If a variable tangent to the curve `x^2y=c^3` makes intercepts `a , bonx-a n dy-a x e s ,` respectively, then the value of `a^2b` is `27c^3` (b) `4/(27)c^3` (c) `(27)/4c^3` (d) `4/9c^3`

If parabolas y^2=lambdax and 25[(x-3)^2+(y+2)^2]=(3x-4y-2)^2 are equal, then the value of lambda is (a)9 (b) 3 (c) 7 (d) 6

If the line joining the points (0,3)a n d(5,-2) is a tangent to the curve y=C/(x+1) , then the value of c is 1 (b) -2 (c) 4 (d) none of these

If a b^2c^3, a^2b^3c^4,a^3b^4c^5 are in A.P. (a ,b ,c >0), then the minimum value of a+b+c is (a) 1 (b) 3 (c) 5 (d) 9

Vertices of a variable acute angled triangle A B C lies on a fixed circle. Also, a ,b ,ca n dA ,B ,C are lengths of sides and angles of triangle A B C , respectively. If x_1, x_2a n dx_3 are distances of orthocenter from A ,Ba n dC , respectively, then the maximum value of ((dx_1)/(d a)+(dx_2)/(d b)+(dx_3)/(d c)) is -sqrt(3) b. -3sqrt(3) c. sqrt(3) d. 3sqrt(3)

If a , b and c are the side of a triangle, then the minimum value of (2a)/(b+c-a)+(2b)/(c+a-b)+(2c)/(a+b-c)i s (a) 3 (b) 9 (c) 6 (d) 1

If a ,b ,c are different, then the value of |0x^2-a x^3-b x^2+a0x^2+c x^4+b x-c0|=0 is c b. c c. b d. 0

If the normal to the curve y=f(x) at the point (3,4) makes an angle (3pi)/4 with the positive x-axis, then f'(3)= (a) -1 (b) -3/4 (c) 4/3 (d) 1

If a + b + c = 0 and a^(2) + b^(2) + c^(3) = 4, them find the value of a^(4) + b^(4) +c^(4) .

The number of tangents to the curve x^(3/2)+y^(3/2)=2a^(3/2),a >0, which are equally inclined to the axes, is 2 (b) 1 (c) 0 (d) 4