Important 2 mark question 2

11th Standard

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Maths

Use blue pen Only

Time : 01:00:00 Hrs
Total Marks : 40

    Part A

    Answer all the questions

    20 x 2 = 40
  1. Write the following in roster form. 
    {x\(\in \)N:x2<121 and x is a prime}.

  2. Write the following in roster form.
    The set of all positive roots of the equation (x-1)(x+1)(x2-1)=0.

  3. By taking suitable sets A, B, C, verify the following results:
    \(\times\) (B\(\cup \)C)=(A\(\times\)B) \(\cup \) (A\(\times\)C)

  4. By taking suitable sets A, B, C, verify the following results:
    C-(B-A) = (C\(\cap \) A) \(\cup \) (C\(\cap \)B')

  5. Let f= {(1, 2), (3,4), (2, 2)} and s = {(2, 1), (3, 1), (4, 2)}. Find gof and fog.

  6. Let f = {(1, 4), (2, 5), (3, 5)} and g = {(4, 1), (5, 2), (6, 4)}. Find gof. Can you find fog?

  7. Consider N = {1, 2, 3, ..........} set of all natural numbers.

  8. Determine the region in the Plane determined by the inequalities.
    \(3x+5y\ge 45,\ x\ge 0,\ y\ge 0\)

  9. if \(\alpha \) and \(\beta \) are the roots of the quadratic equation \({ x }^{ 2 }+\sqrt { 2x } +3=0\) , form a quadratic polynomial with zeros \(\frac { 1 }{ \alpha } ,\frac { 1 }{ \beta } \)

  10. Simplify \(\sqrt{x^2-10x+25}\)

  11. Two vehicles leave the same place P at the same time moving along two different roads. One vehicle moves at an average speed of 60 km/hr and the other vehicle moves at an average speed of 80 km/hr. After half an hour the vehicle reach the destinations A and B. If AB subtends 60 at the initial point P, then find AB.

  12. Find the value of sin 105o

  13. If \(\theta +\phi =\alpha\)  and \(tan​​\theta=k\ \tan\ \phi \) then prove that \(\sin { \left( \theta -\phi \right) } =\frac { k-1 }{ k+1 } \sin { \alpha } \).

  14. Find the value of sin 2θ, when sin θ =\(\frac{12}{13}\),θ lies in the first quadrant.

  15. Find the values of cos 150.

  16. Find the principal value of sin-1\(({\sqrt{3}\over2})\)

  17. If A+B+C=\(\pi\),prove the following 1<cosA+cosB+cosC\(\le\frac{3}{2}\)

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