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 tan x2+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 aΔABC, if (i) \(sin\frac { A }{ 2 } sin\frac { B }{ 2 } sin\frac { C }{ 2 } \) (ii) sinA sinB sinC>0

    (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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