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Show that the relation R in the set A = {1, 2, 3, 4, 5} given by R = {(a, b) : |a – b| is divisible by 2} is an equivalence relation. Write all the quivalence classes of R.

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XII BOARDS PREVIOUS YEAR-BOARD PAPER SOLUTIONS-All Questions
  1. Solve the differential equation : (xsin^2(y/x)-y)dx+xdy=0 given y=pi/4...

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  2. The sum of surface areas of a sphere and a cuboid with sides x/3,x and...

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  3. Show that the relation R in the set A = {1, 2, 3, 4, 5} given by R = {...

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  4. Using properties of determinants, solve for x:|[a+x, a-x, a-x],[ a-...

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  5. A trust fund has Rs. 35,000 is to be invested in two different types o...

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  6. Find the solution f the differential equation (dy)/(dx)=x^3e^(-2y)dot

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  7. In the interval 2/pi<x<pi, find the value of x for which the matrix (2...

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  8. Write the vector equation of the line passing through (1,2,3) and pe...

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  9. Express the matrix A=[2 4-6 7 3 5 1-2 4] as the sum of a symmetric and...

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  10. Write the direction ratios of the vector 3 vec a+2 vec b where vec a=...

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  11. Find the vector and cartesian equations of the plane passing through t...

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  12. Solve the differential equation (dy)/(dx)-3ycotx=sin2x given y=2 when ...

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  13. Solve for x :tan^(-1)((1-x)/(1+x))=1/2tan^(-1)x ,x >0

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  14. Prove that 2tan^(-1)(1/2)+tan^(-1)(1/7)=sin^(-1)((31)/(25sqrt(2)))

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  15. Find : int0^(1/(sqrt(2)))(sin^(-1)x)/((1-x^2)^(3/2))dxdot

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  16. Find : intx/((x^2+1)(x-1))dx

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  17. Find the areas of the region {x , y}: y^2lt=4x ,4x^2+4y^2lt=9}, using ...

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  18. Find the area enclosed by the parabola 4y=3x^2 and the line2y = 3x + ...

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  19. Find the projection of the vector vec a=2 hat i+3 hat j+2 hat k on th...

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  20. If y=A e^(m x)+B e^(n x), show that (d^2y)/(dx^2)-((m+n)dy)/(dx)+m n y...

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