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Model 3 Mark Creative Questions (New Syllabus) 2020

12th Standard EM

    Reg.No. :
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Maths

Time : 01:00:00 Hrs
Total Marks : 48

    Part A

    16 x 3 = 48
  1. Verify that (A-1)T = (AT)-1 for A=\(\left[ \begin{matrix} -2 & -3 \\ 5 & -6 \end{matrix} \right] \).

  2. Find the locus of Z if |3z - 5| = 3 |z + 1| where z=x+iy.

  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. For the hyperbola 3x2 - 6y2 = -18, find the length of transverse and conjugate axes and eccentricity.

  6. If \(\overset { \rightarrow }{ a } +\overset { \rightarrow }{ b } +\overset { \rightarrow }{ c } =0\) then show that \(\overset { \rightarrow }{ a } \times \overset { \rightarrow }{ b } =\overset { \rightarrow }{ b } \times \overset { \rightarrow }{ c } =\overset { \rightarrow }{ c } \times \overset { \rightarrow }{ a } \)

    ()

    lies in the plane containing \(\overset { \rightarrow }{ b } \) and \(\overset { \rightarrow }{ c } \)

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

  8. Find the intervals of monotonicities of the function f(x)=sinx, xદ[0,2π]

  9. If u=log(x2+y2+z2), then prove that \(x\cfrac { { \partial }^{ 2 }u }{ \partial z\partial x } =y\cfrac { { \partial }^{ 2 }u }{ \partial z\partial x } =z\cfrac { { \partial }^{ 2 }u }{ \partial x\partial y } \)

  10. Evaluate : \(\underset { \left( x,y \right) \rightarrow \left( 2,0 \right) }{ lim } \cfrac { \sqrt { 2x-y-2 } }{ 2x-y-4 } \)

  11. Evaluate \(\int _{ 0 }^{ \pi }{ \sqrt { 1+4{ sin }^{ 2 }\cfrac { x }{ 2 } -4sin\cfrac { x }{ 2 } dx } } \) 

  12. Form the D.E to y2=a(b-x)(b+x) by eliminating a and b as its parameters.

  13. Give any three properties of distribution function.

  14. In a meeting, 70% of the members favour a certain proposal while remaining 30% oppose it. A member is selected at random and we let X = 0 if he opposes, and X = 1 if he is in favour. Find E(X) and Var(X).

  15. Let X be a continuous random variable with \(f(x)=\begin{cases} \frac { 2 }{ { x }^{ 4 } } ,x\ge 1 \\ 0,otherwise \end{cases}\) Find the mean and the variance of X.

  16. Show that (Z3-[0],X3) Satisfies closure, identiy and inverse properties.

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