[" (iii) "0,sqrt(5)],[" (y) "4,1]

Given x, y in R , x^(2) + y^(2) gt 0 . Then the range of (x^(2) + y^(2))/(x^(2) + xy + 4y^(2)) is (a) ((10 - 4 sqrt(5))/(3),(10 + 4 sqrt(5))/(3)) (b) ((10 - 4 sqrt(5))/(15),(10 + 4 sqrt(5))/(15)) (c) ((5- 4 sqrt(5))/(15),(5 + 4 sqrt(5))/(15)) (d) ((20- 4 sqrt(5))/(15),(20 + 4 sqrt(5))/(15))

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=4sqrt(5)x+20 (b) y=4sqrt(3)x-12 (c) y=0 (d) y=-4sqrt(5)x-20

Minimum distance between the curve "y^(2)=4x" and " x^(2)+y^(2)-12x+31=0 " ,is equal to 1) sqrt(21) ,2) sqrt(26)-sqrt(5) , 3) sqrt(5) ,4) sqrt(28)-sqrt(5)

The equation of a line whose inclination is (5pi)/(6) and which cuts off an intercept of 4 units on negative direction of y-axis is (i) x+sqrt(3)y+4sqrt(3)=0 (ii) x-sqrt(3)y+4sqrt(3)=0 (iii) x+sqrt(3)y-4sqrt(3)=0 (iv) x-sqrt(3)y-4sqrt(3)=0

If lines x+2y-1=0,ax+y+3=0, and bx-y+2=0 are concurrent,and S is the curve denoting the locus of (a,b), then the least distance of S from the origin is (a) (5)/(sqrt(57)) (b) 5/sqrt(51)(c)5/sqrt(58)(d)5/sqrt(59)

If lines x+2y-1=0,a x+y+3=0, and b x-y+2=0 are concurrent, and S is the curve denoting the locus of (a , b) , then the least distance of S from the origin is 5/(sqrt(57)) (b) 5//sqrt(51) 5//sqrt(58) (d) 5//sqrt(59)

The range of parameter ' a ' for which the variable line y=2x+a lies between the circles x^2+y^2-2x-2y+1=0 and x^2+y^2-16 x-2y+61=0 without intersecting or touching either circle is (a) a in (2sqrt(5)-15 ,0) (b) a in (-oo, 2sqrt(5)-15,) (c) a in (2sqrt(5)-15,-sqrt(5)-1) (d) a in (-sqrt(5)-1,oo)

The range of parameter ' a ' for which the variable line y=2x+a lies between the circles x^2+y^2-2x-2y+1=0 and x^2+y^2-16 x-2y+61=0 without intersecting or touching either circle is (a) a in (2sqrt(5)-15 ,0) (b) a in (-oo, 2sqrt(5)-15,) (c) a in (2sqrt(5)-15,-sqrt(5)-1) (d) a in (-sqrt(5)-1,oo)

The equaiton of the line which bisects the obtuse angle between the lines x-2y+4=0 and 4x-3y+2=0 (A) (4-sqrt(5))x-(3-2(sqrt(5)) y+ (2-4sqrt(5))=0 (B) (3-2sqrt(5)) x- (4-sqrt(5))y+ (2+4(sqrt(5))=0 (C) (4+sqrt(5)x-(3+2(sqrt(5))y+ (2+4(sqrt(5))=0 (D) none of these