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CBSE, Class 10, NCERT

MCQ Questions for Class 10 Maths Circles

Free PDF Download of CBSE Class 10 Maths Chapter 10 Circles Multiple Choice Questions with Answers. MCQ Questions for Class 10 Maths with Answers was Prepared Based on Latest Exam Pattern. Students can solve NCERT Class 10 Maths Circles MCQs with Answers to know their preparation level.

Class 10 Maths MCQs Chapter 10 Circles

Circle Multiple Choice Question 1. The distance between two parallel tangents of acircle of radius 4 cm is
(a) 2 cm
(b) 4 cm
(c) 6 cm
(d) 8 cm

Answer/ Explanation

Answer: d
Explaination:
MCQ Questions for Class 10 Maths Circles with Answers 3
Reason: Here radius, r = 4 cm
Required distance,
AB = OA + OB
= r + r = 2r = 2×4 = 8 cm

2. In the given figure, if ZRPS = 25°, the value of ZROS is
MCQ Questions for Class 10 Maths Circles with Answers 1
(a) 135°
(b) 145°
(c) 165°
(d) 155°

Answer/ Explanation

 

Circles Class 10 MCQ With Answer: dExplaination: Reason: Since OR ⊥ PR and OS ⊥ PS
∴ ∠ORP = ∠OSP = 90°
In □ ORPS, ∠ROS + ∠ORP + ∠RPS + ∠OSP = 360°
∠ROS + 90° + 25° + 90° = 360°
∠ROS = 360° – 205° = 155°

3. A tangent is drawn from a point at a distance of 17 cm of circle C(0, r) of radius 8 cm. The length of its tangent is
(a) 5 cm
(b) 9 cm
(c) 15 cm
(d) 23 cm

Answer/ Explanation

Answer: c
Explaination:
MCQ Questions for Class 10 Maths Circles with Answers 4
Reason: In rt ∆OAP, AP² + OA² = OP²
⇒ AP² + (8)² = (17)² => AP² + 64 = 289
⇒ AP² = 289 – 64 = 225
∴ AP = √225 = 15 cm

4. The length of tangents drawn from an external point to the circle
(a) are equal
(b) are not equal
(c) sometimes are equal
(d) are not defined

Answer/ Explanation

Answer: a
Explaination: Reason: Since the length of tangents drawn from an external point to a circle are equal.

5. Number of tangents drawn at a point of the , circle is/are
(a) one
(b) two
(c) none
(d) infinite

Answer/ Explanation

Answer: a
Explaination: Reason: There is only one tangent at a point of the circle.

6. The tangents drawn at the extremities of the diameter of a circle are
(a) perpendicular
(b) parallel
(c) equal
(d) none of these

Answer/ Explanation

Answer: b
Explaination:
MCQ Questions for Class 10 Maths Circles with Answers 5
Reason: Since OP ⊥ AB and OQ ⊥ CD
∴ Z1 = 90° and Z2 = 90°
⇒ ∠1 = Z2, which are alternate angles.
∴ AB || CD

7. Tangents from an external point to a circle are
(a) equal
(b) not equal
(c) parallel
(d) perpendicular

Answer/ Explanation

 

MCQs of Maths for Class 10 With Answer: aExplaination: Reason: Tangents from external points to a circle are equal.

8. The length of a tangent drawn from a point at a distance of 10 cm of circle is 8 cm. The radius of the circle is
(a) 4 cm
(b) 5 cm
(c) 6 cm
(d) 7 cm

Answer/ Explanation

Answer: c
Explaination:
MCQ Questions for Class 10 Maths Circles with Answers 6
Reason: In rt. AOAP, we have
OA² + AP² = OP²
⇒ OA² + (8)² = (10)2
⇒ OA² + 64 = 100
⇒ OA² = 100 – 64 = 36
∴ OA = √36 = 6 cm

MCQ Questions on Circles for Class 10 Question 9. In given figure, CP and CQ are tangents to a circle with centre O. ARB is another tangent touching the circle at R. If CP = 11 cm and BC = 6 cm then the length of BR is
MCQ Questions for Class 10 Maths Circles with Answers 2
(a) 6 cm
(b) 5 cm
(c) 4 cm
(d) 3 cm

