Applied-Mathematics PYQ

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

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

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:

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:

| $ 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 shopkeeper wants to check the average number of cars sold per call. Past record of sales is shown below: | Sale of cars (Units) | 0 | 1 | 2 | 3 | |---|---|---|---|---| | Probabilities | $\frac{1}{6}$ | $\frac{1}{2}$ | $\frac{3}{10}$ | $\frac{1}{30}$ | The expected number of cars sold is :

If the sum and product of the mean and variance of a binomial distribution are 18 and 72 respectively, then the probability of obtaining atmost one success is

The price relatives and weights of a set of commodities are given as: | Commodity | A | B | C | |---|---|---|---| | Price Relative | 150 | 130 | 180 | | Weight | $x$ | $3x$ | $y$ | If the sum of weights is 30 and the index for the set is 144, then the values of $x$ and $y$ are:

The point on the straight line $3x + 4y = 8$, which is closest to the origin is:

Given the data for the sales of a product in a state is as follows: | Year | 2005 | 2006 | 2007 | 2008 | 2009 | |---|---|---|---|---|---| | Sales (In lakh Rs) | 150 | 130 | 160 | 170 | 200 | The equation of the straight-line trend by method of least squares is:

Between 3 p.m. and 5 p.m. the average number of phone calls per minute coming into the helpline desk of a bank is 5. The probability that during one particular minute there will be only one phone call is :

The maximum value of $Z = 3x + y$ subject to the constraints $x + y \leq 30, 2x + y \leq 40, x, y \geq 0$ is

Match List I with List II | LIST I | LIST II | |---|---| | A. The variance of a Poisson distribution with mean $\lambda$ is | I. $\sqrt{\lambda}$ | | B. The standard deviation of a Poisson distribution with mean $\lambda$ is | II. 4 | | C. In a Poisson distribution, if mean is 4, then the standard deviation is | III. $\lambda$ | | D. In a Poisson distribution, if mean is 4, then the variance is | IV. 2 | Choose the correct answer from the options given below:

A person takes a car loan of Rs 9,00,000 at the rate of 12% per annum for 5 years from a bank. The EMI under flat rate system is:

Match List I with List II | LIST I | LIST II | |---|---| | A. A special characteristic of a population is known as a: | I. statistic | | B. A special characteristic of a sample is known as a: | II. Confidence interval | | C. The uncertainty of a sampling process is expressed by: | III. Estimation | | D. The process by which one makes the inferences about a population based on the information obtained from a sample is known as: | IV. Parameter | Choose the correct answer from the options given below:

If the matrix $\begin{bmatrix} a & -2 & 5b \\ 2 & 0 & -15 \\ 15 & 3c & 0 \end{bmatrix}$ is skew-symmetric, then the value of $a^2 + b^2 + c^2$ is:

Match List I with List II | LIST I | LIST II | |---|---| | A. The solution of $3x + 7 > 12$ is | I. $[-1, \infty)$ | | B. The solution of $\frac{3x+5}{2} \geq 1$ is | II. $\left[\frac{17}{8}, \infty\right)$ | | C. The solution of $2x + 5 < 7x + 9$ is | III. $\left(\frac{5}{3}, \infty\right)$ | | D. The solution of $6x - 5 \geq -2x + 12$ is | IV. $\left(-\frac{4}{5}, \infty\right)$ | Choose the correct answer from the options given below:

If $\begin{bmatrix} 2x + 3 & y + 1 \\ 2x - z & 3y \end{bmatrix} = \begin{bmatrix} 7 & -2 \\ -4 & -9 \end{bmatrix}$, then matrix $\begin{bmatrix} 3z + 1 & 4 \\ -2 & 4 \end{bmatrix}$ is equal to:

The longest side of a triangle is 4 times the shortest side and the third side is 3 cm shorter than the longest side. If the perimeter of the triangle is at least 69 cm, then the minimum length of the shortest side is:

If the probability distribution of a discrete random variable $X$ is given as | X | 0 | 1 | 2 | 3 | 4 | |---|---|---|---|---|---| | P(X) | 0.5 | 2k | 3k | 3k | 2k | Then the value of $k$ is:

Match List I with List II | LIST I | LIST II | |---|---| | A. A matrix that has unequal number of rows and columns is called | I. Non-singular matrix | | B. A matrix whose determinant is non-zero is called | II. Null matrix | | C. A diagonal matrix whose diagonal elements are equal is called | III. Rectangular matrix | | D. A matrix that is both symmetric and skew-symmetric is | IV. Scalar matrix | Choose the correct answer from the options given below:

If the sum of two positive numbers is 25 and their product is maximum when divided in the ratio of cubes of one and squares of the other, then the numbers are: