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

12th Standard EM

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Maths

Time : 01:00:00 Hrs
Total Marks : 57

Part A

19 x 3 = 57
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: 2x+2x-1+2x-2=7x+7x-1+7x-2

4. Evaluate $cos\left[ { cos }^{ -1 }\left( \cfrac { -\sqrt { 3 } }{ 2 } +\cfrac { \pi }{ 6 } \right) \right]$

5. Find the equation of the hyperbola whose conjugate axis is 5 and the distance between the foci is 13.

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. A cylindrical hole 4 mm in diameter and 12 mm deep in a metal block is reboared to increase the diameter to 4.12mm. Estimate the amount of metal removed

8. Find two numbers whose sum is 100 and whose product is a maximum.

9. If w = xy + z where x = cos t; y = sin t; z = t find $\frac{dw}{dt}$

10. If w=xy+z and x=cot, y=sint, z=t then find $\cfrac { dw }{ dt }$

11. z is a homogeneous function in x and y of degree n then prove that $x\cfrac { \partial z }{ \partial x } +y\cfrac { \partial z }{ \partial y } =(ax+by+n)$ ,where v=zeax+by

12. Evaluate $\int _{ 3 }^{ 6 }{ \cfrac { \sqrt { x } }{ \sqrt { 9 } -x+\sqrt { x } } dx }$

13. Evaluate $\int _{ 0 }^{ \frac { \pi }{ 2 } }{ { sin }^{ 0 }xdx }$

14. Form the D.E of the family of curves c(y+c)2=x2,where c is the parameter.

15. Solve :(x2-yx2)dy+(y2+x2y2)dx=0

16. From a lot of 10 bulbs, which includes 3 defective bulbs, a sample of 2 bulbs is drawn at random. Find the probability distribution of defective bulbs.

17. In 3 trials of a binomial distribution, the probability of 2 success is 9 times the probability of 3 success. Find the parameter of p of the distribution.

18. 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.

19. On the set Q of rational numbers, an operation * is defined as a*b=k(a+b) where k is a given non zero number. Is it associative