If `x^3-2x^2y^2+5x+y-5=0` and `y(1)=1`, then (a)`y^(prime)(1)=4/3` (b) `y'(1)=-4/3` (c)`y''(1)=-8(22)/(27)` (d) `y^(prime)(1)=2/3`

If x^3-2x^2y^2+5x+y-5=0a n dy(1)=1,t h e n y^(prime)(1)=4/3 (b) y^(1)=-4/3 y^(1)=-8(22)/(27) (d) y^(prime)(1)=2/3

If (x+y)^3-\ (x-y)^3-6y\ (x^2-y^2)=\ k y^3, then k= (a)1 (b) 2 (c) 4 (d) 8

If x^2+y^2=1,t h e n (a) y y^('')-2(y^(prime))^2+1=0 (b) yy^('')+(y^(prime))^2+1=0 (c) y y^('')+(y^(prime))^(-2)-1=0 (d) y y^('')+2(y^(prime))^2+1=0

Which of the following line is passing through point of intersection of line (x-4)/(2)=(y-3)/(2)=(z-5)/(1) and the plane x+y+z=2 (a) (x)/(2)=(y+1)/(3)=(z-3)/(4) (b) (x-2)/(3)=(y-1)/(3)=(z-3)/(2) (c) (x)/(2)=(y+1)/(3)=(z-2)/(4) (d) (x-2)/(2)=(y+1)/(3)=(z+3)/(4)

If y=y(x) and ((2+sinx)/(y+1))dy/dx=-cosx, y(0)=1 , then y(pi/2) equals (A) 1/3 (B) 2/3 (C) -1/3 (D) 1

If x^2+y^2=t-1/t and x^4+y^4=t^2+1/t^2, then x^3y (dy)/(dx)= (a) 0 (b) 1 (c) -1 (d) none of these

Equation of theine passing through hati+hatj-3hatk and perpendiculr to the plane 2x-4y+3z+5=0 is (A) (x-1)/2=(1-y)/(-4)=(z-3)/3 (B) (x-1)/2=(1-y)/4=(z+3)/3 (C) (x-2)/1=(y+4)/1)=(z-3)/3 (D) (x-1)/(-2)=(1-y)/(-4)=(z-3)/3

Perpendiculars are drawn from points on the line (x+2)/2=(y+1)/(-1)=z/3 to the plane x + y + z=3 The feet of perpendiculars lie on the line (a) x/5=(y-1)/8=(z-2)/(-13) (b) x/2=(y-1)/3=(z-2)/(-5) (c) x/4=(y-1)/3=(z-2)/(-7) (d) x/2=(y-1)/(-7)=(z-2)/5

The locus of the foot of the perpendicular from the origin on each member of the family (4a+ 3)x - (a+ 1)y -(2a+1)=0 (a) (2x-1)^(2) +4 (y+1)^(2) = 5 (b) (2x-1)^(2) +(y+1)^(2) = 5 (c) (2x+1)^(2)+4(y-1)^(2) = 5 (d) (2x-1)^(2) +4(y-1)^(2) = 5

If the hyperbola xy=c^(2) intersects the circle x^(2)+y^(2)=a^(2)" is four points "P(x_(1),y_(1)), Q(x_(2),y_(2)), R(x_(3),y_(3)) and S(x_(4),y_(4)) then show that (i) x_(1)+x_(2)+x_(3)+x_(4)=0 (ii) y_(1)+y_(2)+y_(3)+y_(4)=0 (iii) x_(1)x_(2)x_(3)x_(4)=c^(4) (iv) y_(1)y_(2)y_(3)y_(4)=c^(4)