Important 1mark -1

11th Standard

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Maths

Use blue pen Only

Time : 00:10:00 Hrs
Total Marks : 25

    Part A

    Answer all the questions

    20 x 1 = 20
  1. \(\frac { 1 }{ cos{ 80 }^{ 0 } } -\frac { \sqrt { 3 } }{ sin{ 80 }^{ 0 } } \)=

    (a)

    \(\sqrt{2}\)

    (b)

    \(\sqrt{3}\)

    (c)

    2

    (d)

    4

  2. 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-\(\phi \))

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

    (a)

    cos2x

    (b)

    cosx

    (c)

    cos3x

    (d)

    2cosx

  4. The angle between the minute and hour hands of a clock at 8.30 is

    (a)

    800

    (b)

    750

    (c)

    600

    (d)

    1050

  5. If tanA=\(\frac { a }{ a+1 } \) and B=\(\frac { 1 }{ 2a+1 } \) then the value of A+B is

    (a)

    0

    (b)

    \(\frac { \pi }{ 2 } \)

    (c)

    \(\frac { \pi }{ 3 } \)

    (d)

    \(\frac { \pi }{ 4 } \)

  6. The quadratic equation whose roots are tan75° and cot75° is:

    (a)

    x2+4x+ 1 =0

    (b)

    4x2-x+ 1 =0

    (c)

    4x2+ 4x - 1 = 0

    (d)

    x2 - 4x + 1 = 0

  7. The general solution of cosec\(\theta\) = -2 is

    (a)

    \(2n\pi +(-1)^n({\pi\over 6})\)

    (b)

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

    (c)

    \(2n\pi \pm({\pi\over 6})\)

    (d)

    \(-{\pi\over 6}+n\pi\)

  8. (secA+tanA-1)(secA-tanA+1)-2tanA=

    (a)

    0

    (b)

    1

    (c)

    2

    (d)

    2 tan A

  9. The value of tan 1° tan 2° tan 3°...tan 89° is

    (a)

    \(\infty\)

    (b)

    0

    (c)

    1

    (d)

    \(\sqrt{3}\)

  10. If cosθ+\(\sqrt{3}\)sinθ=2 and θ∈[0,2π] then θ is

    (a)

    \(\frac{\pi}{3}\)

    (b)

    \(\frac{5\pi}{3}\)

    (c)

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

    (d)

    \(\frac{4\pi}{3}\)

  11. The numerical value of tan-11+tan-12+tan-13=

    (a)

    \(\pi\)

    (b)

    \(\frac{\pi}{2}\)

    (c)

    0

    (d)

    \(\frac{\pi}{4}\)

  12. If in a triangle ABC, ∠B=60°, then

    (a)

    (a-b)2=c2-ab

    (b)

    (b-c)2=a2-bc

    (c)

    (c-a)2=b2-ac

    (d)

    a2+b2=c2

  13. Area of triangle ABC is

    (a)

    \(\frac{1}{2}\)ab cos C

    (b)

    \(\frac{1}{2}\)ab sin C

    (c)

    \(\frac{1}{2}\)ab cos B

    (d)

    \(\frac{1}{2}\)bc sin B

  14. \(lim_{x \rightarrow \infty}({x^2+5x+3\over x^2+x+3})^x\)is

    (a)

    e4

    (b)

    e2

    (c)

    e3

    (d)

    1

  15. If f(x)=x(-1)\(\left\lfloor 1\over x \right\rfloor \),\(x\le0\),then the value of \(lim_{x\rightarrow 0}f(x)\) is equal to

    (a)

    -1

    (b)

    0

    (c)

    2

    (d)

    4

  16. \(lim_{\alpha \rightarrow {\pi/4}}{sin \alpha -cos \alpha \over \alpha -{\pi\over 4}}\) is

    (a)

    \(\sqrt{2}\)

    (b)

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

    (c)

    1

    (d)

    2

  17. The function is not defined for x = −1. The value of ( 1) f − so that the function extended by this value is continuous is

    (a)

    \({2\over3}\)

    (b)

    -\({2\over3}\)

    (c)

    1

    (d)

    0

  18. Let A and B be two events such that \(P(\overline{A\cup B})={1\over6}, P(A\cap B)={1\over4}\) and \({P(\overline{A})}={1\over4}\)Then the events A and B are 

    (a)

    Equally likely but not independent

    (b)

    Independent but not equally likely

    (c)

    Independent and equally likely

    (d)

    Mutually inclusive and dependent

  19. If X and Y be two events such that P(X/Y)=\({1\over2},P(Y/X)={1\over3}\) and \(P(X\cap Y)={1\over6}\)then P(x\(\cup\)y)is

    (a)

    \({1\over3}\)

    (b)

    \({2\over5}\)

    (c)

    \({1\over6}\)

    (d)

    \({2\over3}\)

  20. In a certain college 4% of the boys and 1% of the girls are taller than 1.8 meter. Further 60% of the students are girls. If a student is selected at random and is taller than 1.8 meters, then the probability that the student is a girl is

    (a)

    \({2\over 11}\)

    (b)

    \({3\over 11}\)

    (c)

    \({5\over 11}\)

    (d)

    \({7\over 11}\)

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