Important 5mark questions

11th Standard

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Maths

Use blue pen Only

Time : 00:50:00 Hrs
Total Marks : 75

    Part A

    Answer all the questions

    15 x 5 = 75
  1. Let A={1,2,3,4} and B = {a,b,c,d}. Give a function from A\(\rightarrow\)B for each of the following:
    neither one- to -one and nor onto.

  2. Let A={1,2,3,4} and B = {a,b,c,d}. Give a function from A\(\rightarrow\)B for each of the following:
    not one-to-one but onto.

  3. Let A={1,2,3,4} and B = {a,b,c,d}. Give a function from A\(\rightarrow\)B for each of the following:
    one-to-one but not onto.

  4. Find the largest possible domain of the real valued function f(x)=\(\frac { \sqrt { 4-{ x }^{ 2 } } }{ \sqrt { { x }^{ 2 }-9 } } \)

  5. Prove that\(\frac { sin4x+sin2x }{ cos4x+cos2x } =tan3x\)

  6. Prove that\(1+cos2x+cos4x+cos6x=4cosx\quad cos2x\quad cos3x\)

  7. Prove that \(sin\frac { \theta }{ 2 } sin\frac { 7\theta }{ 2 } +sin\frac { 3\theta }{ 2 } sin\frac { 11\theta }{ 2 } =sin2\theta sin5\theta \)

  8. find the value of sin \(\left( -\frac { 11\pi }{ 3 } \right) \)

  9. In ABC, prove that (a2 - b2 +c2) tan B = (a2 +b2 -c2) tan C

  10. If A + B + C = \(\pi\), prove the following
    cos A + cos B + cos C = 1 + 4 sin \(({A\over 2})\)sin \(({B\over 2})\)sin\(({C\over 2})\)

  11. In a triangle  ABC, prove that \({a^2+b^2\over a^2+c^2}={1+cos(A-B)cos C\over 1+cos (A-C)cos B}\)

  12. Using Heron's formula, show that the equilateral triangle has the maximum area for any fixed perimeter. [Hint: In xyz\(\le\)  k, maximum occurs when x = y = z]

  13. A ray of light coming from the point (1,2)is reflected at a point A on the x-axis and it passes through the point (5,3). Find the co-ordinates of the point A.

  14. Find the distance of the line 4x - y = 0 from the point p( 4,1) measured along the line making an angle of 135° with the positive x-axis.

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