Skip to the questions

CBSE Class 10 Maths Question of the Day: chapters 9–11

27 CBSE Class 10 Mathematics puzzles from the Question of the Day rotation, chapters 9–11. Each puzzle is three board-style questions on one chapter, shown as an image with the question text written out below it; the answers, hints and step-marked solutions are on the daily puzzle page.

Chapter 9: Some Applications of Trigonometry

Chapter 9: Some Applications of Trigonometry
Three board-style questions on Some Applications of Trigonometry (CBSE Class 10 Mathematics). No calculator.
1. The shadow of a vertical tower on level ground is equal to its height. The angle of elevation of the Sun is Options: A) 30^∘; B) 45^∘; C) 60^∘; D) 90^∘
2. A straight zip-line cable, 80 m long, runs from the top of a platform down to a point on level ground and makes an angle of 30^∘ with the ground. The height of the platform is Options: A) 40 m; B) 40√3 m; C) 80√3 m; D) 40/(√3) m
3. A 14 m ladder leans against a wall and makes an angle of 60^∘ with the ground. The distance of its foot from the wall is Options: A) 7√3 m; B) 7 m; C) 14√3 m; D) 7/(√3) m
Chapter 9: Some Applications of Trigonometry · A kite string
Three board-style questions on Some Applications of Trigonometry (CBSE Class 10 Mathematics). No calculator. A kite is flying on a straight string 100 m long, which makes an angle of 30^∘ with the level ground.
1. The height of the kite is Options: A) 50√3 m; B) 100√3 m; C) 25 m; D) 50 m
2. If the string made 60^∘ with the ground instead, the height would be Options: A) 75 m; B) 50 m; C) 100√3 m; D) 50√3 m
3. To fly at a height of 50 m with the string at 45^∘, the string must be Options: A) 100 m; B) 50 m; C) 50√2 m; D) 25√2 m
Chapter 9: Some Applications of Trigonometry · Angle of depression
Three board-style questions on Some Applications of Trigonometry (CBSE Class 10 Mathematics). No calculator. From the top of a cliff 75 m high, the angle of depression of a boat is 30^∘. Later it is 60^∘.
1. At first the boat is this far from the foot of the cliff: Options: A) 150 m; B) 75 m; C) 25√3 m; D) 75√3 m
2. Later the boat is this far from the foot of the cliff: Options: A) 25 m; B) 50 m; C) 25√3 m; D) 75√3 m
3. The distance the boat moved towards the cliff is Options: A) 50 m; B) 100√3 m; C) 75 m; D) 50√3 m
Chapter 9: Some Applications of Trigonometry · Walking towards a tower
Three board-style questions on Some Applications of Trigonometry (CBSE Class 10 Mathematics). No calculator. The angle of elevation of the top of a tower from a point P on the ground is 30^∘. After walking 20 m from P straight towards the tower, it is 60^∘.
1. The distance of the second point from the foot of the tower is Options: A) 10√3 m; B) 10 m; C) 30 m; D) 20 m
2. The height of the tower is Options: A) 20√3 m; B) 10 m; C) 10/(√3) m; D) 10√3 m
3. Using √3 = 1.73, the height of the tower is Options: A) 34.6 m; B) 5.77 m; C) 1.73 m; D) 17.3 m
Chapter 9: Some Applications of Trigonometry · A ladder
Three board-style questions on Some Applications of Trigonometry (CBSE Class 10 Mathematics). No calculator. A ladder leans against a vertical wall, making an angle of 60^∘ with the level ground. Its foot is 2.5 m from the wall.
