The area (in square units) bounded by the curves y =  2y-x+3 =0, X -axis and lying in the first quadrant is 

• 9

• 36

• 18

• 18

The intercepts on X- axis made by tangents to the curve,  which are parallel to the line y =2x, are equal to

• ±1

• ±2

• ±3

• ±3

Let I be the purchase value of an equipment and V(t) be the value after it has been used for t years. The value V(t) depreciates at a rate given by differential equationd V(t)/dt = - k(T - t), where k > 0 is a constant and T is the total life in years of the equipment. Then the scrap value V(T) of the equipment is

For x ∈, (0, 5π/2) define f(x). Then f (x) =  has

• local maximum at π and 2π.

• local minimum at π and 2π

• local minimum at π and the local maximum at 2π.

• local minimum at π and the local maximum at 2π.

15.

The area of the region enclosed by the curves y = x, x = e, y =1/x and the positive x-axis is

• 1/2 square units

• 1 square units

• 3/2 square units

• 3/2 square units

The area bounded by the curve y = cos x and y = sin x between the ordinates x = 0 and x = 3π/2 is 

Solution of the differential equation
cos x dy = y (sin x - y) dx, 0 < x < π/2, is 

• sec x = (tan x + C ) y 

•  y sec x = tan x + C

•  y tan x = sec x + C 

•  y tan x = sec x + C 

The area (in sq. units) of the region
{(x, y} : x  ≥ 0, x + y ≤ 3, x2 ≥ 4y and y ≤ 1 +√x}

• 5/2

• 59/12

• 3/2

• 3/2

The area of the region bounded by the parabola (y – 2)2 = x – 1, the tangent to the parabola at the point (2, 3) and the x-axis is 

• 3

• 6

• 9

• 9

The area of the plane region bounded by the curves x + 2y²= 0 and x + 3y²= 1 is equal to 

• 5/3

• 1/3

• 2/3

• 2/3