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Trigonometry - One Mark Questions

11th Standard

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Maths

Time : 00:30:00 Hrs
Total Marks : 15
    15 x 1 = 15
  1. \(\frac { 1 }{ cos{ 80 }^{ 0 } } -\frac { \sqrt { 3 } }{ sin{ 80 }^{ 0 } } \)=

    (a)

    \(\sqrt{2}\)

    (b)

    \(\sqrt{3}\)

    (c)

    2

    (d)

    4

  2. The maximum value of 4sin2x+3cos2x+\(sin\frac { x }{ 2 } +cos\frac { x }{ 2 } \) is

    (a)

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

    (b)

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

    (c)

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

    (d)

    \(\frac { 1 }{ \sqrt { 2 } } \)

  3. cos10+cos20+cos30+: : :+cos1790=

    (a)

    0

    (b)

    1

    (c)

    -1

    (d)

    89

  4. cos2ፀ cos2ф+sin2(ፀ-ф)-sin2(ፀ+ф) is equal to

    (a)

    sin2(ፀ+\(\phi \))

    (b)

    cos2(ፀ+\(\phi \))

    (c)

    sin2(ፀ-\(\phi \))

    (d)

    cos2(ፀ-\(\phi \))

  5. If tan α and tan β are the roots of tan2x + atanx + b = 0; then \(\frac { sin(\alpha +\beta ) }{ sin\alpha sin\beta } \) is equal to

    (a)

    \(\frac { b }{ a } \)

    (b)

    \(\frac { a }{ b } \)

    (c)

    \(\frac { a }{ b } \)

    (d)

    \(\frac { b}{ a } \)

  6. If f(ፀ)=|sinፀ|+|cosፀ|, ፀ\(\in \)R, then f(ፀ) is in the interval     

    (a)

    [0,2]

    (b)

    [1,\(\sqrt { 2 } \)]

    (c)

    [1,2]

    (d)

    [0,1]

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

    (a)

    10\(\pi \) seconds

    (b)

    20\(\pi \) seconds

    (c)

    5\(\pi \) seconds

    (d)

    15\(\pi \) seconds

  8. In a ΔABC, if (i) \(sin\frac { A }{ 2 } sin\frac { B }{ 2 } sin\frac { C }{ 2 } \) > 0 (ii) sinA sinB sinC > 0, Then

    (a)

    Both (i) and (ii) are true

    (b)

    Only (i) is true

    (c)

    Only (ii) is true

    (d)

    Neither (i) nor (ii) is true

  9. If tanx=\(\frac { -1 }{ \sqrt { 5 } } \) and x lies in the IV quadrant, then the value of cosx is

    (a)

    \(\sqrt { \frac { 5 }{ 6 } } \)

    (b)

    \(\frac { 2 }{ \sqrt { 6 } } \)

    (c)

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

    (d)

    \(\frac { 1 }{ \sqrt { 6 } } \)

  10. If cosec x+cotx=\(\frac { 11 }{ 2 } \) then tanx=

    (a)

    \(\frac { 21 }{ 22 } \)

    (b)

    \(\frac { 15 }{ 16 } \)

    (c)

    \(\frac { 44 }{ 117 } \)

    (d)

    \(\frac { 117 }{ 44 } \)

  11. 2tan-1\(\left( \frac { 1 }{ 5 } \right) \) is equal to

    (a)

    tan\(\left( \frac { 5 }{ 12 } \right) \)

    (b)

    \(\frac { 5 }{ 12 } \)

    (c)

    \(\tan^{-1}\left({5 \over 12}\right)\)

    (d)

    tan-1\(\frac { 2 }{ 5 } \)

  12. If sin(45 ° + 10°) - sin(45° -10°) =\(\sqrt{2}\)sin x then x is

    (a)

    0o

    (b)

    (c)

    10°

    (d)

    15°

  13. If 2 sinθ+1=0 and \(\sqrt{3}\)tanθ=1, then the most general value of θ is

    (a)

    \(n\pi\pm\frac{\pi}{6}\)

    (b)

    \(n\pi+(-1)^n\frac{7\pi}{6}\)

    (c)

    \(2n\pi+\frac{7\pi}{6}\)

    (d)

    \(2n\pi+\frac{11\pi}{6}\)

  14. If (A+B)=\(\frac{\pi}{4}\), (cot A-1)(cot B-1)=

    (a)

    0

    (b)

    -2

    (c)

    2

    (d)

    1

  15. Number of solutions of the equation tan x+sec x=2 cos x lying in the interval [0,2π] is

    (a)

    0

    (b)

    1

    (c)

    2

    (d)

    3

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