1. The length of the ladder is Options: A) 5 m; B) 2.5√3 m; C) 1.25 m; D) 5√3 m
2. The height up the wall that the ladder reaches is Options: A) 2.5/(√3) m; B) 5√3 m; C) 5 m; D) 2.5√3 m
3. The foot is moved so that the same ladder makes 45^∘ with the ground. It now reaches a height of Options: A) 2.5 m; B) 2.5√3 m; C) 5√2 m; D) (5√2)/2 m
Chapter 9: Some Applications of Trigonometry · A broken tree
Three board-style questions on Some Applications of Trigonometry (CBSE Class 10 Mathematics). No calculator. A storm breaks a tree. The top part bends over without separating, and its top touches the ground 12 m from the foot of the tree, making an angle of 30^∘ with the ground.
1. The height of the part still standing is Options: A) 12√3 m; B) 6 m; C) 8√3 m; D) 4√3 m
2. The length of the broken part is Options: A) 4√3 m; B) 24 m; C) 8√3 m; D) 12 m
3. The original height of the tree was Options: A) 10√3 m; B) 16√3 m; C) 12√3 m; D) (12 + 4√3) m
Chapter 9: Some Applications of Trigonometry · Building and tower
Three board-style questions on Some Applications of Trigonometry (CBSE Class 10 Mathematics). No calculator. From the top of a building 20 m high, the angle of elevation of the top of a tower is 45^∘ and the angle of depression of its foot is 30^∘. Both stand on level ground.
1. The distance between the building and the tower is Options: A) 20/(√3) m; B) 40 m; C) 20√3 m; D) 20 m
2. The height of the tower is Options: A) 20(√3 - 1) m; B) 20(1 + √3) m; C) 20√3 m; D) 40 m
3. Using √3 = 1.73, the height of the tower is Options: A) 34.6 m; B) 54.6 m; C) 14.6 m; D) 60 m
Chapter 9: Some Applications of Trigonometry · Poles across a road
Three board-style questions on Some Applications of Trigonometry (CBSE Class 10 Mathematics). No calculator. Two poles of equal height stand on opposite sides of a straight road 80 m wide. From a point on the road between them, the angles of elevation of their tops are 60^∘ and 30^∘.
1. The point is this far from the pole whose top has elevation 60^∘: Options: A) 40 m; B) 20 m; C) 20√3 m; D) 60 m
2. The height of each pole is Options: A) 40 m; B) 20√3 m; C) 20/(√3) m; D) 60√3 m
3. In the following question, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option. Assertion (A): As you walk towards a vertical tower on level ground, the angle of elevation of its top increases. Reason (R): tanθ increases as θ increases from 0^∘ to 90^∘. Options: A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).; B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).; C) Assertion (A) is true but Reason (R) is false.; D) Assertion (A) is false but Reason (R) is true.
Chapter 9: Some Applications of Trigonometry · Angle of elevation
Three board-style questions on Some Applications of Trigonometry (CBSE Class 10 Mathematics). No calculator. From a point on level ground 30 m from the foot of a vertical tower, the angle of elevation of its top is 60^∘.
1. The height of the tower is Options: A) 10√3 m; B) 30√3 m; C) 60 m; D) 15 m
2. The distance from the point to the top of the tower is Options: A) 20√3 m; B) 45 m; C) 60 m; D) 30√3 m
3. From how far away from the foot would the angle of elevation of the top be 45^∘? Options: A) 30 m; B) 60 m; C) 10√3 m; D) 30√3 m

