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In a company, the cost of producing one item is ₹100, if the item is sold at ₹150 and ₹50,000 is the fixed cost of the company, then the break-even point is:

Let C = C(x) be the total cost of producing x units of a product and AC is the average cost and MC is the marginal cost, then

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The marginal cost (MC) of producing x units of an item in a factory is given by $MC=0.006x^2-0.001x+4$.

If the fixed cost is ₹1000, then the cost of producing 200 units will be :

The demand function for a commodity is $p = 45 + x - x^2$, then the consumer's surplus at equilibrium price $p_0 = 25$ will be:

Given that the total cost function for x units of a commodity is $C(x) = \dfrac{x^3}{4} + 4x^2 - 8x + 20$. Then the marginal cost when $x=4$ is:

Which of the following statements are true?

(A) The break-even point is the level of production where the revenue from sales is equal to the cost of production and marketing.

(B) If R is the total revenue collected by a company when it sells $x$ units of a product at a price of p per unit, then R is given by $R=px$.

(C) Let $C=C(x)$ be the total cost of producing and marketing $x$ units of a product, then marginal cost, $MC=\frac{dC}{dx}$.

(D) If AC is the average cost, then $AC=\frac{x}{C}$.

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If $R(x)$ is the total revenue received and $C(x)$ is the total cost incurred in the production of x units of a commodity, then the profit function $P(x)$

The second order derivative of the function $y=\log(4x^3+6)$ with respect to 'x' will be:

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$\int_1^4 x^3\log x\, dx$ is equal to:

The area of the region bounded by curves $y=x^2$ and line $y=4$ is:

The relation between 'marginal cost (MC)' and 'average cost (AC)' of producing 'x' units of a product is

For the function $f(x)=2x^3-21x^2+36x-5$, which of the following statements are correct ?

A. $x=2$ is a point of local maxima.

B. $x=6$ is a point of local minima.

C. The local maximum value is 12.

D. The local maximum value is –94.

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If $y = e^{\frac{1}{2}\log(1+ \tan^2 x)}$, then $\frac{d^2y}{dx^2}$ is equal to:

The supply function of a commodity is P = $x^3+2x+18$. When 4 units of commodity are sold , then producer surplus is:

The demand function P for maximising a profit monopolist is given by P=274-x², while the marginal cost is 4+3x for x units of commodity. The consumer surplus is

If the total cost and total revenue of a company that produces and sells $x$ units of a particular product are $C(x) = 5x + 350$ and $R(x) = 50x - x^2$ respectively, then which of the following is/are the breakeven values:

(A) $x = 10$

(B) $x = 25$

(C) $x = 45$

(D) $x = 30$

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A company is selling a certain commodity $x$. The demand function for the commodity is linear. The company can sell $2000$ units when the price is ₹$8$ per unit and it can sell $3000$ units when the price is ₹$4$ per unit. The Marginal revenue at $x=5$ is:

If $x = 2at, y = at^2$, where 'a' is a constant, then $\frac{d^2 y}{dx^2}$ at $x = 2$ is :

The interval in which where the function $f(x) = x^3 - 3x^2 + 4x + 1, x \in R$ is increasing in, is :

The area bounded by the curve $y = x^2$ between $x = 0$ and $x = \pi$ in the first quadrant is :

The order and degree Of the differential equation $\frac{d^2 y}{dx^2} + 2 e^{-x} = 0$, respectively are

the general solution of the differential equation $(1 + y) dx - 2x dy = 0$ is :

If $v = \frac{4}{3} \pi r^3$, at what rate is cubic / unit sec is increasing when $r = 10$, and $\frac{dr}{dt} = 0.01$ ?

The value of the integral $\int_{-3}^{3} (x^3 - x) dx$ is :

$\int \frac{dx}{x^{n+1} - x}\,dx$

The second order derivative of which of the following functions is $5^x$ ?

The degree of the differential equation $\left(1 - \left(\frac{dy}{dx}\right)^2\right)^{3/2} = k \frac{d^2 y}{dx^2}$ is :

If $C(x) = x^3 - \frac{5}{2} x^2 + 10$ represents the total cost of producing x unit by car manufacturing company. The slope of the marginal cost curve at $x = 3$, will be

If x is real, the minimum value of $f(x) = x^2 - 8x + 20$ is :