If two different tangents of `y^2=4x` are the normals to `x^2=4b y ,` then (a)`|b|>1/(2sqrt(2))` (b) `|b|<1/(2sqrt(2))` (c)`|b|>1/(sqrt(2))` (d) `|b|<1/(sqrt(2))`

Radius of the circle that passes through the origin and touches the parabola y^2=4a x at the point (a ,2a) is (a) 5/(sqrt(2))a (b) 2sqrt(2)a (c) sqrt(5/2)a (d) 3/(sqrt(2))a

If the distance between the foci and the distance between the two directricies of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 are in the ratio 3:2, then b : a is (a) 1:sqrt(2) (b) sqrt(3):sqrt(2) (c) 1:2 (d) 2:1

The slopes of the common tanents of the ellipse (x^2)/4+(y^2)/1=1 and the circle x^2+y^2=3 are (a) +-1 (b) +-sqrt(2) (c) +-sqrt(3) (d) none of these

If the distance between the foci and the distance between the two directricies of the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 are in the ratio 3:2, then b : a is 1:sqrt(2) (b) sqrt(3):sqrt(2) 1:2 (d) 2:1

The shortest distance between the parabolas 2y^2=2x-1 and 2x^2=2y-1 is 2sqrt(2) (b) 1/2sqrt(2) (c) 4 (d) sqrt((36)/5)

Normals at two points (x_1y_1)a n d(x_2, y_2) of the parabola y^2=4x meet again on the parabola, where x_1+x_2=4. Then |y_1+y_2| is equal to sqrt(2) (b) 2sqrt(2) (c) 4sqrt(2) (d) none of these

If the third term in expansion of (1+x^(log_2x))^5 is 2560 then x is equal to (a) 2sqrt2 (b) 1/8 (c) 1/4 (d) 4sqrt2

Tangents are drawn to the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1,(a > b), and the circle x^2+y^2=a^2 at the points where a common ordinate cuts them (on the same side of the x-axis). Then the greatest acute angle between these tangents is given by (A) tan^(-1)((a-b)/(2sqrt(a b))) (B) tan^(-1)((a+b)/(2sqrt(a b))) (C) tan^(-1)((2a b)/(sqrt(a-b))) (D) tan^(-1)((2a b)/(sqrt(a+b)))

If tangents P Q and P R are drawn from a point on the circle x^2+y^2=25 to the ellipse (x^2)/16+(y^2)/(b^2)=1,(b (a) (sqrt(5))/4 (b) (sqrt(7))/4 (c) (sqrt(7))/2 (d) (sqrt(5))/3

If a line y=3x+1 cuts the parabola x^2-4x-4y+20=0 at Aa n dB , then the tangent of the angle subtended by line segment A B at the origin is (8sqrt(3))/(205) (b) (8sqrt(3))/(209) (8sqrt(3))/(215) (d) none of these