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Let R be a relation on the set A of orde...

Let R be a relation on the set A of ordered pairs of positive integers defined by (x, y) R (u, v), if and only if xv = yu. Show that R is an equivalence relation.

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ARIHANT PRAKASHAN-VERY SIMILAR TEST 9-Section B
  1. If sin{cot^(-1)(x + 1)} = cos(tan^(-1)x), then find x.

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  2. One kind of cake requires 200 g of flour and 25 g of fat and another k...

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  3. Let R be a relation on the set A of ordered pairs of positive integers...

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  4. Prove that tan{(pi)/(4)+(1)/(2) "cos"^(-1)(a)/(b)}+tan{(pi)/(4)-(1)/(2...

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  5. Two persons A and B throw a die alternately till one of them gets a th...

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  6. A = [(1, 0), (0, 1)], B = [(1, 0), (0, -1)] and C = [(0, 1), (1, 0)], ...

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  7. Prove that abs[[b+c,c+a,a+b],[q+r,r+p,p+q],[y+z,z+x,x+y]]=2abs[[a,b,c]...

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  8. An urn contains 4 white and 6 red balls. Four balls are drawn at rando...

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  9. Using differentials, find the approximate value of (3.68)^(3//2).

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  10. Prove that: y = (4 sin theta)/(2 +cos theta)- theta is an increasing f...

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  11. If xy log(x + y) = 1, then prove that (dy)/(dx) = -(y(x^(2)y + x +...

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  12. If sin 2x = (2t)/(1 + t^(2)), tan y = (2t)/(1 - t^(2)) then find (dy)/...

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  13. Solve (dy)/(dx) + y = cosx - sinx.

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  14. Find the equation of the curve passing through the point (1, 1) whose ...

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  15. Evaluate int(x^(2))/(x^(4)-x^(2)+12)dx.

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  16. Evaluate the following integrals : Evaluate int(0)^(pi//2)(xsinxcosx...

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  17. Find the area bounded by the curve y = x abs(x), X-axis and ordinates ...

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  18. The plane lx+my=0 is rotated about its line of intersection with the p...

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  19. Find the distance of the plane 2x - 3y + 4z - 6 = 0 from the origin an...

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  20. Prove that |veca xx vecb|^(2) = abs(veca)^(2)abs(vecb)^(2) - (veca * v...

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