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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. If y=e^a cos^((-1)x)\ ,\ -1\ lt=xlt=1, show that (1-x^2)(d^2y)/(dx^2)-...

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  2. If x\ sqrt(1+y)+y\ sqrt(1+x\ )\ 0,\ -1<x<1,\ x!=y , then prove that...

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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. Evaluate: int2^3 1/x\ dx

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  5. Three bags contain balls as shown in the table below: Bag Numb...

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  6. A diet is to contain at least 80 units of Vitamin A and 100 units o...

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  7. Using matrices, solve the following system of equations: 2x-3y+5z=11...

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  8. Find the equation of the plane passing through the point (-1,3,2) and ...

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  9. Using the method of integration find the area of the region bounded b...

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  10. Show that: tan(1/2sin^(-1)(3/4))=(4-sqrt(7))/3

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  11. Find the probability of throwing at most 2 sixes in 6 throws of a s...

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  12. Find the equation of the plane passing through the point (1, 3, 2) ...

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  13. A window is in the form of a rectangle surmounted by a semi-circula...

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  14. Using the method of integration, find the area of the region bounde...

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  15. Find the mean number of heads in three tosses of a fair coin.

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  16. The lengths of the sides of an isosceles triangle are 9+x^2,9+x^2 and ...

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  17. If vectors vec a=2 hat i+2 hat j+3 hat k ,\ vec b=- hat i+2 hat j+ h...

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  18. Find the shortest distance between the lines: vec r=6 hat i+2 hat j+2...

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  19. Find the coordinates of the point where the line through (3, –4, –5...

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  20. Show that the function f(x)=|x-3|,\ x in \ |R , is continuous but n...

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