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The envelope of the family of straight l...

The envelope of the family of straight lines whose sum of intercepts on the axes is 4 is

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A DAS GUPTA-Some New Pattern Problems-Exercise
  1. The envelope of the family of straight lines whose sum of intercepts o...

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  2. The envelope of the family of tangents to the curve y^2=x is

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  3. The evolute of the curve x^2=4y is

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  4. The area bounded by the curve y= f(x) and the lines x=0, y=0 and x=t, ...

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  5. The radius of curvature of the curve y^2=4x at the point (1, 2) is

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  6. If e1 is the eccentricity of the conic 9x^2+4y^2=36\ a n d\ e2 is the ...

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  7. int (-pi//2)^(pi//2) sin | x | dx is equal to

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  8. int (sin(1/x)cos^3(1/x))/x^2dx is equal to

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  9. If f''(x) lt 0 AA x in (a,b) and (c, f(c)) is a point lying on the cur...

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  10. The family of parabolas with a common vertex at the origin whose foci ...

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  11. The orthogonal trajectory of the family of parabolas y^2 =4ax is

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  12. The curve passing through the point (1, 2) that cuts each member of th...

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  13. The general solution of the equation ((d^3y)/(dx^3)) - 7 ((d^2y)/(dx^...

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  14. Find the differential equation for which the following value of y is t...

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  15. The general solution of the equation (d^3 y)/ (dx^3) +y=0 is

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  16. The value of |U| where U= [(2,3,4),(3,4,5),(4,5,6)]

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  17. show that matrix A = [(3,4),(1,2)] satisfies the equation A^2-5A+2I=0

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  18. The sum of the elements of the product [3, 2,0] and [(3),(2), (0)] is

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  19. The rank of matrix [(x, -1, 0), (0, x, -1), (-1, 0,x)] is 2 then value...

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  20. One of the eigenvalues of A is where A= [(2,5),(7,4)]

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