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

12th Standard EM

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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 $\overset { \rightarrow }{ a } \times \overset { \rightarrow }{ b } =\overset { \rightarrow }{ b } \times \overset { \rightarrow }{ c } =\overset { \rightarrow }{ c } \times \overset { \rightarrow }{ a }$

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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.