Chapter 10: Circles

Chapter 10: Circles
Three board-style questions on Circles (CBSE Class 10 Mathematics). No calculator.
1. The number of tangents to a circle that are parallel to a given secant is Options: A) 1; B) 2; C) infinitely many; D) 0
2. The common point of a tangent and a circle is called the Options: A) centre; B) point of contact; C) end of a secant; D) chord point
3. The number of tangents that can be drawn to a circle from a point inside it is Options: A) 0; B) 1; C) 2; D) infinitely many
Chapter 10: Circles · Quadrilateral around a circle
Three board-style questions on Circles (CBSE Class 10 Mathematics). No calculator. A quadrilateral ABCD is drawn so that each of its sides touches a circle.
1. If AB = 7 cm, BC = 9 cm and CD = 8 cm, then AD equals Options: A) 10 cm; B) 8 cm; C) 6 cm; D) 7 cm
2. The perimeter of ABCD is then Options: A) 24 cm; B) 15 cm; C) 32 cm; D) 30 cm
3. A parallelogram whose four sides all touch a circle must be a Options: A) rectangle; B) square; C) trapezium; D) rhombus
Chapter 10: Circles · Concentric circles
Three board-style questions on Circles (CBSE Class 10 Mathematics). No calculator.
1. Two concentric circles have radii 5 cm and 3 cm. A chord of the larger circle touches the smaller circle. Its length is Options: A) 4 cm; B) 8 cm; C) 6 cm; D) 2√34 cm
2. For concentric circles of radii 13 cm and 5 cm, such a chord has length Options: A) 24 cm; B) 16 cm; C) 12 cm; D) 18 cm
3. A chord of length 16 cm of a circle of radius 10 cm touches a smaller concentric circle. The smaller radius is Options: A) 2√41 cm; B) 6 cm; C) 8 cm; D) 4 cm
Chapter 10: Circles · Triangle around a circle
Three board-style questions on Circles (CBSE Class 10 Mathematics). No calculator. A circle touches the sides BC, CA and AB of △ ABC at D, E and F. AF = 4 cm, BD = 6 cm and CE = 8 cm.
1. AB equals Options: A) 12 cm; B) 10 cm; C) 14 cm; D) 8 cm
2. BC equals Options: A) 10 cm; B) 18 cm; C) 14 cm; D) 12 cm
3. The perimeter of △ ABC is Options: A) 32 cm; B) 40 cm; C) 36 cm; D) 18 cm
Chapter 10: Circles · Tangents meeting at 60 degrees
Three board-style questions on Circles (CBSE Class 10 Mathematics). No calculator. PA and PB are tangents from P to a circle with centre O and radius 6 cm, and ∠ APB = 60^∘.
1. OP equals Options: A) 6√2 cm; B) 9 cm; C) 12 cm; D) 6√3 cm
2. PA equals Options: A) 6 cm; B) 12 cm; C) 2√3 cm; D) 6√3 cm
3. ∠ AOB equals Options: A) 150^∘; B) 90^∘; C) 60^∘; D) 120^∘
Chapter 10: Circles · Tangent and radius
Three board-style questions on Circles (CBSE Class 10 Mathematics). No calculator.
1. In the following question, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option. Assertion (A): PA and PB are tangents from P to a circle with centre O and ∠ APB = 80^∘. Then ∠ AOB = 100^∘. Reason (R): The tangent at any point of a circle is perpendicular to the radius through the point of contact. Options: A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).; B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).; C) Assertion (A) is true but Reason (R) is false.; D) Assertion (A) is false but Reason (R) is true.
2. The tangent from P touches a circle with centre O at Q. If OP = 25 cm and PQ = 24 cm, the radius is Options: A) 12 cm; B) 49 cm; C) 1 cm; D) 7 cm
3. A tangent at Q meets a line through the centre O at P, with ∠ POQ = 60^∘. If the radius is 7 cm, PQ equals Options: A) 14 cm; B) 7/(√3) cm; C) 7√3 cm; D) 7√2 cm
Chapter 10: Circles · Incircle of a right triangle
Three board-style questions on Circles (CBSE Class 10 Mathematics). No calculator. A circle is inscribed in △ ABC with ∠ C = 90^∘, CA = 6 cm, CB = 8 cm and AB = 10 cm. The tangent lengths from A, B and C are x, y and z.
1. x + y + z equals Options: A) 14; B) 24; C) 12; D) 10
2. The radius of the circle is Options: A) 4 cm; B) 2.4 cm; C) 2 cm; D) 3 cm
3. The tangent length from B is Options: A) 4 cm; B) 8 cm; C) 2 cm; D) 6 cm
Chapter 10: Circles · Length of a tangent
Three board-style questions on Circles (CBSE Class 10 Mathematics). No calculator. PT and PS are tangents from an external point P to a circle with centre O and radius 5 cm, touching it at T and S. OP = 13 cm.
1. ∠ OTP equals Options: A) 60^∘; B) 90^∘; C) 180^∘; D) 45^∘
2. PT equals Options: A) √194 cm; B) 12 cm; C) 8 cm; D) 18 cm
3. PS equals Options: A) 12 cm; B) 13 cm; C) 24 cm; D) 5 cm
Chapter 10: Circles · Angles with tangents
Three board-style questions on Circles (CBSE Class 10 Mathematics). No calculator. PT and PS are tangents from P to a circle with centre O, and ∠ TPS = 70^∘.
1. ∠ TOS equals Options: A) 70^∘; B) 140^∘; C) 110^∘; D) 90^∘
2. ∠ OPT equals Options: A) 20^∘; B) 35^∘; C) 70^∘; D) 55^∘
3. ∠ OTS equals Options: A) 35^∘; B) 55^∘; C) 45^∘; D) 70^∘

