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Sample 3 Mark Creative Questions (New Syllabus) 2020

12th Standard EM

    Reg.No. :
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Maths

Time : 01:00:00 Hrs
Total Marks : 60

    Part A

    20 x 3 = 60
  1. Verify that (A-1)T = (AT)-1 for A=\(\left[ \begin{matrix} -2 & -3 \\ 5 & -6 \end{matrix} \right] \).

  2. Show that \(\left| \frac { z-3 }{ z+3 } \right| \) = 2 represent a circle.

  3. Solve:(x-1)4+(x-5)4=82

  4. Evaluate \(cos\left[ { cos }^{ -1 }\left( \cfrac { -\sqrt { 3 } }{ 2 } +\cfrac { \pi }{ 6 } \right) \right] \)

  5. Find the value of p so that 3x + 4y - p = 0 is a tangent to the circle x2 +y2 - 64 = 0.

  6. Find the value of c if y = x + c is a tangent to the hyperbola 9x2 - 16y2 = 144.

  7. Prove by vector method, that in a right angled triangle the square of the hypotenuse is equal to the sum of the square of the other two sides.

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    Cartesian equation

  8. Find the equation of normal to the curve y4=ax2at(a,a)

  9. Find the intervals of concavity and the point of inflection of the function f(x)=2x2+5x2-4x

  10. If w = xy + z where x = cos t; y = sin t; z = t find \(\frac{dw}{dt}\)

  11. Find the approximate value of \(\left( \cfrac { 17 }{ 81 } \right) ^{ \frac { 1 }{ 4 } }\) using linear approximation.

  12. Evaluate \(\int _{ 0 }^{ 1 }{ \sqrt { 9-4{ x }^{ 2 } } dx } \)

  13. Find the area bounded by the parabolas \({ x }^{ 2 }=\cfrac { y }{ 4 } \) and x2=9y and the straight line y = 2.

  14. Evaluate \(\int _{ -2 }^{ 3 }{ \left| 1-{ x }^{ 2 } \right| } dx\)

  15. Find the D.E of all circles touching y-axis at the origin.

  16. Solve :\(\cfrac { dy }{ dx } -\cfrac { y }{ x } ={ 2x }^{ 2 },x>0\)

  17. Two cards are drawn successively without replacement from a well shuffled pack of 52 cards. Find the probability distribution of number of spades.

  18. In 3 trials of a binomial distribution, the probability of 2 success is 9 times the probability of 3 success. Find the parameter of p of the distribution.

  19. A person tosses a coin and is to receive Rs.4 for a head and has to pay Rs.2 for a tail. Find the variance of the game.

  20. On the set Q of rational numbers, an operation * is defined as a*b=k(a+b) where k is a given non zero number. Is it associative

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