#### 12th Standard English Medium Maths Reduced Syllabus Creative Three Mark Questions with Answer key - 2021(Public Exam )

12th Standard

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Maths

Time : 01:00:00 Hrs
Total Marks : 75

3 Marks

25 x 3 = 75
1. Solve: 2x + 3y = 10, x + 6y = 4 using Cramer's rule.

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

3. If the rank of the matrix $\left[ \begin{matrix} \lambda & -1 & 0 \\ 0 & \lambda & -1 \\ -1 & 0 & \lambda \end{matrix} \right]$ is 2, then find ⋋.

4. Show that the complex numbers 3 + 2i, 5i, -3 + 2i and -i form a square.

5. Find the locus of z if Re$\\ \left( \frac { \bar { z } +1 }{ \bar { z } -i } \right)$ =0.

6. Find the real solutions of the equation
${ tan }^{ -1 }\sqrt { x(x+1) } +{ sin }^{ -1 }\sqrt { { x }^{ 2 }+x+1 } =\cfrac { \pi }{ 2 }$

7. Find the Cartesian form of the equation of the plane $\overset { \rightarrow }{ r } =\left( s-2t \right) \overset { \wedge }{ i } +\left( 3-t \right) \overset { \wedge }{ j } +\left( 2s+t \right) \overset { \wedge }{ k }$

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s, t

8. 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 $\overset { \rightarrow }{ c }$

9. The side of a square is equal to the diameter of a circle. If the side and radius change at the same rate then find the ratio of the change of their areas.

10. The volume of a cube is increasing at the rate of 8cm3/s.How fast is the surface area increasing when the length of an edge is 12cm?

11. Find the intervals of monotonicities and find the local extremum for the following functions
i) f(x)=20-x-x2
ii) f(x)=x(x-1)(x+1) on [0,2]

12. Find the intervals of concavity and the point of inflection of the function f(x)=2x2+5x2-4x

13. Find the approximate value of f (3.02) where f(x) = 3x2 + 5x +3.

14. If f = $\frac { x }{ { x }^{ 2 }+{ y }^{ 2 } }$ then show that = $x\frac { \partial f }{ \partial x } +y\frac { \partial f }{ \partial y }$ = -f

15. Find the linear approximation to $g(z)=\sqrt [ 4 ]{ zat } z=2$

16. Evaluate : $\underset { \left( x,y \right) \rightarrow \left( 0,0 \right) }{ lim } \cfrac { { x }^{ 2 }-xy }{ \sqrt { x } -\sqrt { y } }$

17. Find the area between the curve y=1-|x| and x-axis

18. Solve: $\frac{dy}{dx}+y=cos x$

19. Obtain the D.E of all circles of radius ‘r’

20. Solve :cosx(1+cosy)dx-siny(1+sinx)dy=0.

21. Out of a group of 60 architects 40 are qualified and co-operative while the remaining are qualified but remain reserved. Two architects are selected from the group at random. Find the probability distribution of the number of architects who are qualified and co-operative. Which of the two values, namely co-cooperativeness or reservedness, mentioned above, do you prefer and why?

22. The distribution of a continuous random variable X in range (−3,3) is given by p.d.f

Verify that the area under the curve is unity.

23. A person tosses a coin and is to receive Rs.4 for a head and has to pay Rs.2 for a tail. Find the variance of the game.

24. If on the set Q of rational numbers, a binary operation * is defined as a*b=λ(a+b) were λ is a nonzero fixed number and its given that * is associative, then the value of λ and what can we say about the operation*?

25. On the set of real numbers * is defined as $a\ast b=k\left( a+b+ab \right)$ where k is a non zero real number.What are the conditions on R and k so that * is associative.