Area bounded by the curve y = x (4 − x) between the limits 0 and 4 with x − axis is ________.

(a)

\(\frac{30}{3}\) sq.units

(b)

\(\frac{31}{2}\)sq.units

(c)

\(\frac{32}{3}\) sq.units

(d)

\(\frac{15}{2}\) sq.units

Area bounded by the curve y = e^−2x between the limits 0 ≤ x ≤ ∞ is ________.

(a)

1 sq.units

(b)

\(\frac{1}{2}\) sq.unit

(c)

5 sq.units

(d)

2 sq.units

The given demand and supply function are given by D(x) = 20 − 5x and S(x) = 4x + 8 if they are under perfect competition then the equilibrium demand is ________.

(a)

40

(b)

\(\frac{41}{2}\)

(c)

\(\frac{40}{3}\)

(d)

\(\frac{41}{5}\)

If the marginal revenue MR = 35 + 7x − 3x², then the average revenue AR is ________.

(a)

35x + \(\frac { 7{ x }^{ 2 } }{ 2 } -{ x }^{ 3 }\)

(b)

35x + \(\frac { 7{ x }^{ 2 } }{ 2 } -{ x }^{ 2 }\)

(c)

35 +\(\frac { 7{ x }^{ 2 } }{ 2 } +{ x }^{ 2 }\)

(d)

35 + 7x + x²

The profit of a function p(x) is maximum when ________.

(a)

MC − MR = 0

(b)

MC = 0

(c)

MR = 0

(d)

MC + MR = 0

The area bounded by y = 2x - x² and X-axis is _________ sq. units

(a)

\(\frac{2}{3}\)

(b)

\(\frac{4}{3}\)

(c)

2

(d)

4

The area of the region bounded by the ellipse __________

(a)

\(\pi\)ab sq.units

(b)

\(\frac{\pi a}{b}\) sq.units

(c)

2\(\pi\)ab sq.unit

(d)

\(\frac{\pi}{2}\) ab sq.units

The area unded by the curves y = 2^x, x = 0 and x = 2 is________sq.units.

(a)

log_e2

(b)

3log_e2

(c)

\(\frac{3}{log_e2}\)

(d)

2log_e3

The area of the region bounded by the line 2y = -x + 8, X - axis and the lines x = 2 and x = 4 is ________ sq.units.

(a)

\(\frac{1}{5}\)

(b)

\(\frac{2}{5}\)

(c)

5

(d)

\(\frac{5}{2}\)

The area enclosed by the curve y = cos²x in [0,\(\pi\)] the lines x=0, x = \(\pi\) and the X-axis is ________sq.units.

(a)

2\(\pi\)

(b)

2\(\pi\)

(c)

\(\frac{2}{\pi}\)

(d)

\(\frac{\pi}{2}\)

Cost function

(1)

ഽmc dx+k

Average cost function

(2)

\(\frac{dc}{dx}\)

MC

(3)

Total revenue

Output

(4)

\(\frac{c}{x}\), x ≠ 0

R

(5)

x