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Important 2 Mark Creative Questions (New Syllabus) 2020

12th Standard EM

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Maths

Time : 01:00:00 Hrs
Total Marks : 52

    Part A

    26 x 2 = 52
  1. Show that the system of equations is inconsistent. 2x + 5y= 7, 6x + 15y = 13.

  2. If (cosθ + i sinθ)2 = x + iy, then show that x2+y2 =1

  3. Find the modules of (1+ 3i)3

  4. Find x If \(x=\sqrt { 2+\sqrt { 2+\sqrt { 2+....+upto\infty } } } \)

  5. Find the principal value of \({ cos }^{ -1 }\left( \cfrac { -1 }{ 2 } \right) \)

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

  7. Find the equation of the parabola with vertex at the origin, passing through (2, -3) and symmetric about x-axis

  8. Find the eccentricity of the hyperbola. with foci on the x-axis if the length of its conjugate axis is \({ \left( \frac { 3 }{ 4 } \right) }^{ th }\) of the length of its tranverse axis.

  9. A force of magnitude 6 units acting parallel to \(\overset { \wedge }{ 2i } -\overset { \wedge }{ 2j } +\overset { \wedge }{ k } \) displaces the point of application from (1, 2, 3) to (5, 3, 7). Find the work done.

    ()

    b

  10. Flnd the equation of the plane containing the line of intersection of the planes x + y + Z - 6 = 0 and
    2x + 3y + 4z + 5 = 0 and passing through the point (1, 1, 1)

    ()

    x = -1 is one root

  11. 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?

  12. Verify Lagrange’s Mean Value theorem for \(f(x)=\sqrt { x-2 } \) in the interva [2,6]

  13. Prove that the function f(x)=2x2+3x is strictly increasing on \(\left[ -\cfrac { 1 }{ 2 } ,\cfrac { 1 }{ 2 } \right] \)

  14. Use differentials to find \(\sqrt{25.2}\)

  15. If w=xyexy find \(\cfrac { { \partial }^{ 2 }u }{ \partial x\partial y } \)

  16. Evaluate \(\int _{ 0 }^{ \frac { \pi }{ 2 } }{ log(tanx)dx } =0\)

  17. Find the volume of the solid generated when the region enclosed by \(y=\sqrt { x } ,y=2\)  and x = 0 is revolved about y-axis.

  18. Find the area enclosed between the parabola y2=4ax and the line x=a,x=9a.

  19. Solve: x\(\frac{dy}{dx}=x+y\)

  20. Form the D.E of family of parabolas having vertex at the origin and axis along positive y-axis.

  21. How many types of random variables are there? What are they?

  22. Prove that E(aX+b)=aE(X)+b

  23. Is it possible that the mean of a binomial distribution is 15 and its standard deviation is 5?

  24. In the set of integers under the operation * defined by a * b = a + b - 1. Find the identity element.

  25. A and B are Boolean matrices of order 2X2.If AVB=A, is it necessary that \(B=\left( \begin{matrix} 0 & 0 \\ 0 & 0 \end{matrix} \right) \)

  26. p:N is divisible buy 4 and q:N is an even number. Whether p➝q is true.

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