Exercise 3.12: Choose the correct or the most suitable answer

CHAPTER : Trigonometry

Choose the correct answer or the most suitable answer:

1. 1/cos 80ÌŠ  - √3/sin 80ÌŠ =

(1) √2

(2) √3

(3) 2

(4) 4

Solution

2. If cos 28ÌŠ  + sin 28ÌŠ  = k³, then cos 17ÌŠ  is equal to

(1) k³/√2

(2) -k³/√2

(3) ± k³/√2

(4) - k³/√2

Solution

3. The maximum value of 4 sin²x + 3cos²x + sin x/2 + cos x/2 is

(1) 4 + √2

(2) 3 + √2

(3) 9

(4) 4

Solution

4. 

(1) 1/8

(2)1/2

(3)1/√3

(4)1/√2

Solution

5. If , equal to

(1) -2cosθ

(2) -2sinθ

(3) 2cosθ

(4) 2sinθ

Solution (Option : (4) 2sinθ or (1) -2cosθ ??????? Please don't refer this solution for examination)

6. If tan40ÌŠ = λ, then 

(1) 1-λ²/ λ

(2) 1+λ²/ λ

(3) 1+λ²/ 2λ

(4) 1-λ²/ 2λ

Solution

7. cos 1̊ + cos 2̊ + cos 3̊ + …. + cos 179̊ =

(1) 0

(2) 1

(3) -1

(4) 89

Solution

8. Let f_k(x) =1/k [sin^kx + cos^kx] where x ∊ R and k ≥ 1. Then f₄(x) - f₆(x) =

(1)1/4

(2)1/12

(3)1/6

(4)1/3

Solution

9. Which of the following is not true?

(1) sin θ = -3/4

(2) cos θ = -1

(3) tan θ = 25

(4) sec θ =1/4

Solution

10. cos2θ cos2Ï• + sin² (θ - Ï•) - sin² (θ + Ï•) is equal to

(1) sin 2(θ + ϕ)

(2) cos 2(θ + ϕ)

(3) sin 2(θ - ϕ)

(4) cos 2(θ - ϕ)

Solution

11. 

(1) sinA + sinB + sinC

(2) 1

(3) 0

(4) cosA + cosB + cosC

Solution

12. If cos pθ + cos qθ = 0 and if p ≠ q, then θ is equal to (n is any integer)

Ans: 2

Solution

13.If tanα and tanβ are the roots of x² + ax + b = 0, then  is equal to

(1)b/a

(2)a/b

(3) –a/b

(4) –b/a

Solution

14. In a triangle ABC, sin²A + sin²B + sin²C = 2, then the triangle is

(1) equilateral triangle

(2) isosceles triangle

(3) right triangle

(4) scalene triangle.

Solution

15. If f(θ) = |sin θ| + |cosθ| , θ ∊ R, then f(θ) is in the interval

(1) [0, 2]

(2) [1,√2]

(3) [1, 2]

(4) [0, 1]

Solution

16. cos 6x + 6 cos 4x + 15 cos 2x + 10 / cos 5x + 5 cos 3x + 10 cos x is equal to

(1) cos2x

(2) cos x

(3) cos 3x

(4) 2 cos x

Solution

17. The triangle of maximum area with constant perimeter 12m

(1) is an equilateral triangle with side 4m

(2) is an isosceles triangle with sides 2m, 5m, 5m

(3) is a triangle with sides 3m, 4m, 5m

(4) Does not exist.

Solution

18. A wheel is spinning at 2 radians/second. How many seconds will it take to make 10 complete rotations?

(1) 10Ï€ seconds

(2) 20 π seconds

(3) 5 π seconds

(4) 15Ï€ seconds

Solution

19. If sinα + cosα = b, then sin 2α  is equal to

(1) b² - 1, if b ≤ √2

(2) b² - 1, if b > √2

(3) b² - 1, if b ≥ 1

(4) b² - 1, if b ≥√2

Solution

20. In a ∆ABC, if

(i) sin A/2 sin B/2 sin C/2> 0

(ii) sinAsinB sinC > 0 then

(1) Both (i) and (ii) are true

(2) Only (i) is true

(3) Only (ii) is true

(4) Neither (i) nor (ii) is true.

Solution