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#### Important 2 Mark Creative Questions (New Syllabus) 2020

12th Standard EM

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Maths

Time : 01:00:00 Hrs
Total Marks : 52

Part A

26 x 2 = 52
1. Show that the system of equations is inconsistent. 2x + 5y= 7, 6x + 15y = 13.

2. If (cosθ + i sinθ)2 = x + iy, then show that x2+y2 =1

3. Find the modules of (1+ 3i)3

4. Find x If $x=\sqrt { 2+\sqrt { 2+\sqrt { 2+....+upto\infty } } }$

5. Find the principal value of ${ cos }^{ -1 }\left( \cfrac { -1 }{ 2 } \right)$

6. Prove that $2{ tan }^{ -1 }\left( \cfrac { 2 }{ 3 } \right) ={ tan }^{ -1 }\left( \cfrac { 12 }{ 5 } \right)$

7. Find the equation of the parabola with vertex at the origin, passing through (2, -3) and symmetric about x-axis

8. Find the eccentricity of the hyperbola. with foci on the x-axis if the length of its conjugate axis is ${ \left( \frac { 3 }{ 4 } \right) }^{ th }$ of the length of its tranverse axis.

9. A force of magnitude 6 units acting parallel to $\overset { \wedge }{ 2i } -\overset { \wedge }{ 2j } +\overset { \wedge }{ k }$ displaces the point of application from (1, 2, 3) to (5, 3, 7). Find the work done.

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b

10. Flnd the equation of the plane containing the line of intersection of the planes x + y + Z - 6 = 0 and
2x + 3y + 4z + 5 = 0 and passing through the point (1, 1, 1)

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x = -1 is one root

11. A man 2 m high walks at a uniform speed of 5 km/ hr away from a lamp post 6 m high. Find the rate at which the length of his shadow increases?

12. Verify Lagrange’s Mean Value theorem for $f(x)=\sqrt { x-2 }$ in the interva [2,6]

13. Prove that the function f(x)=2x2+3x is strictly increasing on $\left[ -\cfrac { 1 }{ 2 } ,\cfrac { 1 }{ 2 } \right]$

14. Use differentials to find $\sqrt{25.2}$

15. If w=xyexy find $\cfrac { { \partial }^{ 2 }u }{ \partial x\partial y }$

16. Evaluate $\int _{ 0 }^{ \frac { \pi }{ 2 } }{ log(tanx)dx } =0$

17. Find the volume of the solid generated when the region enclosed by $y=\sqrt { x } ,y=2$  and x = 0 is revolved about y-axis.

18. Find the area enclosed between the parabola y2=4ax and the line x=a,x=9a.

19. Solve: x$\frac{dy}{dx}=x+y$

20. Form the D.E of family of parabolas having vertex at the origin and axis along positive y-axis.

21. How many types of random variables are there? What are they?

22. Prove that E(aX+b)=aE(X)+b

23. Is it possible that the mean of a binomial distribution is 15 and its standard deviation is 5?

24. In the set of integers under the operation * defined by a * b = a + b - 1. Find the identity element.

25. A and B are Boolean matrices of order 2X2.If AVB=A, is it necessary that $B=\left( \begin{matrix} 0 & 0 \\ 0 & 0 \end{matrix} \right)$

26. p:N is divisible buy 4 and q:N is an even number. Whether p➝q is true.