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51.

The solution  of the differential equation (2x-3y+5)dx+(9y+6x-7) dy =0 , is 


A) 3x-3y+8 log |6x-9y-1|=c

B) 3x-9y+8 log |6x-9y-1|=c

C) 3x-9y+8 log |2x-3y-1|=c

D) 3x-9y+4 log |2x-3y-1|=c



52.

The differential equation representing the family of circles of constant radius r is 


A) r^{2} y"=[1+(y')^{2}]^{2}

B) r^{2} (y")^{2}=[1+(y')^{2}]^{2}

C) r^{2} (y")^{2}=[1+(y')^{2}]^{3}

D) (y")^{2}=r^{2}[1+(y')^{2}]^{2}



53.

Area of the region (in sq units)  bounded by the curve y =\sqrt{x}, x= \sqrt{y} and the lines x=1, x=4 , is 


A) \frac{8}{3}

B) \frac{49}{3}

C) \frac{16}{3}

D) \frac{14}{3}



54.

Consider the function f(x)=2x^{3}-3x^{2}-x+1     and the  intervals I_{1}=[-1,0],I_{2}= [0,1], I_{3}  =[1,2], I_{4}=[-2,-1]

Then,


A) f(x) =0 has a root in the intervals I_{1} and I_{4} only

B) f(x) =0 has a root in the intervals I_{1} and I_{2} only

C) f(x) =0 has a root in every interval except in I_{4}

D) f(x)=0 has a root in all the four given intervals



55.

If y=\sqrt{x+\sqrt{y+\sqrt{x+\sqrt{y+..........\infty}}}}, then \frac{dy}{dx}


A) \frac{y^{3}-x}{2y^{2}-2xy+1}

B) \frac{x+y^{3}}{2y^{2}-x}

C) \frac{y+x}{y^{2}-2x}

D) \frac{y^{2}-x}{2y^{3}-2xy-1}



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