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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)

    ()

    -1

  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.

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