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41.

Let the orthocentre and centroid of a triangle be  A ( -3,5) and B ( 3,3) respectively. If C is the circumcentre of this triangle, then the radius of  the circle having line segment AC as diameter , is


A) 10

B) 210

C) 352

D) 352



42.

A straight line through a fixed point ( 2,3) intersects the coordinate axes at distinct  point P and Q, If O is the origin and the rectangle OPRQ is completed, then the locus of R is 


A) 3x+2y=6

B) 2x+3y=xy

C) 3x+2y=xy

D) 3x+2y=6xy



43.

Let f( x)=x^{2}+\frac{1}{x^{2}} and  g( x)=x^{}-\frac{1}{x^{'}} x \in R - {-1,0,1}. If h( x)=\frac{f( x)}{g( x)} , then the local minimum value of h(x) is


A) 3

B) -3

C) -2\sqrt{2}

D) 2\sqrt{2}



44.

If the curves y^{2}=6x,9x^{2}+by^{2}=16  intersect each other at right angles, then the value of b is


A) 6

B) \frac{7}{2}

C) 4

D) \frac{9}{2}



45.

The sum of the coefficients of all odd degree terms in the expansion is

(x+\sqrt{x^{3}-1})^{5}+(x-\sqrt{x^{3}-1} )^{5},(x>1)is


A) -1

B) 0

C) 1

D) 2



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