Chapter 11: Areas Related to Circles

Chapter 11: Areas Related to Circles
Three board-style questions on Areas Related to Circles (CBSE Class 10 Mathematics). No calculator.
1. The length of an arc of a circle of radius 21 cm subtending an angle of 60^∘ at the centre is (π=22/7) Options: A) 44 cm; B) 22 cm; C) 231 cm; D) 66 cm
2. The perimeter of a sector of radius r and central angle θ is Options: A) (θ)/360×2π r; B) 2r+(θ)/360×2π r; C) r+(θ)/360×2π r; D) 2r+(θ)/360×π r²
3. The area of a sector of angle 90^∘ of a circle of radius 14 cm is (π=22/7) Options: A) 154 cm²; B) 308 cm²; C) 44 cm²; D) 616 cm²
Chapter 11: Areas Related to Circles · Segment for 60 degrees
Three board-style questions on Areas Related to Circles (CBSE Class 10 Mathematics). No calculator. A chord AB of a circle with centre O and radius 6 cm makes ∠ AOB = 60^∘.
1. The area of the minor sector OAB is Options: A) 36π cm²; B) 12π cm²; C) 6π cm²; D) 3π cm²
2. The area of △ OAB is Options: A) 9√3 cm²; B) 18 cm²; C) 18√3 cm²; D) 36√3 cm²
3. The area of the major sector is Options: A) 24π cm²; B) 36π cm²; C) 30π cm²; D) 6π cm²
Chapter 11: Areas Related to Circles · Segment for 120 degrees
Three board-style questions on Areas Related to Circles (CBSE Class 10 Mathematics). No calculator. A chord AB of a circle with centre O and radius 12 cm makes ∠ AOB = 120^∘. M is the foot of the perpendicular from O to AB.
1. The length of the chord AB is Options: A) 24√3 cm; B) 12√3 cm; C) 6√3 cm; D) 12 cm
2. The area of △ OAB is Options: A) 36√3 cm²; B) 18√3 cm²; C) 72√3 cm²; D) 72 cm²
3. The area of the minor segment is Options: A) (144π - 36√3) cm²; B) (48π + 36√3) cm²; C) (48π - 36√3) cm²; D) (48π - 72√3) cm²
Chapter 11: Areas Related to Circles · Arc, angle and area
Three board-style questions on Areas Related to Circles (CBSE Class 10 Mathematics). No calculator. A sector of a circle of radius 9 cm has an arc of length 6π cm.
1. The central angle of the sector is Options: A) 120^∘; B) 240^∘; C) 60^∘; D) 90^∘
2. The area of the sector is Options: A) 54π cm²; B) 27π cm²; C) 81π cm²; D) 18π cm²
3. If the radius of a sector is doubled and its angle is halved, its area is multiplied by Options: A) 2; B) 1; C) 4; D) 1/2
Chapter 11: Areas Related to Circles · Quadrants in a square
Three board-style questions on Areas Related to Circles (CBSE Class 10 Mathematics). No calculator. ABCD is a square of side 14 cm. With each vertex as centre, a quadrant of radius 7 cm is drawn inside the square. Take π = 22/7.
1. The area of one quadrant is Options: A) 49 cm²; B) 154 cm²; C) 38.5 cm²; D) 77 cm²
2. The total area of the four quadrants is Options: A) 42 cm²; B) 154 cm²; C) 196 cm²; D) 616 cm²
