CHAPTER : Trigonometry
Choose
the correct answer or the most suitable answer:
1. 1/cos 80̊ - √3/sin 80̊ =
(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 tan40̊ = 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 fk(x) =1/k [sinkx + coskx] 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 cos2ϕ + sin2 (θ - ϕ) - sin2
(θ + ϕ) 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
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