Class 10 Mathematics Part 2 (Geometry) – Daily Revision MCQ (English Medium)
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Two triangles are similar and their corresponding sides are in the ratio 2 : 3. What is the ratio of their areas?
Chapter 1: Similarity
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Answer: B. 4 : 9
For similar triangles, ratio of areas = ratio of squares of corresponding sides = 2² : 3² = 4 : 9.In ΔABC, D is on side AB and E is on side AC with DE ∥ BC. If AD = 3 cm, DB = 2 cm and AE = 6 cm, what is EC?
Chapter 1: Similarity
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Answer: A. 4 cm
By the basic proportionality theorem AD/DB = AE/EC, so 3/2 = 6/EC, giving EC = 4 cm.In a right-angled triangle with acute angles 30° and 60°, the hypotenuse is 10 cm. How long is the side opposite the 30° angle?
Chapter 2: Pythagoras Theorem
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Answer: C. 5 cm
In a 30°-60°-90° triangle the side opposite 30° is half the hypotenuse: 10 ÷ 2 = 5 cm (5√3 cm is opposite 60°).Which of these is a Pythagorean triplet?
Chapter 2: Pythagoras Theorem
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Answer: D. (9, 40, 41)
9² + 40² = 81 + 1600 = 1681 = 41², so the square of the largest equals the sum of squares of the other two.A circle has radius 5 cm. A point P is 13 cm from the centre. What is the length of the tangent segment drawn from P to the circle?
Chapter 3: Circle
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Answer: C. 12 cm
The tangent is perpendicular to the radius at the point of contact, so tangent² = 13² − 5² = 169 − 25 = 144, tangent = 12 cm.An inscribed angle intercepts an arc of measure 140°. What is the measure of the inscribed angle?
Chapter 3: Circle
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Answer: A. 70°
Inscribed angle theorem: an inscribed angle is half the measure of the arc it intercepts, 140° ÷ 2 = 70°.To construct a tangent at a point P on a circle with centre C (using the centre), the line through P is drawn how?
Chapter 4: Geometric Constructions
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Answer: B. Perpendicular to the radius CP
The construction uses the tangent theorem: the line through P perpendicular to radius CP is the tangent.What is the distance between the points A(1, 2) and B(4, 6)?
Chapter 5: Co-ordinate Geometry
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Answer: B. 5
Distance formula: AB = √[(4 − 1)² + (6 − 2)²] = √(9 + 16) = √25 = 5.If sin θ = 3/5 and θ is an acute angle, what is cos θ?
Chapter 6: Trigonometry
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Answer: D. 4/5
sin²θ + cos²θ = 1, so cos²θ = 1 − 9/25 = 16/25 and cos θ = 4/5.What is the area of a sector of a circle of radius 7 cm whose central angle is 90°? (π = 22/7)
Chapter 7: Mensuration
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Answer: C. 38.5 cm²
Area of sector = (θ/360) × πr² = (90/360) × (22/7) × 49 = 154 ÷ 4 = 38.5 cm² (11 cm is the arc length).
Class 10: MCQ in other subjects
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All questions are written by PadhaiNotes in our own words from the chapters of the official Maharashtra State Board Balbharati textbook (ebalbharati.in). Each question shows its chapter.