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Show that the relation R in the set A={x...

Show that the relation R in the set `A={x in Z :0lexle12}` is given by `R={(a,b) : |a-b|" is a multiple of 4"}` is an equivalence relation .

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Hence R is an equivalence relation
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Show that the relation R in the set A = {x in Z : 0 le x le 12} given by R = {a , b) : |a - b| is a multiple of 4} is an equivalence relation.

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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 even}, is an equivalence relation. Show that all the elements of {1,3,5} are related to each other and all the elements of {2,4} are related to each other. But no element of {1,3,5} is related to any element of {2,4}.

Show that the relation R in the set A={1,2,3,4,5} given by R={(a,b) : |a-b| is even}, is an equivalence relation.

Show that the relation R in the set of all natural number, N defined by is an R = {(a , b) : |a - b| "is even"} in an equivalence relation.

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Prove that the relation R in the set of integers z defined by R = { ( x , y) : x-y is an integer } is an equivalence relation.

Show that the relation R in the set of all integers, Z defined by R = {(a, b) : 2 "divides" a - b} is an equivalence relation.

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SUNSTAR PUBLICATION-ANNUAL EXAM QUESTION PAPER MARCH - 2016-PART - C (Answer any ten questions)
  1. Find two numbers whose product is 100 and whose sum is minimum.

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  2. Find the area lying between the curve y^(2) = 4x and the line y=2x

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  3. For any three vectors overset(to)(a) , overset(to)(b) and overset(to) ...

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  4. Find the distance between the lines overset(to)(r ) = hat(i) + 2 hat(j...

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  5. Find the sine of the angle between the vectors hat(i) + 2 hat(j) + 2 h...

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  6. Find the equation of the curve passing through the point (1,1), given ...

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  7. Show that tan^(-1)""(1)/(2) + tan^(-1)""(2)/( 11) + tan^(-1)""(4)/(3) ...

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  8. Using elementary transformations, find the inverse of the matrices ...

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  9. Show that the relation R in the set A={x in Z :0lexle12} is given by R...

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  10. Verify Mean Value Theorem if f(x)= x^(3) - 5x^(2) - 3x in the interval...

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  11. If x=a cos ^(3) theta and y = a sin^(3) theta then (dy)/( dx) =

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  12. Box-I contains 2 gold coins, while another Box-II contains 1 gold and...

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  13. Find int(xdx)/((x+1)(x+2))

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  14. Integrate (2x)/( ( x^(2) + 1) ( x^(2) + 2) ) with respect to x.

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  15. Find two numbers whose product is 100 and whose sum is minimum.

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  16. Find the area lying between the curve y^(2) = 4x and the line y=2x

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  17. For any three vectors overset(to)(a) , overset(to)(b) and overset(to) ...

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  18. Find the distance between the lines overset(to)(r ) = hat(i) + 2 hat(j...

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  19. Find the sine of the angle between the vectors hat(i) + 2 hat(j) + 2 h...

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  20. Find the equation of the curve passing through the point (1,1), given ...

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