10th cbse Mathematics QUIZ — Introduction to Trigonometry 100 MCQS

Class 10 Mathematics — Introduction to Trigonometry

10 MCQ Tests × 10 Questions = 100 Questions

Practice questions based on the uploaded Trigonometry Introduction material.

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Test 1

Class 10 Mathematics — Introduction to Trigonometry

10 Questions

Q1. A tower is 25 m from a point on the ground and its angle of elevation is 45°. The height of the tower is:

A. 25√2 m B. 25√3 m C. 25 m D. 12.5 m

Q2. The length of a tower's shadow is √3 times its height. The angle of elevation of the sun is:

A. 45° B. 30° C. 60° D. 90°

Q3. A 150 m high tower has an angle of depression of 30° to a car. The distance of the car from the tower is:

A. 50√3 m B. 150√3 m C. 150√2 m D. 75 m

Useful Resource: Ravi Test Papers

Q4. A kite is 30 m above the ground and its string is 60 m long. The angle of elevation is:

A. 45° B. 30° C. 60° D. 90°

Q5. A ladder makes 60° with the ground and its foot is 2 m from the wall. The ladder length is:

A. 4/√3 m B. 4√3 m C. 2√2 m D. 4 m

Q6. If tan θ = 3/2, then the value of (4 sin θ + 3 cos θ)/(4 sin θ − 3 cos θ) is:

A. 7/√13 B. 1/√13 C. 3 D. Does not exist

Useful Resource: CBSE Class 10 Maths

Q7. If cot θ = 7/8, then ((1+sin θ)(1−sin θ))/((1+cos θ)(1−cos θ)) equals:

A. 8/7 B. 49/64 C. 7/8 D. 64/49

Q8. If tan x = 3 cot x and x is acute, then x is:

A. 45° B. 60° C. 30° D. 15°

Q9. If cos A = 4/5 and A is acute, tan A is:

A. 3/5 B. 3/4 C. 4/3 D. 5/3

Useful Resource: CBSE Class 10 Science

Q10. If tan θ = 8/15, then cosec θ is:

A. 17/8 B. 8/17 C. 17/15 D. 15/17

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Test 2

Class 10 Mathematics — Introduction to Trigonometry

10 Questions

Q1. If cos(α+β)=0 for acute α+β, then cos((α+β)/2) is:

A. 1/√2 B. 1/2 C. 0 D. √2

Q2. If 3cot θ = 4, then (5 sin θ + 3 cos θ)/(5 sin θ − 3 cos θ) equals:

A. 1/3 B. 3 C. 1/9 D. 9

Q3. (cosec θ − cot θ)² is equal to:

A. (1+cos θ)/(1−cos θ) B. (1−cos θ)/(1+cos θ) C. (1+sin θ)/(1−sin θ) D. None of these

Useful Resource: CBSE Class 10 English

Q4. (1−tan²45°)/(1+tan²45°) is:

A. tan90° B. 1 C. sin45° D. 0

Q5. If θ=45°, then 2tanθ/(1+tan²θ) is:

A. 1 B. 0 C. 2 D. 3

Q6. If 5θ and 4θ are acute and sin5θ = cos4θ, then 2sin3θ − √3tan3θ equals:

A. 1 B. 0 C. −1 D. 1+√3

Useful Resource: CBSE Class 10 Social Science

Q7. If 3x = cosec θ and 3/x = cot θ, then 3x² − 1/x² equals:

A. 1/27 B. 1/81 C. 1/3 D. 1/9

Q8. tan45° × cot45° equals:

A. 0 B. 1 C. 2 D. 1/2

Q9. If cos9α = sinα and 9α<90°, then tan5α is:

A. 1/√3 B. √3 C. 1 D. 0

Useful Resource: CBSE Class 10 All Subjects

Q10. If a cosθ+b sinθ=4 and a sinθ−b cosθ=3, then a²+b² is:

A. 7 B. 12 C. 25 D. None of these

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Test 3

Class 10 Mathematics — Introduction to Trigonometry

10 Questions

Q1. tan5° tan25° tan30° tan65° tan85° equals:

A. √3 B. 1/√3 C. 1 D. None of these

Q2. tan θ/(sec θ−1) + tan θ/(sec θ+1) equals:

