Eamcet - Maths - Limits

If x√(1+y)+y√(1+x)=0 then dy/dx is equal to

A.  1/(1+x)2

B.  -[1/(1+x)2]

C.  1/1+x2

D.  1/1-x2

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If ∫sin-1[2x/(1+x2)]dx=f(x)-log(1+x2)+c then f(x) is equal to

A.  2x tan -1 x

B.  -2x tan -1 x

C.  x tan -1 x

D.  -x tan -1 x

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If x2y-x3(dy/dx)=y4cosx then x3y is equal to

A.  sin x

B.  2 sin x + c

C.  -3 sin x + c

D.  3 cos x +c

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If (dy/dx)=[y+xtan(y/x)]/x then sin(y/x) is equal to

A.  cx2

B.  cx

C.  cx3

D.  cx4

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The equation of the hyperbola with its transverse axis is parallel to x-axis, and its centre is (-2,1), the length of transverse axis is 10 and eccentricity 6/5 is

A.  (x-3)2/16-(y+2)2/9=1

B.  (x+2)2/25-(y-2)2/9=1

C.  (x-3)2/16-(y-1)2/11=1

D.  (x-3)2/16-(y-3)2/19=1

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