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A variable plane moves in such a way tha...

A variable plane moves in such a way that the sum of the reciprocals of its intercepts on the three coordinate axes is constant. Prove that the plane passes through a fixed point.

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A variable plane moves in such a way that the sum of the reciprocals of its intercepts on three coordinate axes is constant . Prove that the plane passes through a fixed point.

A straight line moves in such a manner that the sum of the reciprocals of its intercepts upon the axes is always constant. Show that the line passes throught a fixed point .

A straight line moves in such a maaner that the sum of the reciprocals of its intercepts upon the coordinate axes is always (1)/(2) . Show that line always passes through the point (2,2)

Show that the sum of the intercepts of the tangent to the curve sqrtx+sqrty=sqrta on the coordinate axes is constant.

Sum of the reciprocal intercepts on the axes by a moving straight line in its all position remain constant .Show that straight line always passes throguh a fixed point .

If the sum of the squares of the distance of a point from the three coordinate axes is 36, then find its distance from the origin.

A straigh line passes through the point (2,3) and is such that the sum of its intercepts on the coordinate axes is 10. Find the equation of the straight line.

Find the equation of a line that cuts off equal intercepts on the coordinate axes and passes through the point (2,3).

A point P is moving in a cartesian plane in such a way that the area of the rectangle formed by the lines through P parallel to the coordinate axes together with ccordinate axes is constant. Find the equation of the locus of P .

Prove that the locus of the point that moves such that the sum of the squares of its distances from the three vertices of a triangle is constant is a circle.

UNITED BOOK HOUSE-SET 13-EXERCISE
  1. Prove that the function(sin(x + alpha))/(sin(x + beta)) has neither a ...

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  2. Using the method of differentail find the approximate value of sqrt 0....

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  3. A variable plane moves in such a way that the sum of the reciprocals o...

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  4. If A and B are two independent events, prove that A^C and B are also i...

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  5. Five cards are drawn successively with replacement from a well-shuffle...

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  6. If sin(alpha + beta) = 4/5 and sin (alpha - beta)= 5/13, find the valu...

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  7. If A and B are tow matrices such that AB =O, can we deduce that eithe...

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  8. (AB)^(-1) = B^(-1)A ^(-1) where A and B are invertible matrices satisf...

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  9. Answer the foll. Question : 2.show that |[1+a,1,1],[1,1+b,1],[1,1,1+c]...

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  10. Evaluate:int (dx)/(sqrt (sin^3 xsin(x+alpha)

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  11. Evaluate: int(log(logx)+1/((logx)^2))dx

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  12. Solve:cos^2x (dy)/(dx) + y= tanx(0 le x le pi/2).

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  13. Prove, by vector method or otherwise, that the point of intersectio...

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  14. Find the value of lambda if three vectors veca= 2hati-hatj+hatk,vecb= ...

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  15. A candidate is selected for interview for the three posts. For the fir...

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  16. For a random variable X, it is given, E(x) = 10 and var(x) = 25. Find ...

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  17. A stone is dropped into a quiet lake and waves moves in circles at a s...

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  18. If the sum of the lengths of the hypotenuse and another side of a righ...

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  19. Find the equations of the tangents to the ellipse 2x^2 + 3y^2 = 30, wh...

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  20. Find the foot of the perpendicular drawn from the point (2 hati - hatj...

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