Answer/ Explanation

Answer: b
Explaination: Reason: Since
BQ = BR …(i) [∵ Tangents drawn from external points are equal]
CQ = CP …[Using (i)]
BC + BQ = 11
⇒ 6 + BR = 11
⇒ BR = 11 – 6 = 5 cm

10. From a point P which is at a distance of 13 cm from the centre O of a circle of radius 5 cm, the pair of tangents PQ and PR to the circle are drawn. Then the area of the quadrilateral PQOR is
(a) 60 cm²
(b) 65 cm²
(c) 30 cm²
(d) 32.5 cm²

Answer/ Explanation

Answer: a
Explaination:
MCQ Questions for Class 10 Maths Circles with Answers 10
Reason: OP² = OQ² + PQ²
169 = 25 + PQ²
PQ² = 144
PQ = 12
Area PQOR = ar (AOPQ) + ar (AOPR)
= 12 × 12 × 5 + 12 × 12 × 5 = 60 cm²

MCQ Questions for Class 10 Maths Question 11. In the given figure, AB and AC are tangents to the circle with centre O such that ∠BAC = 40°, then ∠BOC is equal to [AI2011]
MCQ Questions for Class 10 Maths Circles with Answers 8
(a) 40°
(b) 50°
(c) 140°
(d) 150°

Answer/ Explanation

Answer: c
Explaination:
(c) In quadrilateral ABOC
∠ABO + ∠BOC + ∠OCA + ∠BAC = 360°
⇒ 90° + ∠BOC + 90° + 40° = 360°
⇒ ∠BOC = 360° – 220° = 140°

12. In the given figure, point P is 26 cm away from the centre O of a circle and the length PT of the tangent drawn from P to the circle is 24 cm. Then the radius of the circle is [Foreign 2011]
MCQ Questions for Class 10 Maths Circles with Answers 9
(a) 25 cm
(b) 26 cm
(c) 24 cm
(d) 10 cm

Answer/ Explanation

Answer: d
Explaination: (d) v OT is radius and PT is tangent
MCQ Questions for Class 10 Maths Circles with Answers 21
∴ OT ⊥ PT
Now, in AOTP,
⇒ OP² = PT² + OT²
⇒ 26² = 24² + OT²
⇒ 676 – 576 = OT²
⇒ 100 = OT²
⇒ 10 cm = OT

13. A line through point of contact and passing through centre of circle is known as
(a) tangent
(b) chord
(c) normal
(d) segment

Answer/ Explanation

Answer: c
Explaination: (c) normal

Maths MCQ for Class 10 Cbse With Answers Pdf Question 14. C (O, r1) and C(O, r2) are two concentric circles with r1 > r2 AB is a chord of C(O, r1) touching C(O, r,2) at C then
(a) AB = r1
(b) AB = r2
(c) AC = BC
(d) AB = r1 + r2

Answer/ Explanation

Answer: c
Explaination:
(c) ∵ AB touches
C(0, r<sub>2</sub>)
∴ OC ⊥ AB
MCQ Questions for Class 10 Maths Circles with Answers 22
Also, perpendicular from the centre to a chord bisects the chord.
∴ AC = BC

15. Two parallel lines touch the circle at
points A and B respectively. If area of the circle is 25 n cm2, then AB is equal to
(a) 5 cm
(b) 8 cm
(c) 10 cm
(d) 25 cm

Answer/ Explanation

Answer: c
Explaination:
(c) Let radius of circle = R
∴ πR² = 25π
⇒ R = 5 cm
∴ Distance between two parallel tangents = diameter = 2 × 5 = 10 cm.

