Mathematics Class 10 Introduction to Trigonometry MCQ Test Paper -

Q 1 – The value of the expression [cosec (75° + θ)
– sec (15° – θ) – tan (55° + θ) + cot (35° – θ)1 is:

(A) -1

(B) 0

(C) 1

(D) $\frac{3}{2}$

Ans. option (B) is Correct.

Q 2 – If cos (α + β) = 0, then sin (α – β) can be reduced to

(A) cos β

(B) cos 2β

(C) sin α

(D) sin 2α

Ans. Option (B) is correct.

Q 3 – The value of (tan 1° tan 2° tan 3°… tan 89°) is:

(A) 0

(B) 1

(C) 2

(D) $\frac{1}{2}$

Ans. Option (B) is Correct.

Q 4 – If cos 9α = sin a and 9α < 90°, then the value of tan 5α is:

(A) $\frac{1}{\sqrt{3}}$

(B) √3

(C) 1

(D) 0

Ans. Option (C) is correct.

Q 5 – If ∆ABC is right angled at C, then the value of cos (A+ B) is:

(A) 0

(B) 1

(C) $\frac{1}{2}$

(D) $\frac{\sqrt{3}}{2}$

Ans. option (A) is Correct.

Q 6 – Given that sin α = {latex]\frac{1}{2}[/latex]and cos β = $\frac{1}{2}$ then the value of (α+β) is:

(A) 0°

(B) 30°

(C) 60°

(D) 90°

Ans. Option (D) is Correct.

Q 7 – If cos A = $\frac{4}{5}$ then the value of tan A is:

(A) $\frac{3}{5}$

(B) $\frac{3}{4}$

(D) $\frac{1}{8}$

Ans. Option (B) is Correct.

Q 8 – If sin A= $\frac{1}{2}$ then the value of A is

(A)√3

(B) $\frac{1}{\sqrt{3}}$

(C) $\frac{\sqrt{3}}{2}$

(D) 1

Ans. option (A) is Correct.

Q 9 – If sin A + sin^2: A = 1, then the value of the expression (cos² A + cos⁴ A) is:

(A) 1

(B) $\frac{1}{2}$

(C) 2

(D) 3

Ans. option (A) is correct

Q 10 – The value of 9 sec² A – 9 tan² A is

(A) 1

(B) 9

(C) 8

(D) 0

Ans. option (B) is Correct.

Q 11 – The value of (sec A + tan A) (1 – sin A) is

(A) sec A

(B) sin A

(C) cosec A

(D) cos A

Ans. option (D) is correct.

Directions : In the following questions, A statement of Assertion (A) is followed by a statement of

Reason (R). Mark the correct choice as.

(A) Both A and R are true and R is the correct explanation of A

(B) Both A and R are true but R is NOT the correct explanation of A

(C) A is true but R is false

(D) A is false and R is True

Q 12 – Assertion (A): Cot A is the product of Cot and A.

Reason (R): The value of sine increases as 0 increases.

Ans. Option (D) is correct.

Q 13 – Assertion (A): The value of $\frac{tan47°}{cot43°}$ is 1.

Reason (R): The value of the expression (sin 80°-cos 80°) is negative.

Ans. option (C) is Correct.

Q 14 – Assertion (A): If tan A = cot B, then the value of (A + B) is 90°.

Reason (R): If sec θ sin θ = 0, then the value of θ is 0°

Ans. option (B) is Correct.

Q 15 – Assertion (A): If x = 2 sin² θ and y = 2 cos² θ + 1 then the value of x + y = 3.

Reason (R): If tan a = $\frac{5}{12}$ then the value of sec a is $\frac{13}{12}$ .

Ans. option (B) is Correct.

Q 16 – Assertion (A): If k + 1 = sec² θ (1 + sin θ) (1 – sin θ), then the value of k is 1.

Reason (R): If sin θ + cos θ =√3 then the value of tan θ + cot θ is 1

Ans. option (D) is Correct.

Q 17 – Assertion (A): If sin A= $\frac{\sqrt{3}}{2}$ then the value of 2 cot² A -1 is $\frac{-1}{3}$

Reason (R): If θ be an acute angle and 5 cosec θ = 7, then the value of sin θ + cos² θ -1 is 10.

Ans. option (C) is correct.

Attempt any four sub-parts from each question. Each sub-part carries 1 mark.

Read the following text and answer the following question on the basis of the same:

Skysails’ is that genre of engineering science that uses extensive utilization of wind energy to move a vessel in the sea water. The sky sails technology allows the towing kite to gain a height of anything between 100 m to 300 m. The sailing kite is made in such a way that it can be raised to its proper elevation and then brought back with the help of a telescopic mast that enables the kite to be raised properly and effectively.

Q 18 – 1n the given figure, if tan θ= cot (30° + θ), where θ and 30° + θ are acute angles, then the value of θ is

(A) 45°

(C) 60°

(B) 30°

(D) None of these

Ans. Option (B) is correct.

Q 19 – The value of tan 30°. cot 60° is:

(A) √3

(B) $\frac{1}{\sqrt{3}}$

(C) 1

(D) $\frac{1}{3}$

Q 20 – What should be the length of the rope of the kite sail in order to pull the ship at the angle 0 and be at a vertical height of 200 m ?

(A) 400 m

(B) 300 m

(C) 100 m

(D) 200 m

Ans. option (A) is correct.

Q 21 – If cos A= $\frac{1}{2}$ then the value of 9 cot²A-1 is:

(A) 1

(B) 3

(C) 2

(D) 4

Ans. Option (C) is Correct.

Q 22 – In the given figure, the value of (sin C + cos A) is:

(A) 1

(B) 2

(C) 3

(D) 4

Ans. Option (A) is Correct.

Read the following text and answer the following question on the basis of the same:

Authority wants to construct a slide in a city park for children. The slide was to be constructed for children below the age of 12 years. Authority prefers the top of the slide at a height of 4 m above the ground and inclined at an angle of 30° to the ground.

Q 23 – The distance of AB is :

(A) 8 m

(B) 6 m

(C) 5 m

(D) 10m

Ans. Option (A) is correct.

Q 24 – The value of sin²30 + cos ²60 is:

(A) $\frac{1}{4}$

(B) $\frac{1}{2}$

(C) $\frac{3}{4}$

(D) $\frac{3}{2}$

Ans. Option (B) is Correct.

Q 25 – If cos A = $\frac{1}{2}$ , then the value of 12 cot² A – 2 is:

(A) 5

(B) 4

(C) 3

(D) 2

Ans. Option (D) is correct.

Q 26 – In ther given figure, the value of (sin C x cos A) is:

(A) $\frac{1}{3}$

(B) $\frac{1}{2}$

(C) $\frac{1}{4}$

(D) $\frac{1}{5}$

Ans. Option (B) is correct.

Q 27 – In the given figure, if AB + BC = 25 cm and AC = 5 cm, then the value of BC is:

(A) 25 cm

(B) 15 cm

(C) 10 cm

(D) 12 cm

Ans. Option (D) is correct.

Q 28 –The Value of (1+tan θ + sec θ) (1+cot θ -cosec θ) is

(A) 0

(B) 1

(C) 2

(D) -1

Ans. Option (C) is Correct.