3. The area of the square not covered by the quadrants is Options: A) 49 cm²; B) 42 cm²; C) 154 cm²; D) 56 cm²
Chapter 11: Areas Related to Circles · Sectors, wheels and rings
Three board-style questions on Areas Related to Circles (CBSE Class 10 Mathematics). No calculator.
1. In the following question, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option. Assertion (A): The area of a sector of angle 90^∘ of a circle is one quarter of the area of the circle. Reason (R): The area of a sector of angle θ of a circle of radius r is (θ)/(360^∘) × π r^2. Options: A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).; B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).; C) Assertion (A) is true but Reason (R) is false.; D) Assertion (A) is false but Reason (R) is true.
2. A wheel has diameter 70 cm. Taking π = 22/7, the number of complete turns it makes in rolling 22 km is Options: A) 100000; B) 10000; C) 5000; D) 1000
3. The area between two concentric circles of radii 10 cm and 4 cm is Options: A) 6π cm²; B) 36π cm²; C) 84π cm²; D) 116π cm²
Chapter 11: Areas Related to Circles · Sector of 90 degrees
Three board-style questions on Areas Related to Circles (CBSE Class 10 Mathematics). No calculator. A sector of a circle of radius 14 cm has central angle 90^∘.
1. Its area is Options: A) 14π cm²; B) 49π cm²; C) 196π cm²; D) 98π cm²
2. The length of its arc is Options: A) 7π cm; B) 28π cm; C) (7π)/2 cm; D) 14π cm
3. Taking π = 22/7, the perimeter of the sector is Options: A) 36 cm; B) 44 cm; C) 50 cm; D) 22 cm
Chapter 11: Areas Related to Circles · A clock's minute hand
Three board-style questions on Areas Related to Circles (CBSE Class 10 Mathematics). No calculator. The minute hand of a clock is 21 cm long. Take π = 22/7.
1. In 20 minutes the minute hand turns through Options: A) 90^∘; B) 200^∘; C) 60^∘; D) 120^∘
2. The area swept by the minute hand in 20 minutes is Options: A) 231 cm²; B) 1386 cm²; C) 154 cm²; D) 462 cm²
3. The distance moved by the tip of the minute hand in 20 minutes is Options: A) 132 cm; B) 22 cm; C) 66 cm; D) 44 cm
Chapter 11: Areas Related to Circles · Segment for a right angle
Three board-style questions on Areas Related to Circles (CBSE Class 10 Mathematics). No calculator. A chord AB of a circle with centre O and radius 10 cm makes ∠ AOB = 90^∘.
1. The area of sector OAB is Options: A) 5π cm²; B) 25π cm²; C) 50π cm²; D) 100π cm²
2. The area of △ OAB is Options: A) 25√3 cm²; B) 100 cm²; C) 25 cm²; D) 50 cm²
3. Taking π = 3.14, the area of the minor segment is Options: A) 50 cm²; B) 28.5 cm²; C) 78.5 cm²; D) 21.5 cm²

More Question of the Day puzzles

Other chapters: Chapters 1–4 · Chapters 5–8 · Chapters 9–11 · Chapters 12–14. See all CBSE Maths daily and weekly questions.