MCQ Questions for Class 10 Maths Circles Question 16. From a point P which is at a distance of 13 cm from the centre O of a circle of radius 5 cm, the pair of tangents PQ and PR to the circle are drawn. Then the area of the quadrilateral PQOR is [NCERT Exemplar Problems]
(a) 60 cm²
(b) 65 cm²
(c) 30 cm²
(d) 32.5 cm²

Answer/ Explanation

Answer: a
Explaination:
MCQ Questions for Class 10 Maths Circles with Answers 23

17. In figure AT is a tangent to the circle with centre O such that OT = 4 cm and ∠OTA = 30°. Then AT is equal to [NCERT Exemplar Problems]
(a) 4 cm
(b) 2 cm
(c) 2√3 cm
(d) 4√3 cm
MCQ Questions for Class 10 Maths Circles with Answers 10

Answer/ Explanation

Answer: c
Explaination:
MCQ Questions for Class 10 Maths Circles with Answers 24

18. In figure if O is centre of a circle, PQ is a chord and the tangent PR at P makes an angle of 50° with PQ, then ∠POQ is equal to [NCERT Exemplar Problems]
MCQ Questions for Class 10 Maths Circles with Answers 11
(a) 100°
(b) 80°
(c) 90°
(d) 75°

Answer/ Explanation

Answer: a
Explaination:
(a) OP ⊥ PR [Y Tangent and radius are ⊥ to each other at the point of contact]
∠OPQ = 90° – 50° = 40°
OP = OQ [Radii]
∴ ∠OPQ = ∠OQP = 40°
In ∆OPQ,
⇒ ∠POQ + ∠OPQ + ∠OQP = 180°
⇒ ∠POQ + 40° + 40° = 180°
∠POQ = 180° – 80° = 100°.

19. Match the column:

(1) The tangent at any point of a circle is … (A) known as tangent to the circle
(2) The line containing the radius through the point of contact is … (B) to the radius through the point of
(3) The lengths of tangents drawn from an external point to a circle are… (C) called the ‘normal’ to circle
(4) When two end points of the corresponding chord of a  secant coincide, it is … (D) equal

(a) 1 → A, 2 → B, 3 → C, 4 → D
(b) 1 → B, 2 → A, 3 → D, 4 → C
(c) 1 → D, 2 → A, 3 → C, 4 → B
(d) 1 → B, 2 → C, 3 → D, 4 → A

Answer/ Explanation

Answer:
Explaination: Properties of circle.

Questions on Circles for Class 10 Question 20. In figure, O is the centre of a circle, AB is a chord and AT is the tangent at A. If ∠AOB = 100°, then ∠BAT is equal to [Delhi 2011]
MCQ Questions for Class 10 Maths Circles with Answers 12
(a) 100°
(b) 40°
(c) 50°
(d) 90°

Answer/ Explanation

Answer: c
Explaination:
(c) ∠AOB = 100°
∠OAB = ∠OBA (∵ OA and OB are radii)
Now, in ∆AOB,
∠AOB + ∠OAB + ∠OBA = 180°
(Angle sum property of A)
⇒ 100° + x + x = 180° [Let ∠OAB = ∠OBA = x]
⇒ 2x = 180° – 100°
⇒ 2x = 80°
⇒ x = 40°
Also, ∠OAB + ∠BAT = 90°
[∵ OA is radius and TA is tangent at A]
⇒ 40° + ZBAT = 90°
⇒ ∠BAT = 50°

21. In the figure PA and PB are tangents to the circle with centre O. If ∠APB = 60°, then ∠OAB is [Delhi 2011]
MCQ Questions for Class 10 Maths Circles with Answers 13
(a) 30°
(b) 60°
(c) 90°
(d) 15°

Answer/ Explanation

MCQ Questions for Class 10 Maths With Answer: a
Explaination:
(a) Given ∠APB = 60°
∵ ∠APB + ∠PAB + ∠PBA = 180°
⇒ APB + x + x = 180°
[∵ PA = PB ∴ ∠PAB = ∠PBA = x (say)]
⇒ 60° + 2x = 180°
⇒ 2x = 180° – 60°
⇒ 2x = 120°
⇒ x = 120°2 = 60°
Also, ∠OAP = 90°
⇒ ∠OAB + ∠PAB = 90°
⇒ ∠OAB + 60°= 90°
⇒ ∠OAB = 30°

Maths Multiple Choice Questions With Answers for Class 10 Question 22. In the given figure, TP and TQ are two tangents to a circle with centre O, such that ∠POQ = 110°. Then ∠PTQ is equal to [Foreign 2011]
Multiple Choice Questions on Circles
(a) 55°
(b) 70°
(c) 110°
(d) 90°

