Applied-Mathematics PYQ

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) $x = 30$ Choose the correct answer from the options given below:

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

If the random variable X follows the Poisson distribution such that P[X = k] = P[X = k+1], then the mean value of X 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 $y = e^{\frac{1}{2}\log(1+ \tan^2 x)}$, then $\frac{d^2y}{dx^2}$ is equal to:

| $ X $ | -2 | -1 | 0 | 1 | 2 | | --- | --- | --- | --- | --- | --- | | $ P(X) $ | $ 0.2 $ | $ 0.1 $ | $ 0.3 $ | $ 0.2 $ | $0.2$ | The variance of $X$ will be :

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:

A motor boat can row at the speed of 12 kilometres per hour in Still water . if the river is flowing at 4 kilometer per hour and it takes 12 hours for a round trip , then the distance between the two places is

If the mean of a binomial distribution is 24 and its standard deviation is 4 , then the probability of getting success is :

The minimum value of $f(x) = 4x^3 - 48x + 105$ in the interval [1,3] is :

Consider the following hypothesis test : $H_0 : \mu \leq 24$, $H_a : \mu > 24$ A sample of 64 provided a sample mean of 24.3 . The population standard deviation is 2. The value of the test statistic is :

If $x = 2t^2 + 3, y = 3t^2 + 6t + 5$, then the value of $\frac{d^2y}{dx^2}$ is :

The quantity of water that must be added to 36 litres of pure milk at $1\frac{1}{2}$ litres for Rs. 75 so as to have mixture worth Rs. 40 a litre is :

If $x = \log t$ and $y = \frac{1}{t^2}$, then $\frac{d^2 y}{d x^2}$ is equal to

Corner points of the feasible region for an LPP are : (0, 2), (3, 0), (6, 0), (6, 8) and (0, 5). Let $z = 4x + 6y$ be the objective function. Then, Max z $-$ Min z is equal to :

Which of the following is not true

The Solution set of the inequality three $3x + 4y \leq 12$ is :

For a manufacturer, total cost function is given by $C = \frac{x^2}{25} + 2x$. Which of the following are correct ? A. 2.6 is the marginal cost when 5 units are produced. B. $\frac{2x}{25} + 2$ is the marginal cost function. C. $\frac{x}{25} + 2$ is the average cost function. D. 2.4 is the marginal cost when 5 units are produced. E. $\frac{x}{25} + 1$ is the average cost function. Choose the correct answer from the options given below:

Match **List - I** with **List - II**. | | List - I | | List - II | |---|---|---|---| | (A) | Left tailed test | (I) | $H_0 : \mu = 50$ | | (B) | Two tailed test | (II) | $H_1 : \mu > 50$ | | (C) | Null hypothesis | (III) | $H_1 : \mu < 50$ | | (D) | Right tailed test | (IV) | $H_1 : \mu \neq 50$ | Choose the **correct** answer from the options given below :

If $x\%$ of $y + y\%$ of $30 = 61\%$ of $xy$, then $x =$

A retailer has 250 kg of rice a part of which he sells at 10% profit. The remaining quantity of rice is of low quality and he sold it at 5% loss. Overall he made a profit of 7%. The quantity of rice sold at 5% loss is :

The value of a for which the function $f(x) = a^x$ is increasing on R are given by :

The effective rate equivalent to a nominal rate of 8% per annum compounded semi annually is :

A car costing ₹ 8,00,000 has scrap value of ₹ 3,00,000. If the book value of car at the end of fourth year is ₹ 6,00,000, then the useful life of the car is :