If `x ,y in R a n d2x^2+6x y+5y^2=1,t h e n` a. `|x|lt=sqrt(5)` b. `|x|geqsqrt(5)` c. `y^2lt=2` d. `y^2lt=4`

If x ,y in R satify the equation x^2+y^2-4x-2y+5=0, then the value of the expression [(sqrt(x)-sqrt(y))^2+4sqrt(x y)]//(x+sqrt(x y)) is a. sqrt(2)+1 b. (sqrt(2)+1)/2 c. (sqrt(2)-1)/2 d. (sqrt(2)+1)/(sqrt(2))

If a,b, x in R, a lt b and y =(x^(2) -ab)/(2x-a -b), then-

xy=( x+y )^n and dy/dx = y/x then n= 1 b. 2 c. 3 d. 4

If x ,y ,z are real and 4x^2+9y^2+16 z^2-6x y-12 y z-8z x=0,t h e nx , y,z are in a. A.P. b. G.P. c. H.P. d. none of these

The equation of the line that touches the curves y=x|x| and x^2+(y-2)^2=4 , where x!=0, is: (a)y=4 sqrt(5) x +20 (b)y=4 sqrt(3) x -12 (c)y=0 (d) y=-4 sqrt(5) x -20

The image of the pair of lines represented by a x^2+2h x y+b y^2=0 by the line mirror y=0 is a. a x^2-2h x y-b y^2=0 b. b x^2-2h x y+a y^2=0 c. x^2+2h x y+a y^2=0 d. a x^2-2h x y+b y^2=0

The locus of a point that is equidistant from the lines x+y - 2sqrt2 = 0 and x + y - sqrt2 = 0 is (a) x+y-5sqrt2=0 (b) x+y-3sqrt2=0 (c) 2x+2y-3 sqrt2=0 (d) 2x+2y-5sqrt5=0

IF x^3-2x^2y^2+5x+y-5=0 and y(1)=1, then -

If y=a x^(n)+b x^(-n) ,then x^2(d^2y)/(dx^2) is equal to

The ellipse 4x^2+9y^2=36 and the hyperbola a^2x^2-y^2=4 intersect at right angles. Then the equation of the circle through the points of intersection of two conics is (a) x^2+y^2=5 (b) sqrt(5)(x^2+y^2)-3x-4y=0 (c) sqrt(5)(x^2+y^2)+3x+4y=0 (d) x^2+y^2=25