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SSC Trigonometry : Advance math series 2000 most important questions (Part-1)

SSC Trigonometry Part 1: Advance math series 2000 most important questions.

Q1. In circular measure, the value of the angle 11°15’ is

(a) π°/16

(b) π°/8

(c) π°/4

(d) π°/12

Q2. If the sum of two angles is 135° and their difference is π/12 , then the circular measure of the greater angle is

(a) 2π/3

(b) 5π/5

(c) 5π/12

(d) π/3

Q3. If cosec 39° = x, the value  of is

(a) (b) (c) (d) Q4. The value of tan 1° tan 2° tan 3°…..tan 89° Is :

(a) 1

(b) 0

(c) √3

(d) 1/√3

Q5. If Θ be an acute angle and 7 sin2Θ = 4, then the value of tanΘ is

(a) √3

(b) 1/√3

(c) 1

(d) 0 Q6. The value of sin2 + sin2 + sin2 + …+ sin289° is

(a) 11½

(b) 11√2

(c) 11

(d) 11/√2

Q7. If sin 17°=x/y  , then the value of (sec 17° – sin 73°) is

(a) (b) (c) (d) Q8. Maximum value of (2 sinθ  + 3 cosθ ) is

(a) 2

(b) √13

(c) √15

(d) 1

Q9. The minimum value of 4 tan2 θ + 9 cotθ   is equal to

(a) 0

(b) 5

(c) 12

(d) 13

Q10. If  Θ be an acute and tanθ+Cotθ=2, then the  value of tan5θ+cot10θ is

(a) 1

(b) 2

(c) 3

(d) 4

Q11. If sin α sec (30° + α) = 1 (0 <α< 60°), then the value of sinα  + cos 2α is

(a) 1

(b) (c) 0

(d) √2

Q12. If = 3, then the value of sin4 θ– cos4 θ is

(a) 1/5

(b) 2/5

(c) 3/5

(d) 4/5

Q13. In a right – angled triangle XYZ right  – angled at Y, if XY = 2√6 and XZ – YZ = 2, then sec X + tan X is

(a) 1/√6

(b) √6

(c) 2√6

(d) √6 /2

Q14. If tan 7θ tan 2θ= 1, then the value of tan 3θ is

(a) √3

(b) -1/√3

(c) 1/√3

(d) -√3

Q15. If (1+sinα) (1+sinβ) (1+sinγ) = (1-sinα)(1-sinβ)(1-sinγ), then each side is equal to

(a) ±cosα cosβ cosγ

(b) ±sinα sinβ sinγ

(c) ±sinα cosβ cosγ

(d) ±sinα sinβ cosγ

Q16. If cos x + cos2x = 1, the numerical value of (sin12x+3 sin10x+3 sin8x+sin6x-1) is:

(a) -1

(b) 2

(c) 0

(d) 1

Q17. In  ΔABC, ∠B = 90° and AB: BC = 2 : 1. The value of sin A + cot C is

(a) 3+√5

(b) (c) 2+√5

(d) 3√5

Q18. If x2 – 2x + 2, then the value of x is

(a) 0

(b) 1

(c) -1

(d) None of these

Q19. If 3 sinθ  + 5 cosθ  = 5, then the value of 5 sinθ   – 3 cosθ will be

(a) ±3

(b) ±5

(c) ±2

(d) ±1 Q21. ABC is a right angled triangle, right angled at B and ∠A = 60° and AB = 20 cm, then the ratio of sides BC and CA is

(a) √3 : 1

(b) 1:√3

(c) √3 : √2

(d) √3 : 2

Q22. The angle of elevation of the top of a tower from two points A and B lying on the horizontal through the foot of the tower are respectively 15° and 30°.  If A and B are on the same side of the tower and AB = 48 metre, the height of the tower is:

(a) 24√3 metre

(b) 24  metre

(c) 24√2 metre

(d) 96 metre

Q23. The distance between two pillars of length 16 metres and 9 metres is x metres.  It two angles of elevation of their respective top from the bottom of the other are complementary  to each other, then the value of x(in metres) is

(a) 15

(b) 16

(c) 12

(d) 9

Q24. A telegraph post is bent at a point above the ground due to storm. Its top just meets the ground at a distance of 8√3 metres from its foot and makes an angle of 30°, then the height of the post is:

(a) 16 metres

(b) 23 metres

(c) 24 metres

(d) 10 metres

Q25. If the angle of elevation of a balloon from two consecutive kilometre – stones along a road are 30° and 60° respectively, then the height of the balloon above the ground will be

(a) √3/2 km

(b) ½ km

(c) 2/√3 km

(d) 3√3 km

Q26. From an aeroplane just over a river, the angle of depression of two palm trees on the opposite bank of the river are found to be 60° and 30° respectively. If the breadth of the river is 400 metres, then the height of the aeroplane above the river at that instant is

(a) 173.2 metres

(b) 346.4 metres

(c) 519.6 metres

(d) 692.8 metres

Q27. The value of is

Q28. If , then find the value of is

Q29. If  0<θ<90° tanθ= , then find the value of sec2θ is

Q30. If acosθ+bsinθ=m and asinθ-bcosθ=x then the value of a2+b2 is

Q31.If A + B = 450, then the value of (1 + tan A)(1 + tan B) is.

Q32. In the given ΔABC if AB=4cm ,BC= 8 cm and CA= 5 cm then find the value of cosβ

Q33. = ?

Q34. If x sin3θ + y cos3 θ= sinθcosθ and xsinθ=ycosθ then x2 + y2= ?

(a) 0

(b) 2

(c) 4

(d) 1

Q35. If sinθ+sin2θ=1, then find the value of cos12θ +3cos10θ+3cos8θ +cos6θ+2cos4θ +2cos2θ-2 is

(a) -1

(b) 1

(c) 2

(d) -2

Q36. If =1, then the value of is

(a) 4

(b) 0

(c) 1/8

(d) 1

Q37. is equals to

(a) cosec x + cot x

(b) cosec x + tan x

(c) sec x + tan x

(d) sec x + cot x

Q38. If cos (A – B) = 1/2 and sin (A + B) =1/2, then the lowest positive value of A is

(a) 135°

(b) 60°

(c) 30°

(d) 105°

Q39.  If A= tan11° tan 29° and B=2cot61° cot79°  then which is correct in the following?

(a) A = 2B

(b) A = – 2B

(c) 2A = B

(d) 2A = – B

Q40. log10 tan1°+log10 tan2°+log10 tan3°+log10 tan4°+………………..+log10 tan89° is equal to

(a) 1

(b) 45 log10 tan1°

(c) 45 log10 (tan 89°)

(d) 0

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3 Responses to “SSC Trigonometry : Advance math series 2000 most important questions (Part-1)”

• vijayant says:

very good