Let p ( x ) = a0 + a1 x2 + a2 x4 + - - - - - - an x2n be a polynomial in real variable x with 0 < a0 < a1, < a2 - - - - - < an. The function P (x ) has
Only one minimum
Only one maximum
Neither a max nor min
f (x ) = √3 sin x + 3 cos x is max at x =
π/3
π/2
π/6
2π/3
The length of the subnormal to the parabola y2 = 4dx at any point is equal to:
√2 a
2√2 a
a/√2
2a
The slope of the tangent to the curve y = 16 - x2 at x = 0 is
0
-2
2
16
Minimum value of f(x) = Sinx in -π/2≤x≤π/2 is
The largest value of ax3 - 3x2 - 12x = 5 for -2 ≤ x ≤ 4 occurs at x =
If u = f(x2 + y2) then ∂u/∂x:∂u/∂y is
x2:y2
1/x2:1/y2
x:y
None of these
The point on the curve y = x2 - 2x + 3 where the tangent is parallel to x axis is
( 1, 2 )
( 1, 3 )
( 3, 1 )
( 2, 1 )
Two towns A and B are 60 km a part A school is to be built to serve 150 students.If the total distance to be traveled by all 200 students is to be as small as possible, then the school should be built at
Town B
Town A
45 km from town B
The side of a cube is equal to the diameter of a sphere. If the side and radius increases at the same rate then the ratio of the increase of their surface is.