Answer/ Explanation

Answer: b
Explaination:
(b) In quadrilateral POQT,
∠PTQ + ∠TPO + ∠TQO + ∠POQ
= 360°
⇒ ∠PTQ + 90° + 90° + 110° = 360°
⇒ ∠PTQ + 290° = 360°
⇒ ∠PTQ = 360° – 290° = 70°

23. Infigure,PQandPRaretangentstoacirclewith centreA. If ∠QPA=27°, then ∠QAR equals to [Foreign 2012]
MCQ Questions for Class 10 Maths Circles with Answers 15
(a) 63°
(b) 153°
(c) 110°
(d) 90°

Answer/ Explanation

Answer: c
Explaination:
(c) ∠QPA = ∠RPA
[∵ ∆AQP ≅ ∆ARP (RHS congruence rule)]
⇒ ∠RPA = 27°
∴ ∠QPR = ∠QPA + ∠RPA
= 27° + 27° = 54°
MCQ Questions for Class 10 Maths Circles with Answers 27
Now,
∠QAR + ∠AQP + ∠ARP + ∠QPR = 360°
⇒ ∠QAR = 90° + 90° + 54° = 360°
⇒ ∠QAR = 360° – 234° = 126°

Circles MCQ Class 10 Question 24. In figure if PQR is the tangent to a circle at Q whose centre is O, AB is a chord parallel to PR and ∠BQR = 70°, then ∠AQB is equal to [NCERT Exemplar Problems]
MCQ Questions for Class 10 Maths Circles with Answers 16
(a) 20°
(b) 40°
(c) 35°
(d) 45°

Answer/ Explanation

Answer:
Explaination:
(b) AB || PR
∴ ∠ABQ =∠BQR
[Alternate interior angles]
⇒ ∠ABQ = 70°
Also, ∠BQR = ∠BAQ [Angles in alternate segment]
⇒ ∠BAQ = 70°
In ∆AQB,
∠BAQ + ∠ABQ + ∠AQB = 180°
⇒ 70° + 70° + ∠AQB = 180°
⇒ ∠AQB = 180° – 140° = 40°.

25. The common point of the tangent and the circle is called _____ .

Answer/ Explanation

Answer:
Explaination: point of contact

26. Two concentric circles are of radii 13 cm and 5 cm. The length of the chord of larger circle which touches the smaller circle is _____ .

Answer/ Explanation

Answer:
Explaination: 24 cm. Hint: ∵ AB touches the smaller circle
MCQ Questions for Class 10 Maths Circles with Answers 33
∴ OC ⊥ AB and hence AC = BC
In right ∆OCA,
OA² = OC² + AC²
⇒ AC²= 13² – 5²
⇒ AC = 12
∴ AB = 2 × 12 = 24 cm.

MCQ on Circles Class 10 Question 27. A quadrilateral ABCD is drawn to circumscribe a circle. If AB =12 cm, BC = 15 cm and CD = 14 cm, then AD is equal to _____ .

Answer/ Explanation

Answer:
Explaination: 11 cm. Hint: AB + CD = BC + AD
MCQ Questions for Class 10 Maths Circles with Answers 26
⇒ 12+ 14= 15+ AD
⇒ AD =11 cm.

28. Number of tangents to a circle which are parallel to a secant is ____ .

Answer/ Explanation

Answer:
Explaination: 2

Circle Objective Question 29. A tangent PQ at a point P of a circle of radius 7 cm meets a line through centre O at a point Q so that OQ = 25 cm length PQ is ____ .

Answer/ Explanation

Answer: 24 cm
Explaination:
MCQ Questions for Class 10 Maths Circles with Answers 28
24 cm.
Hint: PQ² = OQ² – OP² = 252²- 7²
⇒ PQ = 24 cm.

