TS Board 10th Previous Questions -Solutions

Statistics (1 Mark) – Complete Solutions Statistics (1 Mark) – Complete Solutions Important Statistics Concepts: • Mean = Sum of all observations / Total number of observations • Median = Middle value when data is arranged in order • Mode = Most frequently occurring value • Assumed Mean Method: A = Assumed mean, d = … Read more

Probability – 1 Mark Solutions Probability – 1 Mark Solutions Important Probability Concepts: • Probability = Number of favorable outcomes / Total number of outcomes • 0 ≤ P(E) ≤ 1 • P(E) + P(not E) = 1 • Prime numbers: Numbers with exactly two factors (1 and itself) • Composite numbers: Numbers with more … Read more

Applications of Trigonometry – 1 Mark Solutions Applications of Trigonometry – 1 Mark Solutions Important Trigonometric Concepts: • Angle of Elevation: Angle between horizontal line and line of sight when looking up • Angle of Depression: Angle between horizontal line and line of sight when looking down • tan θ = Opposite/Adjacent • Height = … Read more

Trigonometry – 1 Mark Solutions Trigonometry -1 Mark Solutions Important Trigonometric Formulas: • sin²θ + cos²θ = 1 • 1 + tan²θ = sec²θ • 1 + cot²θ = cosec²θ • sin(90° – θ) = cosθ • cos(90° – θ) = sinθ • tan(90° – θ) = cotθ • sin(A+B) = sinA cosB + cosA … Read more

Mensuration- 1 Mark Solutions Mensuration- 1 Mark Solutions Important Mensuration Formulas: • Volume of Cylinder = πr²h • Volume of Cone = (1/3)πr²h • Volume of Sphere = (4/3)πr³ • Volume of Hemisphere = (2/3)πr³ • Curved Surface Area of Cylinder = 2πrh • Curved Surface Area of Cone = πrl (l = slant height) … Read more

Tangents and Secants to Circles – 1 Mark Solutions Tangents and Secants to Circles – 1 Mark Solutions Important Geometric Principles: • Tangent Length Formula: PT = √(OP² – OT²) where O is center, P is external point, T is tangent point • Area of Sector: (θ/360°) × πr² • Tangent is perpendicular to radius … Read more

Similar Triangles – 1 Mark Problems Similar Triangles – 1 Mark Problems Important Concepts: • Basic Proportionality Theorem (Thales Theorem):   If a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally. • Midpoint Theorem:   The line segment joining midpoints of two sides is parallel to the third … Read more

Coordinate Geometry – 1 Mark Problems Coordinate Geometry – 1 Mark Problems Important Formulas: • Distance between (x₁, y₁) and (x₂, y₂): √[(x₂-x₁)² + (y₂-y₁)²] • Midpoint of (x₁, y₁) and (x₂, y₂): [(x₁+x₂)/2, (y₁+y₂)/2] • Centroid of triangle with vertices (x₁, y₁), (x₂, y₂), (x₃, y₃):   [(x₁+x₂+x₃)/3, (y₁+y₂+y₃)/3] • Slope of line through (x₁, … Read more

Progressions – 1 Mark Problems Progressions – 1 Mark Problems Important Formulas: Arithmetic Progression (AP): • nth term: aₙ = a + (n-1)d • Sum of first n terms: Sₙ = n/2 [2a + (n-1)d] • Common difference: d = aₙ – aₙ₋₁ Geometric Progression (GP): • nth term: aₙ = a · rⁿ⁻¹ • … Read more

Quadratic Equations – 1 Mark Problems Quadratic Equations – 1 Mark Problems Important Formulas: • Standard form: ax² + bx + c = 0 • Discriminant (D) = b² – 4ac • Nature of roots:   – D > 0: Two distinct real roots   – D = 0: Two equal real roots   – D < 0: ... Read more

Linear Equations Problems and Solutions Pair of Linear Equations in Two Variables 1-Mark Questions 1 For what value of k, the following system of equations has a unique solution: x – ky = 2 and 3x + 2y = -5 (M’15) Step 1: Condition for unique solution For a system of linear equations a₁x + … Read more

Polynomial Problems and Solutions Polynomial Problems and Solutions 1-Mark Questions 1 If x ≠ –1, then find the quotient of (x⁵ + x⁴ + x³ + x²) / (x³ + x² + x + 1) (M’15) Step 1: Factor numerator and denominator Numerator: x⁵ + x⁴ + x³ + x² = x²(x³ + x² + … Read more

Set Theory Problems – 1 Mark Questions Set Theory Problems – 1 Mark Questions Set Operations and Representations 1 If A = {x : x ∈ N and x < 20} and B = {x : x ∈ N and x ≤ 5} then write the set A – B in the set builder form. ... Read more

Real Numbers 1 mark Solutions Real Numbers 1 mark Solutions 1. Insert 4 rational numbers between 3/4 and 1 without using formula a + b/2 (M’15) We convert to a common denominator: 3/4 = 15/20, 1 = 20/20 Choose four numbers between 15/20 and 20/20: 16/20, 17/20, 18/20, 19/20 Simplifying: 4/5, 17/20, 9/10, 19/20 2. … Read more