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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).

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