30. If the angle between two tangents drawn from an external point P to a circle of radius a and centre O, is 60°, then find the length of OP. [Delhi 2017]

Answer/ Explanation

Answer:
Explaination:
MCQ Questions for Class 10 Maths Circles with Answers 29

31. In the given fig., there are two concentric circles with centre O. PRT and PQS are tangents to the inner circle from a point P lying on the outer circle. If PR = 5 cm, find the length of PS. [Delhi 2017 (C)]
MCQ Questions for Class 10 Maths Circles with Answers 17

Answer/ Explanation

Circle MCQ With Answer:
Explanation:
PR and PQ are tangents to the circle from common external point P.

MCQ Questions for Class 10 Maths Circles with Answers 30
∴ PR = PQ
∴ PQ = 5 cm (∵ PR = 5 cm)
PS = 2PQ (∵ OQ ⊥ PS)
= 2 × 5 = 10 cm

Circle MCQ Pdf Question 32. In the given Fig., O is the centre of the circle, PQ is a chord and PT is tangent to the circle at P. If ∠POQ = 70°, find ∠TPQ. [AI 2017 (C)]
MCQ Questions for Class 10 Maths Circles with Answers 18

Answer/ Explanation

MCQ on Circles With Answer:
Explanation:
Given: O is centre of the circle, PQ is chord and PT is tangent at P.
To find: ∠TPQ
Solution: In ∆OPQ
∠POQ + ∠OPQ + ∠OQP = 180°
⇒ 70° + ∠OPQ + ∠OPQ = 180°
(∵ OP = OQ, radii of the circle)
⇒ 70° + 2∠OPQ = 180°
⇒ 2∠OPQ = 110°
⇒ ∠OPQ = 55°
OP is perpendicular to the tangent at P.
∴ ∠OPT = 90°
⇒ ∠OPQ + ∠TPQ = 90°
⇒ 55° + ∠TPQ = 90°
⇒ ∠TPQ = 90° – 55°
∠TPQ = 35°

33. What is the distance between two parallel tangents of a circle of radius 7 cm?

Answer/ Explanation

Answer:
Explaination:
Two parallel tangents of a circle can be drawn only at the end points of the diameter
MCQ Questions for Class 10 Maths Circles with Answers 31
⇒ l<sub>1</sub> || l<sub>2</sub>
⇒ Distance between l<sub>1</sub> and l<sub>2</sub> = AB
= Diameter of the circle
= 2 × r = 2 × 7 cm = 14 cm

MCQ on Circle Question 34. In the given figure, find ∠QSR.
MCQ Questions for Class 10 Maths Circles with Answers 19

Answer/ Explanation

Answer:
Explaination:
Given: PQ and PR are tangents to a circle with centre O and ∠QPR = 50°.
To find: ∠QSR
∠QOR + ∠QPR =180°
⇒ ∠QOR +50° = 180°
⇒ ∠QOR = 130°
⇒ ∠QSR = 12 ∠QOR [Degree measure theorem]
⇒ ∠QSR =12 × 130° = 65°

Circle MCQ Question 35. In the given figure, AB, AC and AD are tangents. If AB = 5 cm, find AD.
MCQ Questions for Class 10 Maths Circles with Answers 20

Answer/ Explanation

Answer:
Explaination:
Given: AB, AC and AD are tangents. AB = 5 cm.
MCQ Questions for Class 10 Maths Circles with Answers 32
To find: AD
Sol. AB and AC are tangents from the same point to the circle with centre O.
⇒ AB = AC …(i)
(Length of the tangents from the same external point are equal).
AC and AD are tangents from the same point to the circle with centre O.
⇒ AC = AD …(ii)
(Length of the tangents from the same external point are equal)
From (i) and (ii)
∵ AB = AC = AD = 5 cm

We hope the given MCQ Questions for Class 10 Maths Circles with Answers will help you. If you have any query regarding CBSE Class 10 Maths Chapter 10 Circles Multiple Choice Questions with Answers, drop a comment below and we will get back to you at the earliest.

CBSE, Class 10, NCERT

MCQ Questions for Class 10 Maths Application of Trigonometry with Answers

Free PDF Download of CBSE Class 10 Maths Chapter 9 Application of Trigonometry Multiple Choice Questions with Answers. MCQ Questions for Class 10 Maths with Answers was Prepared Based on Latest Exam Pattern. Students can solve NCERT Class 10 Maths Application of Trigonometry MCQs with Answers to know their preparation level.

