[CLASS 10] Mathematics MCQs on Trigonometric Ratios of Specific Angles

Mathematics Written Test Questions and Answers for Class 10 on “Trigonometric Ratios of Specific Angles – 2”.

1. What is the value of tan θ when θ is 30°?
a) ( frac {1}{sqrt 3})
b) 1
c) 0
d) 2
Answer: a
Clarification: Tan θ = ( frac {Sin , theta}{Cos , theta} = frac {Sin , 30^{circ }}{Cos , 30^{circ }} )
= ( frac {1/2}{sqrt 3/2})
= ( frac {1}{2} times frac {2}{sqrt 3})
= ( frac {1}{sqrt 3})

2. What is the value of sec 0° + cosec 90°?
a) 0
b) 2
c) 1
d) ∞
Answer: b
Clarification: The value of sec 0° is 1 and the value of cosec 90° is 1.
sec 0° + cosec 90° = 1 + 1
= 2

3. Evaluate sin² 30.
a) 2
b) 0
c) ( frac {1}{4})
d) ∞
Answer: c
Clarification: Sin² 30° = (( frac {1}{2}))²
= ( frac {1}{4})

4. What is the value of cos 45° + sin 45°?
a) 1
b) ( frac {1}{4})
c) ( frac {3}{4})
d) √2
Answer: d
Clarification: cos 45° + sin 45° = ( frac {1}{sqrt 2} + frac {1}{sqrt 2})
= 2 × ( frac {1}{sqrt 2}) ( Since, 2 = √2 × √2 )
= √2

5. 135° lies in the third quadrant.
a) True
b) False
Answer: b
Clarification: A plane is divided into four quadrants. The second quadrant ranges from 90° to 180°. So, 135° lies between 90° to 180° which is in the second quadrant of a plane not in the third quadrant.

6. What is the value of sec 60° – ( frac {1}{cosec , 90^{circ }})?
a) Cot 30°
b) Cot 45°
c) Cot 60°
d) Tan 60°
Answer: b
Clarification: sec 60° – ( frac {1}{cosec , 90^{circ }}) = 2 – ( frac {1}{1})
= 1
= cot 45°

7. Tan 90° is _____
a) Not defined
b) 1
c) 0
d) 2
Answer: a
Clarification: Tan 90° = (frac {Sin , 90^{circ }}{Cos , 90^{circ }} = frac {1}{0})
Any number divided with 0 is always not defined.

8. The value of sin² 90° + √2 cos 45° + √3 cot 30° is_____
a) 2
b) 0
c) 4
d) 5
Answer: d
Clarification: sin² 90° + √2 cos 45° + √3 cot 30° = 1² + √2 (( frac {1}{sqrt 2})) + √3 (√3)
= 1 + 1 + 3
= 5

9. The product of sec 30° and cos 60° is _____
a) 0
b) 2
c) 1
d) ( frac {1}{sqrt 3})
Answer: d
Clarification: (sec 30°) (cos 60°) = (( frac {2}{sqrt 3}) ( frac {1}{2} ))
= ( frac {1}{sqrt 3})

10. ( frac {1 – cot , 45^{circ}}{1+ cot , 45^{circ}}) is _____
a) 0
b) 2
c) 3
d) 1
Answer: a
Clarification: ( frac {1 – cot , 45^{circ}}{1 + cot , 45^{circ}} = frac {1-1}{1+1})
= ( frac {0}{1})
= 0

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