2.If `(3)/(x+y)+(2)/(x-y)=2` and `(9)/(x+y)-(4)/(x-y)=1`,then a) `x=(1)/(2),y=(3)/(2),`b) `x=(5)/(2),y=(1)/(2),` c) `x=(3)/(2),y=(1)/(2),` d) `x=(1)/(2),y=(5)/(2)`

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)

Find (x+y)-:(x-y), if (i) x=2/3, y=3/2 (ii) x=2/5, y=1/2 (iii) x=5/4, y=(-1)/3

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 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)

The value of |(a_(1) x_(1) + b_(1) y_(1),a_(1) x_(2) + b_(1) y_(2),a_(1) x_(3) + b_(1) y_(3)),(a_(2) x_(1) +b_(2) y_(1),a_(2) x_(2) + b_(2) y_(2),a_(2) x_(3) + b_(2) y_(3)),(a_(3) x_(1) + b_(3) y_(1),a_(3) x_(2) + b_(3) y_(2),a_(3) x_(3) + b_(3) y_(3))| , is

Find (x+y)+(x-y), if x=5/4, y=(-1)/3 (ii) x=2/7, y=4/3 (iii) x=1/4, y=3/2

Find (x+y)+(x-y), if x=2/3, y=3/2 (ii) x=2/5, y=1/2

The image of the line (x-1)/3=(y-3)/1=(z-4)/(-5) in the plane 2x-y+z+3=0 is the line (1) (x+3)/3=(y-5)/1=(z-2)/(-5) (2) (x+3)/(-3)=(y-5)/(-1)=(z+2)/5 (3) (x-3)/3=(y+5)/1=(z-2)/(-5) (3) (x-3)/(-3)=(y+5)/(-1)=(z-2)/5

If x_(1),x_(2) "and" y_(1),y_(2) are the roots of the equations 3x^(2) -18x+9=0 "and" y^(2)-4y+2=0 the value of the determinant |{:(x_(1)x_(2),y_(1)y_(2),1),(x_(1)+x_(2),y_(1)+y_(2),2),(sin(pix_(1)x_(2)),cos (pi//2y_(1)y_(2)),1):}| is

Find the horizontal, vertical and oblique asymptotes of each of the curves. {:((a),y=x/(x+4),,(b),y=(x^(2)+4)/(x^(2)-1)),((c),y=x^(3)/(x^(2)+3x-10),,(d),y=(x^(3)+1)/(x^(3)+x)),((e),y=x/(root(4)(x^(4)+1)),,(f),y=(x-9)/(sqrt(4x^(2)+3x+2))),((g),y=1/(2^(x)-1),,(h),y=1/(log_(e) x)),((i),y= 1/(2^(x) - 1),,,):}