isosceles triangle are equal | [] | Given: AB=AC. Draw bisector AD. Triangles ABD and ACD are congruent by SAS. Therefore angle B = angle C | Proof uses triangle congruence (SAS rule) to establish base angles are equal | Hard | CBSE | 2,011 |
Q013 | Mathematics | IX | Heron's Formula | Area of Triangle | Short Answer | 3 | Find the area of triangle with sides 5cm, 12cm, and 13cm using Heron's formula | [] | 30 sq cm | s = (5+12+13)/2 = 15. Area = √(15×10×3×2) = √900 = 30 sq cm | Medium | CBSE | 2,011 |
Q014 | Mathematics | IX | Statistics | Mean | Short Answer | 2 | Find the mean of: 4, 7, 2, 9, 8, 3, 5, 1, 6, 5 | [] | 5 | Sum = 4+7+2+9+8+3+5+1+6+5 = 50. Mean = 50/10 = 5 | Easy | CBSE | 2,011 |
Q015 | Mathematics | IX | Statistics | Median and Mode | Short Answer | 2 | Find the median and mode of: 2, 3, 4, 5, 3, 3, 6, 7 | [] | Median = 3.5, Mode = 3 | Sorted: 2,3,3,3,4,5,6,7. Median=(3+4)/2=3.5. Mode=3 (appears 3 times) | Medium | CBSE | 2,011 |
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