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#### Sample 3 Mark Creative Questions (New Syllabus) 2020

12th Standard EM

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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