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

If the marginal revenue function of a firm is MR = \({ e }^{ \frac { -x }{ 10 } }\), then revenue is ________.

(a)

\(-10{ e }^{ \frac { -x }{ 10 } }\)

(b)

\(1-{ e }^{ \frac { -x }{ 10 } }\)

(c)

\(10\left( 1-{ e }^{ \frac { -x }{ 10 } } \right) \)

(d)

\({ e }^{ \frac { -x }{ 10 } }+10\)

The demand function for the marginal function MR = 100 − 9x² is ________.

(a)

100 − 3x²

(b)

100x − 3x²

(c)

100x − 9x²

(d)

100 + 9x²

The producer’s surplus when the supply function for a commodity is P = 3 + x and x₀ = 3 is ________.

(a)

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

(b)

\(\frac{9}{2}\)

(c)

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

(d)

\(\frac{7}{2}\)

If MR and MC denote the marginal revenue and marginal cost and MR − MC = 36x − 3x² − 81 , then the maximum profit at x is equal to ________.

(a)

3

(b)

6

(c)

9

(d)

5

For a demand function p, if \(\int \frac{d p}{p}=k \int \frac{d x}{x}\) then k is equal to ________.

(a)

\(\eta \)_d

(b)

-\(\eta \)_d

(c)

\(\frac{-1}{\eta_{d}}\)

(d)

\(\frac{1}{\eta_{d}}\)

The area bounded by the parabola y² = 4x bounded by its latus rectum is ________.

(a)

\(\frac { 16 }{ 3 } \) sq.units

(b)

\(\frac { 8 }{ 3 } \) sq.units

(c)

\(\frac { 72 }{ 3 } \) sq.units

(d)

\(\frac { 1 }{ 3 } \) sq.units

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 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 lying above the X-axis and under the parabola y = 4x - x² is ______ sq. units

(a)

\(\frac{16}{3}\)

(b)

\(\frac{8}{3}\)

(c)

\(\frac{32}{3}\)

(d)

\(\frac{64}{3}\)