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#### Model 2 Mark Creative Questions (New Syllabus) 2020

12th Standard EM

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Maths

Time : 01:00:00 Hrs
Total Marks : 40

Part A

20 x 2 = 40
1. Show that the system of equations is inconsistent. 2x + 5y= 7, 6x + 15y = 13.

2. If 1, ω, ω2 are the cube roots of unity show that (1+ω2)3 - (1+ω)3 =0

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. Find the principal value of sin-1(-l).

5. Prove that $2{ tan }^{ -1 }\left( \cfrac { 2 }{ 3 } \right) ={ tan }^{ -1 }\left( \cfrac { 12 }{ 5 } \right)$

6. If a parabolic reflector is 24 cm in diameter and 6 cm deep, find its locus.

7. Find the equation of the hyperbola whose vertices are (0, ±7) and e = $\frac { 4 }{ 3 }$

8. Find the Cartesian equation of a.line passing through the pointsA(2, -1, 3) and B(4, 2, 1)

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9. A man 2 m high walks at a uniform speed of 5 km/ hr away from a lamp post 6 m high. Find the rate at which the length of his shadow increases?

10. Expand the polynomial f(x)=x2-3x+2 in power of (x-2)

11. If f (x, y) = 2x3 - 11x2y + 3y3, prove that $x\frac { \partial f }{ \partial x } +y\frac { \partial f }{ \partial y } =3f$

12. If $w={ e }^{ { x }^{ 2 }+{ y }^{ 2 } }$ ,x=cosθ,y=sinθ, find $\cfrac { dw }{ d\theta }$

13. Prove that $\int _{ 0 }^{ \frac { \pi }{ 2 } }{ log(tan \ x)dx }$

14. Find the area bounded by the curve y=sin2x between the ordinates x=0.x=π and x-axis.

15. Form the differential equation satisfied by are the straight lines in my-plane.

16. What is meant by the expected value of a random variable X?

17. The probability distribution of a random variable X is given under :

Find (i) k
(ii) E(X)

18. Show that p v (q ∧ r) is a contingency.

19. In Z, the set of integers, an operation * is defined as a✳️b=2(a+b). Check whether * is associative.

20. Form the truth table of (~q)^p.