Class 10 Mathematics Part 2 (Geometry) – Daily Revision MCQ (English Medium)
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Lines l ∥ m ∥ n are cut by transversal t₁ at A, B, C and by transversal t₂ at P, Q, R. If AB = 4 cm, BC = 6 cm and PQ = 6 cm, what is QR?
Chapter 1: Similarity
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Answer: C. 9 cm
Intercepts made by three parallel lines on two transversals are in the same ratio: AB/BC = PQ/QR ⇒ 4/6 = 6/QR ⇒ QR = 9 cm.In ΔABC, M is the midpoint of side BC. If AM = 5 cm and BC = 8 cm, what is the value of AB² + AC²?
Chapter 2: Pythagoras Theorem
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Answer: A. 82
Apollonius theorem: AB² + AC² = 2AM² + 2BM² = 2(25) + 2(16) = 50 + 32 = 82 (BM = 4 cm).In a right-angled triangle both acute angles measure 45° and the hypotenuse is 6√2 cm. What is the length of each perpendicular side?
Chapter 2: Pythagoras Theorem
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Answer: B. 6 cm
In a 45°-45°-90° triangle each perpendicular side is 1/√2 times the hypotenuse: 6√2 × 1/√2 = 6 cm.Two circles of radii 7 cm and 4 cm touch each other internally. What is the distance between their centres?
Chapter 3: Circle
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Answer: D. 3 cm
For circles touching internally, the distance between the centres equals the difference of the radii: 7 − 4 = 3 cm.Seg PQ is a diameter of a circle and R is any other point on the circle. What is the measure of ∠PRQ?
Chapter 3: Circle
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Answer: B. 90°
An angle inscribed in a semicircle is a right angle, so ∠PRQ = 90°.ΔA′BC′ is to be constructed similar to ΔABC (vertex B common) so that each side of ΔA′BC′ is 4/7 of the corresponding side of ΔABC. Into how many equal parts is seg BC divided?
Chapter 4: Geometric Constructions
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Answer: A. 7
For the ratio 4/7, seg BC is divided into 7 equal parts, C′ is taken at the end of the 4th part from B, and C′A′ is drawn parallel to CA.The vertices of a triangle are (2, 3), (4, −1) and (6, 7). What are the co-ordinates of its centroid?
Chapter 5: Co-ordinate Geometry
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Answer: C. (4, 3)
Centroid formula: ((2 + 4 + 6)/3, (3 − 1 + 7)/3) = (12/3, 9/3) = (4, 3).If tan θ = 12/5 and θ is an acute angle, what is the value of sec θ?
Chapter 6: Trigonometry
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Answer: D. 13/5
1 + tan²θ = sec²θ ⇒ sec²θ = 1 + 144/25 = 169/25 ⇒ sec θ = 13/5.What is the length of an arc of measure 60° in a circle of radius 21 cm? (π = 22/7)
Chapter 7: Mensuration
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Answer: B. 22 cm
Length of arc = (θ/360) × 2πr = (60/360) × 2 × (22/7) × 21 = 22 cm.What is the volume of a solid hemisphere of radius 3 cm?
Chapter 7: Mensuration
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Answer: A. 18π cm³
Volume of a hemisphere = (2/3)πr³ = (2/3) × π × 27 = 18π cm³.
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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.