Class 10 Maths MCQs Chapter 9 Application of Trigonometry

MCQ On Application Of Trigonometry Class 10 Question 1. The shadow of a tower is equal to its height at 10-45 a.m. The sun’s altitude is
(a) 30°
(b) 45°
(c) 60°
(d) 90°

Answer/ Explanation

Answer: b
Explaination: Reason: Let the height of tower BC = rm and sun’s altitude = θ
Then Length of its shadow, AB = x m
MCQ Questions for Class 10 Maths Application of Trigonometry with Answers 9
In rt. ∆ABC, tan θ = BCAB = xx = 1
⇒ tan θ = tan 450
∴ θ = 45°

2. In given figure, the value of CE is
MCQ Questions for Class 10 Maths Application of Trigonometry with Answers 1
(a) 12 cm
(b) 6 cm
(c) 9 cm
(d) 6√3 cm

Answer/ Explanation

Answer: a
Explaination: Reason: In rt. ∆EBC, cos 60° = BCCE
⇒ 12 = 6CE
⇒ CE = 12 cm

MCQ Questions For Class 10 Maths Trigonometry Question 3. In given figure, the value of ZC is
MCQ Questions for Class 10 Maths Application of Trigonometry with Answers 2
(a) 90°
(b) 45°
(c) 30°
(d) 60°

Answer/ Explanation

Answer: d
Explaination: Reason: In rt. ∆ABC, cos C = BCAB = 714 = 12
⇒ cos C = cos 60°
∴ C = 60°

MCQ On Application Of Trigonometry Question 4. In given Fig., the angle of depression from the observing position D and E of the object at A are
MCQ Questions for Class 10 Maths Application of Trigonometry with Answers 3
(a) 60°, 60°
(b) 30°, 30°
(c) 30°, 60°
(d) 60°, 30°

Answer/ Explanation

Answer: c
Explaination:
MCQ Questions for Class 10 Maths Application of Trigonometry with Answers 10
Reason: ∵ APD, ∠1 = 90° – 60° = 30°
∴ APE, ∠2 = ∠EAB …[alt Zs]
∴ ∠2 = 60°
Hence the angles of depression at D and E are 30° and 60° respectively.

Some Applications Of Trigonometry Class 10 MCQ Question 5. In given figure, the length of AP is
MCQ Questions for Class 10 Maths Application of Trigonometry with Answers 4

Answer/ Explanation

Answer: b
Explaination:
MCQ Questions for Class 10 Maths Application of Trigonometry with Answers 11

MCQ NCERT Application Of Trigonometry Class 10 Question 6. In given figure, the value of AE is
MCQ Questions for Class 10 Maths Application of Trigonometry with Answers 5

Answer/ Explanation

Answer: a
Explaination: Reason: ∠AED = ∠EAB = 30°
MCQ Questions for Class 10 Maths Application of Trigonometry with Answers 12
In rt. ∆AED, sin 30° = ADAP
⇒ 12 = 45AE
⇒ AE = 90 cm

Trigonometry MCQ Class 10 Question 7. In given figure, AD = 4 cm, BD = 3 cm and CB = 12 cm. The value of tan θ is
MCQ Questions for Class 10 Maths Application of Trigonometry with Answers 6

Answer/ Explanation

Answer: c
Explaination: Reason: In rt ∆ADB,
AB² = AD² + BD² = (4)² + (3)² = 16 + 9 = 25
∴ AB = √25 = 5
∴ In rt ∆ABC, tan θ ABBC = 512

8. In figure given ABCD is a rectangle, the value of CE is
MCQ Questions for Class 10 Maths Application of Trigonometry with Answers 7
(a) 1 cm
(b) 2 cm
(c) 3 cm
(d) 4 cm

Answer/ Explanation

Answer: d
Explaination: Reason: Since ABCD is a rectangle
∴ BC = AD = 8 cm and B = 90°
In rt ∆CBE, cos 60° = CEBC
⇒ 12 = CE8
∴ CE = 82 = 4 cm

