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

12th Standard EM

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Maths

Time : 01:00:00 Hrs
Total Marks : 38

Part A

19 x 2 = 38
1. Find the rank of the matrix A =$\left[ \begin{matrix} 4 \\ 7 \end{matrix}\begin{matrix} 5 \\ -3 \end{matrix}\begin{matrix} -6 \\ 0 \end{matrix}\begin{matrix} 1 \\ 8 \end{matrix} \right]$.

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

3. Find value of a for which the sum of the squares of the equation x2 - (a- 2) x - a-1=0 assumes the least value.

4. Ecalute $sin\left( { cos }^{ -1 }\left( \cfrac { 3 }{ 5 } \right) \right)$

5. Find the length of the tangent from (2, -3) to the circle x2 + y2 - 8x - 9y + 12 = 0.

6. 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.

7. If the planes ${ \overset { \rightarrow }{ r } }.\left( \overset { \wedge }{ i } +2\overset { \wedge }{ j } +3\overset { \wedge }{ k } \right) =7$=and ${ \overset { \rightarrow }{ r } }.\left( \lambda \overset { \wedge }{ i } +2\overset { \wedge }{ j } -7\overset { \wedge }{ k } \right) =26$ are perpendicular. Find the value of λ.

()

∆=4

8. At what point on the curve y=x2 on [-2,2] is the tangent parallel to X-axis?

9. Verify Rolle ’s Theorem for $f(x)=\left| x-1 \right| ,O\le x\le 2$

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

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

12. Evaluate $\int _{ 1 }^{ 2 }{ \frac { 3x }{ { 9x }^{ 2 }-1 } dx }$

13. Evaluate $\int _{ 0 }^{ \infty }{ \left( { a }^{ -x }-{ b }^{ -x } \right) } dx$

14. Find the area bounded by y=cosx,y=x+1,y=0.

15. Solve: $\frac{dy}{dx}=1+e^{x-y}$

16. Define discrete random variable

17. A coin is tossed twice. If X is a random variable defined as the number of heads minus the number of tails, then obtain its probability distribution.

18. Show that p v (q ∧ r) is a contingency.

19. Form the truth table of (~P)➝(~q).