A. 2tanθ B. 2secθ C. 2cosecθ D. 2tanθsecθ

Q3. The expression cosec(75°+θ) − sec(15°−θ) − tan(55°+θ) + cot(35°−θ) equals:

A. −1 B. 0 C. 1 D. 3/2

Useful Resource: Ravi Test Papers .in

Q4. If cot θ=7/8, then ((1+sinθ)(1−sinθ))/((1+cosθ)(1−cosθ)) is:

A. 8/7 B. 49/64 C. 7/8 D. 64/49

Q5. If tan x=3cot x and x is acute, x is:

A. 45° B. 60° C. 30° D. 15°

Q6. If cos A=4/5, then tan A is:

A. 3/5 B. 3/4 C. 4/3 D. 5/3

Useful Resource: RAVI MATHS TUITION CENTRE YouTube

Q7. (1−sin A)/(1+sin A) is equal to:

A. secA+tanA B. secA−tanA C. secA tanA D. None of these

Q8. sin²29° + sin²61° equals:

A. 1 B. 0 C. 2sin²29° D. 2cos²61°

Q9. If tan θ=8/15, then cosec θ equals:

A. 17/8 B. 8/17 C. 17/15 D. 15/17

Useful Resource: Ravi Test Papers

Q10. If 8tan x=15, then sinx−cosx equals:

A. 8/17 B. 17/7 C. 1/17 D. 7/17

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Test 4

Class 10 Mathematics — Introduction to Trigonometry

10 Questions

Q1. If x tan45° cos60° = sin60° cot60°, then x is:

A. 1 B. √3 C. 1/2 D. 1/√2

Q2. sin30° × cosec30° equals:

A. 1 B. 0 C. 1/2 D. 2

Q3. If tan θ=a/b, then (a sinθ−b cosθ)/(a sinθ+b cosθ) equals:

A. (a²+b²)/(a²−b²) B. (a²−b²)/(a²+b²) C. a²/(a²+b²) D. b²/(a²+b²)

Useful Resource: CBSE Class 10 Maths

Q4. tan1° tan2° tan3° ... tan89° equals:

A. 0 B. 1 C. 2 D. 1/2

Q5. If tan²45°−cos²30° = x sin45° cos45°, then x is:

A. 2 B. −2 C. 1/2 D. −1/2

Q6. sec²A−sec²?A is represented in the source as sec⁴A−sec²A. Its simplified value is:

A. tan²A−tan⁴A B. tan⁴A−tan²A C. tan⁴A+tan²A D. tan²A+tan⁴A

Useful Resource: CBSE Class 10 Science

Q7. If tan θ=1/√7, then (cosec²θ−sec²θ)/(cosec²θ+sec²θ) is:

A. 5/7 B. 3/7 C. 1/12 D. 3/4

Q8. cot1° cos2° cos3° ... cos180° equals:

A. −1 B. 1 C. 0 D. 1/2

Q9. If sin A=1/2, then cot A is:

A. √3 B. 1/√3 C. √3/2 D. 1

Useful Resource: CBSE Class 10 English

Q10. If cos(α+β)=0 for α+β=90°, then sin(α−β) is:

A. sinα B. cosβ C. sin2α D. cos2β

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Test 5

Class 10 Mathematics — Introduction to Trigonometry

10 Questions

Q1. For θ=30°, cos2θ equals:

A. 0 B. 1 C. 1/2 D. √3/2

Q2. In a right triangle, if tan A=1, then 2sinA cosA equals:

A. −1 B. 1 C. 2 D. 0

Q3. If 7tanθ=4, then (7sinθ−3cosθ)/(7sinθ+3cosθ) equals:

A. 1/7 B. 5/7 C. 3/7 D. 5/14

Useful Resource: CBSE Class 10 Social Science

Q4. If cosA+cos2A=1, then sin2A+sin4A equals:

A. 1 B. 2 C. 4 D. 3

Q5. If 5tanα=4, then (5sinα−3cosα)/(5sinα+2cosα) is:

A. 1/4 B. 1/6 C. 1/5 D. 4/5

Q6. If 4tanθ=3, then (4sinθ−cosθ)/(4sinθ+cosθ) equals:

A. 2/3 B. 1/3 C. 1/2 D. 3/4

Useful Resource: CBSE Class 10 All Subjects

Q7. (cos³20°−cos³70°)/(sin³70°−sin³20°) equals:

A. 1/2 B. 1/√2 C. 1 D. 2

Q8. If sinθ+sin2θ=1, then cos2θ+cos4θ is:

A. −1 B. 1 C. 0 D. None of these

Q9. 2tan30°/(1−tan²30°) equals:

A. cos60° B. sin60° C. tan60° D. sin30°

Useful Resource: Ravi Test Papers .in

Q10. 4tanA−4secA equals:

A. −1 B. −4 C. 0 D. 4

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Test 6

Class 10 Mathematics — Introduction to Trigonometry

10 Questions

Q1. The identity sin²θ+cos²θ is equal to:

A. 0 B. 1 C. 2 D. sinθ

Q2. The identity 1+tan²θ is equal to:

A. cosec²θ B. sec²θ C. cot²θ D. 1

Q3. The identity 1+cot²θ is equal to:

A. sec²θ B. tan²θ C. cosec²θ D. 1

Useful Resource: RAVI MATHS TUITION CENTRE YouTube

Q4. The reciprocal of sinθ is:

A. cosθ B. secθ C. cosecθ D. cotθ

Q5. The reciprocal of cosθ is:

A. secθ B. cosecθ C. tanθ D. cotθ

Q6. The reciprocal of tanθ is:

A. cotθ B. secθ C. cosecθ D. sinθ

Useful Resource: Ravi Test Papers

Q7. tan45° is:

A. 0 B. 1/2 C. 1 D. √3

Q8. sin30° is:

A. 1 B. √3/2 C. 1/2 D. 0

Q9. cos60° is:

A. 0 B. 1/2 C. √3/2 D. 1

Useful Resource: CBSE Class 10 Maths

Q10. tan60° is:

A. 1/√3 B. 1 C. √3 D. 2

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Test 7

Class 10 Mathematics — Introduction to Trigonometry

10 Questions

Q1. If tanθ=3/4 for an acute θ, then sinθ is:

A. 3/5 B. 4/5 C. 5/3 D. 4/3

Q2. If tanθ=3/4 for an acute θ, then cosθ is:

A. 3/5 B. 4/5 C. 5/4 D. 1/4

Q3. If tanθ=3/4, then secθ is:

A. 3/5 B. 4/3 C. 5/4 D. 5/3

Useful Resource: CBSE Class 10 Science

Q4. If tanθ=3/4, then cosecθ is:

A. 5/3 B. 5/4 C. 4/5 D. 3/5

Q5. If sinθ=5/13 for an acute θ, then cosθ is:

A. 5/12 B. 12/13 C. 13/12 D. 8/13

Q6. If cosθ=12/13 for an acute θ, then tanθ is:

A. 12/5 B. 5/12 C. 5/13 D. 13/5

Useful Resource: CBSE Class 10 English

Q7. If cotθ=5/12 for an acute θ, then sinθ is:

A. 5/13 B. 12/13 C. 13/12 D. 5/12

Q8. If tanθ=√3 and θ is acute, then θ is:

A. 30° B. 45° C. 60° D. 90°

Q9. If sinθ=1/2 and θ is acute, then θ is:

A. 30° B. 45° C. 60° D. 90°

Useful Resource: CBSE Class 10 Social Science

Q10. If cosθ=√3/2 and θ is acute, then θ is:

A. 30° B. 45° C. 60° D. 90°

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Test 8

Class 10 Mathematics — Introduction to Trigonometry

10 Questions

Q1. A tower is 30 m from an observation point and the angle of elevation is 45°. The tower height is:

A. 15 m B. 30 m C. 30√3 m D. 10√3 m

Q2. If a tower's shadow is √3 times its height, the sun's angle of elevation is:

A. 45° B. 30° C. 60° D. 90°

Q3. A 150 m tower has angle of depression 30° to a car. Its horizontal distance is:

A. 50√3 m B. 150√3 m C. 150√2 m D. 75 m

Useful Resource: CBSE Class 10 All Subjects

Q4. A 2 m ladder foot is away from a wall and ladder makes 60° with ground. Ladder length is:

A. 4/√3 m B. 4√3 m C. 2√2 m D. 4 m

Q5. A kite is 30 m high with a 60 m string. Angle of elevation is:

A. 45° B. 30° C. 60° D. 90°

Q6. If 4tanθ=3, then tanθ is:

A. 3/4 B. 4/3 C. 1/2 D. 3

Useful Resource: Ravi Test Papers .in

Q7. If 8tanx=15, then tanx is:

A. 8/15 B. 15/8 C. 7/17 D. 17/8

Q8. If 7tanθ=4, then tanθ is:

A. 7/4 B. 4/7 C. 3/7 D. 1/7

Q9. If 5tanα=4, then tanα is:

A. 5/4 B. 4/5 C. 1/5 D. 4

Useful Resource: RAVI MATHS TUITION CENTRE YouTube

Q10. If 3cotθ=4, then cotθ is:

A. 4/3 B. 3/4 C. 1/3 D. 3

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Test 9

Class 10 Mathematics — Introduction to Trigonometry

10 Questions

Q1. If θ=45°, then sinθ+cosθ equals:

A. 1 B. √2 C. 1/√2 D. 2

Q2. If θ=45°, then sinθ cosθ equals:

A. 1 B. 1/2 C. 1/√2 D. 1/4

Q3. The value of 2tan45°/(1+tan²45°) is:

A. 0 B. 1 C. 2 D. 1/2

Useful Resource: Ravi Test Papers

Q4. The value of (1−tan²45°)/(1+tan²45°) is:

A. 0 B. 1 C. −1 D. 1/2

Q5. The value of tan45° cot45° is:

A. 0 B. 1 C. 2 D. 1/2

Q6. If cos(10°+θ)=sin30°, θ is:

A. 50° B. 40° C. 80° D. 20°

Useful Resource: CBSE Class 10 Maths

Q7. If cos9α=sinα and 9α<90°, then α is:

A. 9° B. 10° C. 15° D. 45°

Q8. If cos(α+β)=0 and α+β is acute, α+β equals:

A. 45° B. 60° C. 90° D. 180°

Q9. If 5θ and 4θ are acute and sin5θ=cos4θ, then θ is:

A. 5° B. 10° C. 15° D. 20°

Useful Resource: CBSE Class 10 Science

Q10. If sin2A=2sinA, the acute/nonnegative solution given in the source is:

A. 0° B. 30° C. 45° D. 60°

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Test 10

Class 10 Mathematics — Introduction to Trigonometry

10 Questions

Q1. Which ratio represents perpendicular/hypotenuse in a right triangle?

A. sinθ B. cosθ C. tanθ D. cotθ

Q2. Which ratio represents base/hypotenuse?

A. sinθ B. cosθ C. tanθ D. cosecθ

Q3. Which ratio represents perpendicular/base?

A. sinθ B. cosθ C. tanθ D. secθ

Useful Resource: CBSE Class 10 English

Q4. Which ratio represents hypotenuse/perpendicular?

A. sinθ B. cosθ C. cosecθ D. cotθ

Q5. Which ratio represents hypotenuse/base?

A. secθ B. cosecθ C. tanθ D. cotθ

Q6. Which ratio represents base/perpendicular?

A. tanθ B. cotθ C. secθ D. cosecθ

Useful Resource: CBSE Class 10 Social Science

Q7. If sinθ=a/b, then cosθ is:

A. b/√(b²−a²) B. b/a C. √(b²−a²)/b D. a/√(b²−a²)

Q8. If tanθ=a/b, then the expression (a sinθ−b cosθ)/(a sinθ+b cosθ) is:

A. (a²+b²)/(a²−b²) B. (a²−b²)/(a²+b²) C. a²/(a²+b²) D. b²/(a²+b²)

Q9. If tanθ=8/15, then the hypotenuse-to-perpendicular ratio is:

A. 8/17 B. 17/8 C. 15/17 D. 17/15

Useful Resource: CBSE Class 10 All Subjects

Q10. If 4tanθ=3, then (4sinθ−cosθ)/(4sinθ+cosθ) is:

A. 2/3 B. 1/3 C. 1/2 D. 3/4

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Ravi Test Papers — Useful Links

• Ravi Test Papers
• CBSE Class 10 Maths
• CBSE Class 10 Science
• CBSE Class 10 English
• CBSE Class 10 Social Science
• CBSE Class 10 All Subjects
• Ravi Test Papers .in
• RAVI MATHS TUITION CENTRE YouTube

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