Trigonometry MCQ Questions Question 9. In given figure, ABCD is a || gm. The lenght of AP is
MCQ Questions for Class 10 Maths Application of Trigonometry with Answers 8
(a) 2 cm
(b) 4 cm
(c) 6 cm
(d) 8 cm

Answer/ Explanation

Answer: c
Explaination: Reason: Since ABCD is a || gm
∴ AD = BC = 4√3
In rt ∆APD, sin 60° = APAD
⇒ 3√2=AP43√
⇒ 2AP = 4 × 3 = 12
∴ AP = 6 cm

MCQ On Trigonometry For Class 10 With Solutions Question 10. When the length of shadow of a vertical pole is equal to √3 times of its height, the angle of elevation of the Sun’s altitude is
(a) 30°
(b) 45°
(c) 60°
(d) 15°

Answer/ Explanation

Answer: a
Explaination: Reason: Let the height of the vertical pole, BC = h m
∴ Shadow AB = √3 h m and the angle of elevation ZBAC = θ
MCQ Questions for Class 10 Maths Application of Trigonometry with Answers 13
In rt ∆ABC, tan θ = BCAB=h3√h=13√ = tan 30°
∴ θ = 30°
Hence the Sun’s altitude is 30°

MCQ Trigonometry Class 10 Question 11. The angle of elevation of top of a tower from a point on the ground, which is 30 m away from the foot of the tower is 30°. The length of the tower is
(a) √3 m
(b) 2√3 m
(c) 5√3m
(d) 10√3 m

Answer/ Explanation

Answer: d
Explaination:
MCQ Questions for Class 10 Maths Application of Trigonometry with Answers 14

MCQ Questions On Trigonometry For Class 10 Question 12. A plane is observed to be approaching the airport. It is at a distance of 12 km from the point of observation and makes an angle of elevation of 60°. The height above the ground of the plane is
(a) 6√3 m
(b) 4√3 m
(c) 3√3 m
(d) 2√3 m

Answer/ Explanation

Answer: a
Explaination:
MCQ Questions for Class 10 Maths Application of Trigonometry with Answers 15

Trigonometry Multiple Choice Questions And Answers Pdf Question 13. The upper part of a tree is broken by the wind and makes an angle of 30° with the ground. The distance from the foot of the tree to the point where the top touches the ground is 5 m. The height of the tree is
(a) 10√33 m
(b) 5√33 m
(c) √3 m
(d) √3/5 m

Answer/ Explanation

Answer: b
Explaination:
MCQ Questions for Class 10 Maths Application of Trigonometry with Answers 16

MCQ On Trigonometry 10th Question 14. The angles of elevation of the top of a rock from the top and foot of 100 m high tower are respectively 30° and 45°. The height of the rock is
(a) 50 m
(b) 150 m
(c) 5o√3m
(d) 50(3 + √3)

Answer

Answer: d

Trigonometry MCQs Question 15. The tops of two poles of height 20 m and 14 m are connected by a wire. If the wire makes an angle of 30° with horizontal, the length of the wire is
(a) 6 m
(b) 10 m
(c) 12 m
(d) 20 m

Answer

Answer: c

Trigonometry MCQ Questions For 10th Pdf Question 16. The angle of depression of a car, standing on the ground, from the top of a 75 m high tower, is 30°. The distance of the car from the base of the tower (in m) is:
(a) 25√3
(b) 50√3
(c) 75√3
(d) 150

Answer/Explanation

Answer: c
Explaination:
MCQ Questions for Class 10 Maths Application of Trigonometry with Answers 17

MCQ On Trigonometry Class 10 Question 17. A ladder 15 m long just reaches the top of a vertical wall. If the ladder makes an angle of 60° with the wall, then the height of the wall is
MCQ Questions for Class 10 Maths Application of Trigonometry with Answers 32

Answer/Explanation

Answer: b
Explaination:
MCQ Questions for Class 10 Maths Application of Trigonometry with Answers 18

MCQs On Trigonometry Question 18. The line drawn from the eye of an observer to the point in the object viewed by the observer is known as
(a) horizontal line
(b) vertical line
(c) line of sight
(d) transversal line

