At what point of curve `y=2/3x^3+1/2x^2,` the tangent makes equal angle with the axis? (a) `(1/2,2/(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)`

Find the equation of the line passing through the points (1,2,3)a n d(-1,0,4)dot

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

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)

Which of the following sets of points form an equilateral triangle? (a) (1,0),(4,0),(7,-1) (b) (0,0),(3/2,4/3),(4/3,3/2) (c) (2/3,0),(0,2/3),(1,1) (d) None of these

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)

The straight lines 4a x+3b y+c=0 , where a+b+c are concurrent at the point a) (4,3) b) (1/4,1/3) c) (1/2,1/3) d) none of these

Find the equation of the plane through the points (2, 3,1)a n d(4,-5,3) and parallel to the x-axis.

The derivative of y=(1-x)(2-x)....(n-x) at x=1 is (a) 0 (b) (-1)(n-1)! (c) n !-1 (d) (-1)^(n-1)(n-1)!

Find the equation of the plane passing through the points (1,0,-1)a n d(3,2,2) and parallel to the line x-1=(1-y)/2=(z-2)/3dot

If (log)_4 5=aa n d(log)_5 6=b , then (log)_3 2 is equal to 1/(2a+1) (b) 1/(2b+1) (c) 2a b+1 (d) 1/(2a b-1)