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Under which conditions the straight line...

Under which conditions the straight line `(x-a)/l = (y-b)/m = (z-c)/n` intersects the plane `Ax + By + Cz = 0` at a point other than (a,b,c)?

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MODERN PUBLICATION-SAMPLE PAPER 2014-EXERCISE
  1. Write the differential equation of the family of straight lines parall...

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  2. Is vec 0 unique

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  3. Under which conditions the straight line (x-a)/l = (y-b)/m = (z-c)/n i...

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  4. How many straight lines in space through the origin are equally inclin...

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  5. What is the value of : C3^20 + C4^20 + C5^20 + ..........+ C17^20 ?

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  6. If an event A is independent of it self, then what is P(A)?

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  7. If y=cosec^(-1)x, then find (dy)/(dx) and determine its value at x=-2.

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  8. Show that no two normals to a parabola are parallel.

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  9. Examine the differentiability of ln x^(2) for all real values of x.

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  10. Interpret Lagrange's mean value theorem geometrically.

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  11. Find the following limits:lim(xrarr0)(sinx/x)^(1/x)

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  12. Evaluate the following integrals : int(dx)/(x^(1/2)+x^(1/3))

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  13. Evaluate : int (xe^x)/(x+1)^(2) dx

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  14. Evaluate : int (0)^(3/2) [x^(2)]dx.

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  15. Find the area of the region bounded by the curve y=sin^(3)x and the st...

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  16. Solve the following differential equations (1+y^2)dx+(x-e^(-tan^(-1)...

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  17. Solve : (x+y)dy +(x-y)dx = 0.

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  18. Find the differential equation whose general solution is ax^(2) + by =...

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  19. If the sum of two unit vectors is a unit vectors find the magnitude of...

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  20. Find the equation of the plane Paralel to the plane 2x-y+3z+1=0 and at...

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