Answer

Answer: c

MCQ On Trigonometry Question Question 19. The tops of two poles of heights 20 m and 14 m are connected by a wire. If the wire makes an angle of 30° with the horizontal, then the length of the wire is
(a) 8 m
(b) 10 m
(c) 12 m
(d) 14 m

Answer/Explanation

Answer: c
Explaination:
MCQ Questions for Class 10 Maths Application of Trigonometry with Answers 19

Trigonometry MCQs With Answers Question 20. If two towers of heights h1 and h2 subtend angles of 60° and 30° respectively at the mid-point of the line joining their feet, then h1 : h2 =
(a) 1 : 2
(b) 1 : 3
(c) 2 : 1
(d) 3 : 1

Answer/Explanation

Answer: d
Explaination:
MCQ Questions for Class 10 Maths Application of Trigonometry with Answers 20
MCQ Questions for Class 10 Maths Application of Trigonometry with Answers 21

MCQ On Trigonometry For Class 10 Question 21. The angle of elevation of the top of a tower from a point 20 metres away from its base is 45°. The height of the tower is
(a) 10 m
(b) 20 m
(c) 30 m
(d) 20√3 m

Answer/Explanation

Answer: b
Explaination:
MCQ Questions for Class 10 Maths Application of Trigonometry with Answers 22

Maths Application Questions Question Question 22. Two poles are 25 m and 15 m high and the line joining their tops makes an angle of 45° with the horizontal. The distance between these poles is
(a) 5 m
(b) 8 m
(c) 9 m
(d) 10 m

Answer/Explanation

Answer: c
Explaination:
MCQ Questions for Class 10 Maths Application of Trigonometry with Answers 23
MCQ Questions for Class 10 Maths Application of Trigonometry with Answers 24

Multiple Choice Questions On Trigonometry Question 23. A portion of a 60 m long tree is broken by tornado and the top struck up the ground making an angle of 30° with the ground level. The height of the point where the tree is broken is equal to
(a) 30 m
(b) 35 m
(c) 40 m
(d) 20 m

Answer/Explanation

Answer:
Explaination:
MCQ Questions for Class 10 Maths Application of Trigonometry with Answers 25

Trigonometry Objective Questions For Class 10 Question 24. The angle of elevation of the top of a 15m high tower at a point 15m away from the base of the tower is ____ .

Answer/Explanation

Answer:
Explaination:
Hints:
∵ Height of tower = distance of point from the base
∴ Angle of elevation = 45°.

25. The ratio of the height of a tower and the length of its shadow on the ground is √3 : 1. What is the angle of elevation of the sun? [Delhi 2017]

Answer/Explanation

Answer:
Explaination:
MCQ Questions for Class 10 Maths Application of Trigonometry with Answers 26

26. An observer, 1.5 m tall, is 28.5 m away from a 30 m high tower. Determine the angle of elevation of the top of the tower from the eye of the observer. [Delhi 2017 (C)]

Answer/Explanation

Answer:
Explaination:
MCQ Questions for Class 10 Maths Application of Trigonometry with Answers 27
Here, AB = DM = 1.5 m
CM = CD – DM
= 30 – 1.5 = 28.5 m
Let 0 be the angle of elevation of the top of the tower from the eye of the observer.
∴ In ∆ACM
tan θ = CMAM=28.528.5
tan θ = 1
tan θ = tan 45°
θ = 45°

27. If a tower 30 m high, casts a shadow 10√3 m long on the ground, then what is the angle of elevation of the sun?
[AI 2017]

Answer/Explanation

Answer:
Explaination:
MCQ Questions for Class 10 Maths Application of Trigonometry with Answers 28

28. If two towers of height h1 and h2 subtends angles of 60° and 30° respectively at the mid points of line joining their feet, find h1 : h2

Answer/Explanation

Answer:
Explaination:
MCQ Questions for Class 10 Maths Application of Trigonometry with Answers 29
MCQ Questions for Class 10 Maths Application of Trigonometry with Answers 30

29. At some time of the day the length of the shadow of a tower is equal to its height. Find the sun’s altitude at that time. [Foreign 2011]

Answer/Explanation

Answer:
Explaination:
MCQ Questions for Class 10 Maths Application of Trigonometry with Answers 31

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