Class 10 Mathematics Part 2 (Geometry) – Daily Revision MCQ (English Medium)
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Two triangles have equal heights. Their bases are 6 cm and 9 cm. What is the ratio of their areas?
Chapter 1: Similarity
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Answer: B. 2 : 3
Triangles with equal heights have areas in the ratio of their bases: 6 : 9 = 2 : 3.In ΔPQR, ray PS bisects ∠QPR and meets side QR at S. If PQ = 6 cm, PR = 8 cm and QS = 3 cm, what is SR?
Chapter 1: Similarity
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Answer: A. 4 cm
By the angle bisector theorem, QS/SR = PQ/PR, so 3/SR = 6/8, which gives SR = 4 cm.In ΔABC, ∠ABC = 90° and seg BD ⊥ hypotenuse AC. If AD = 4 cm and DC = 9 cm, what is BD?
Chapter 2: Pythagoras Theorem
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Answer: C. 6 cm
By the theorem of geometric mean, BD² = AD × DC = 4 × 9 = 36, so BD = 6 cm.□ABCD is a cyclic quadrilateral. If ∠A = 75°, what is ∠C?
Chapter 3: Circle
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Answer: B. 105°
Opposite angles of a cyclic quadrilateral are supplementary, so ∠C = 180° − 75° = 105°.From a point E outside a circle, a secant meets the circle at A and B, and a tangent touches it at T. If EA = 2 cm and EB = 8 cm, what is ET?
Chapter 3: Circle
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Answer: D. 4 cm
By the tangent secant segments theorem, ET² = EA × EB = 2 × 8 = 16, so ET = 4 cm.To draw tangents to a circle with centre O from an external point P, the points of contact are found where the given circle meets which figure?
Chapter 4: Geometric Constructions
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Answer: A. A circle with seg OP as diameter
The angle in a semicircle is a right angle, so the circle on diameter OP cuts the given circle where radius ⊥ tangent; those are the points of contact.What is the slope of the line passing through the points (1, 2) and (3, 8)?
Chapter 5: Co-ordinate Geometry
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Answer: C. 3
Slope m = (y₂ − y₁)/(x₂ − x₁) = (8 − 2)/(3 − 1) = 6/2 = 3.From a point on the ground 10√3 m away from the foot of a tower, the angle of elevation of the top of the tower is 60°. What is the height of the tower?
Chapter 6: Trigonometry
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Answer: B. 30 m
tan 60° = height / 10√3 and tan 60° = √3, so height = 10√3 × √3 = 30 m.What is the volume of a cone whose base radius is 3 cm and perpendicular height is 7 cm? (π = 22/7)
Chapter 7: Mensuration
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Answer: D. 66 cm³
Volume of a cone = ⅓πr²h = ⅓ × 22/7 × 3 × 3 × 7 = 66 cm³.What is the surface area of a sphere of radius 3.5 cm? (π = 22/7)
Chapter 7: Mensuration
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Answer: A. 154 cm²
Surface area of a sphere = 4πr² = 4 × 22/7 × 3.5 × 3.5 = 154 cm².
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.