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Prove that the curves x = y^(2) and xy =...

Prove that the curves `x = y^(2) and xy = k` cut at right angles, if `8k^(2) = 1`.

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MODERN PUBLICATION-TEST PAPER 4-PROBLEM
  1. If f(x)={(ax^2+b if x lt1),(1 if x=1),(2ax-b if xgt1):} is continuous...

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  2. Show that 2 sin x + than x ge 3x all x in (0, pi/20).

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  3. Prove that the curves x = y^(2) and xy = k cut at right angles, if 8k^...

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  4. Evaluate the following integrals int(dx)/(sinx(3+2cosx) put cosx=z

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  5. int0^(pi//2)(sqrttanx+sqrtcotx)dx

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  6. Determine the area of the region bounded by y^2=x^3 and the double ord...

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  7. Vectors vec(a), vec(b) and vec(c) are such that vec(a) + vec(b) + vec(...

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  8. If l(1), m(1), n(1) and l(2), m(2), n(2)  are the direction cosines of...

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  9. Find the equation of the plane Which contains the line of intersection...

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  10. Find the distance of the point (-1,-5,-10) from the point of intersect...

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  11. Let R be the relation on the set R of real numbers such that aRb iff a...

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  12. Prove that the following. [[a-b-c,2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]]=...

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  13. Find the minimum distance of a point on the curve 2/x^2+1/y^2= 1 from...

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  14. A variable plane meets the coordinate axes at A, B, C and is at a cons...

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  15. Find x and y if [[1,3],[2,-1]][[x],[y]] = [[4],[1]].

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  16. If [[3,5,3],[2,4,2],[lambda,7,8]] is a singular matrix, write the valu...

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  17. Let f={(1,a),(2,b),(3,c),(4,d)} and g={(a,x),(b,x),(c,y),(d,x)} Determ...

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  18. Express the value of "cosec"("cos"^(-1) 3/5 +"cos"^(-1) 4/5) in simple...

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  19. Let x Epsilon (2 π/4, π), y=| cos x | +| sin x | what is dy/dx ?

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  20. Write the least value of a for which the function f defined by f(x)=x^...

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