Important questions2

11th Standard

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Maths

Use blue pen Only

Time : 00:50:00 Hrs
Total Marks : 30

    Part A 

    Answer all the questions

    10 x 1 = 10
  1. If tan400=λ, then \(\frac { tan{ 140 }^{ 0 }-tan{ 130 }^{ 0 } }{ 1+tan{ 140 }^{ 0 }.tan{ 130 }^{ 0 } } \)=

    (a)

    \(\frac { 1-\lambda ^{ 2 } }{ \lambda } \)

    (b)

    \(\frac { 1+{ \lambda }^{ 2 } }{ \lambda } \)

    (c)

    \(\frac { 1+{ \lambda }^{ 2 } }{ 2\lambda } \)

    (d)

    \(\frac { 1-{ \lambda }^{ 2 } }{ 2\lambda } \)

  2. Let fk(x)=\(\frac { 1 }{ k } \)[sinkx+coskx] where x\(\in \)R and k≥1. Then f4(x)-f6(x)=

    (a)

    \(\frac { 1 }{ 4 } \)

    (b)

    \(\frac { 1 }{ 12 } \)

    (c)

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

    (d)

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

  3. Which of the following is not true?

    (a)

    sinፀ=-\(\frac { 3 }{ 4 } \)​​​​​​​

    (b)

    cosፀ=-1

    (c)

    tanፀ=25

    (d)

    secፀ=\(\frac { 1 }{ 4 } \)

  4. \(\frac { cos6x+6cos4x+15cos2x+10 }{ cos5x+5cos3x+10cosx } \) equal to

    (a)

    cos2x

    (b)

    cosx

    (c)

    cos3x

    (d)

    2cosx

  5. 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

  6. The value of sin2\(\frac { 5\pi }{ 12 } -sin^{ 2 }\frac { \pi }{ 12 } \) is

    (a)

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

    (b)

    \(\frac { \sqrt { 3 } }{ 2 } \)

    (c)

    1

    (d)

    0

  7. \(\frac { cos3x }{ 2cos2x-1 } \) is

    (a)

    cos x

    (b)

    sin x

    (c)

    tan x

    (d)

    cot x

  8. The value of sin\({\pi\over 48}cos {\pi \over 48} cos {\pi \over 24}cos {\pi \over 12}cos{\pi \over 6}cos {\pi \over 3}\) is

    (a)

    \(\sqrt{3}\over32\)

    (b)

    \(\sqrt{3}\over64\)

    (c)

    \({3}\over32\)

    (d)

    \({3}\over64\)

  9. If sinθ=sin\(\alpha\), then the angles θ and \(\alpha\) are related by

    (a)

    \(\theta=n\pi\pm\alpha\)

    (b)

    \(\theta=2n\pi+(-1)^n\alpha\)

    (c)

    \(\alpha=n\pi\pm(-1)^n\theta\)

    (d)

    \(\theta=(2n+1)\pi+\alpha\)

  10. If in a triangle a=5, b=4 and cos(A-B)=\(\frac{31}{32}\) then the third side C is equal to

    (a)

    5

    (b)

    6

    (c)

    3

    (d)

    12

  11. Part B

    Answer all the questions

    10 x 2 = 20
  12. Identify the Quadrant in which a given measure lies; 3280

  13. A fighter jet has to hit a small target by flying a horizontal distance. When the target is sighted, the pilot measures the angle of depression to be 300. If after 100km, the target has an angle of depression of 450, how far is the target from the fighter jet at that instant?

  14. If \(\sin { x } =\frac { 15 }{ 17 } \) and \(\cos {y } =\frac { 12 }{ 13 } \), 0 < x < \(\frac{\pi}{2}\), 0 < y < \(\frac{\pi}{2}\), find the value of tan (x + y)

  15. For given Angle, find a coterminal angle with a measure \(\theta\) of such that \(0\le \theta \le 360°\) 
    3950 

  16. if sin \(\theta\) + cos \(\theta\) = m, show that cos6\(\theta\) + sin6\(\theta\)  = \(\frac { 4-3({ m }^{ 2 }-1)^{ 2 } }{ 4 } \) where m2 \(\le \) 2

  17. if x = \(\sum _{ n=0 }^{ \infty }{ { cos }^{ 2n } } \theta ;\) y = \(y=\sum _{ n=0 }^{ \infty }{ { sin }^{ 2n } } \theta \) and z = \(\sum _{ n=0 }^{ \infty }{ { cos }^{ 2n }\theta } \) sin2n\(\theta \), 0 < \(\theta \) < \(\frac { \pi }{ 2 } \),then show that xyz = x+y+z  
    Hint :1+x+x2+x3+.......= \(\frac { 1 }{ 1-x } \)where \(\left| x\right| \)< 1].

  18. It sec \(\theta\) + tan \(\theta\) = p, obtain the values of sec \(\theta\), tan \(\theta\) and sin \(\theta\) in terms of p

  19. Find the value of tan\(\frac { \pi }{ 2 } \).

  20. In a ΔABC if a=3, b=5 and c=7, find cosA and cosB.

  21. Evaluate sin\(\left( cos^{ -1 }\left( \frac { 3 }{ 5 } \right) \right) \)

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