At what point of curve `y=2/3x^3+1/2x^2,` the tangent makes equal angle with the axis? `(1/2,5/(24))a n d(-1,-1/6)` `(1/2,4/9)a n d(-1,0)` `(1/3,1/7)a n d(-3,1/2)` `(1/3,4/(47))a n d(-1,-1/3)`

At what point of curve y=2/3x^3+1/2x^2, the tangent makes equal angle with the axis? (a) (1/2,5/(24))a n d(-1,-1/6) (b) (1/2,4/9)a n d(-1,0) (c) (1/3,1/7)a n d(-3,1/2) (d) (1/3,4/(47))a n d(-1,-1/3)

The point on the curve y^2=x where tangent makes 45^o angle with x-axis is (a) (1//2,\ 1//4) (b) (1//4,\ 1//2) (c) (4,\ 2) (d) (1,\ 1)

Find a point on the curve y=x^3-3x where the tangent is parallel to the chord joining (1,-2)a n d(2,2)dot

The angle between the tangents to the curves y=x^2a n dx=y^2a t(1,1) is cos^(-1)(4/5) (b) sin^(-1)(3/5) tan^(-1)(3/4) (d) tan^(-1)(1/3)

{(1/3)^2}^4 is equal to (a) (1/3)^6 (b) (1/3)^8 (c) (1/3)^(24) (d) (1/3)^(16)

The normal to the curve y(x-2)(x-3)=x+6 at the point where the curve intersects the y-axis , passes through the point : (1) (1/2,-1/3) (2) (1/2,1/3) (3) (-1/2,-1/2) (4) (1/2,1/2)

Which pair of points lies on the same side of 3x-8y-7=0? a) (0,-1)a n d(0,0) b) (4, -3) and (0, 1) c) (-3,-4)a n d(1,2) d) (-1,-1)a n d(3,7)

Using section formula, show that the points A(2,-3,4),\ B(-1,2,1)\ a n d\ C(0,1/3,2)\ are collinear.

The abscissas of point Pa n dQ on the curve y=e^x+e^(-x) such that tangents at Pa n dQ make 60^0 with the x-axis are. )a) 1n((sqrt(3)+sqrt(7))/7)a n d1n((sqrt(3)+sqrt(5))/2) (b) 1n((sqrt(3)+sqrt(7))/2) (c) 1n((sqrt(7)-sqrt(3))/2) (d) +-1n((sqrt(3)+sqrt(7))/2)

The abscissas of point Pa n dQ on the curve y=e^x+e^(-x) such that tangents at Pa n dQ make 60^0 with the x-axis are. 1n((sqrt(3)+sqrt(7))/7)a n d1n((sqrt(3)+sqrt(5))/2) 1n((sqrt(3)+sqrt(7))/2) (c) 1n((sqrt(7)-sqrt(3))/2) +-1n((sqrt(3)+sqrt(7))/2)