Applied-Mathematics PYQ — Page 3

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:

A book consisting of 2000 pages has 540 misprints distributed randomly throughout the book. The average number of misprints in one page of the book is:

The total cost of producing $x$ generators is given by TC = $x^3 - 60x^2 + 1500x + 2000$. The Marginal Cost (MC), when $x = 10$ units is:

Consider the following hypothesis test : $\mu_o : \mu \leq 26$ $\mu_a : \mu > 26$ A sample of 36 is provided with a sample mean of 25.75. The population standard deviation is 3. The value of the test statistic is :

Using simple average of relatives method, the price index for 2011, taking 2001 as base year, was found to be 127. If $\Sigma p_0 = 263$, then x and y from the following data are : | Commodities | A | B | C | D | E | F | |---|---|---|---|---|---|---| | Prices (in Rs.) in 2001 | 80 | 70 | x | 20 | 18 | 25 | | Prices (in Rs.) in 2011 | 100 | 87.50 | 61 | 22 | y | 32.50 |

The purchase price P of a Rs. 50,000, 6% bond, dividends payable semi-annually, redeemable at par in 10 years, if the yield rate is to be 5% compounded semi-annually. Then P is equal : [Given $(1.025)^{-20} = 0.61027094$]

Match List - I with List - II. | List - I | List - II | |----------|-----------| | (A) A special characteristic of a population is called | (I) Sample Size | | (B) The number of statistical individuals in a sample is called | (II) Statistic | | (C) A special characteristic of a sample is called | (III) Standard error | | (D) The standard deviation of the sampling distribution of a statistic is known as its | (IV) Parameter | Choose the correct answer from the options given below :

The corner points of the feasible region determined by the system of linear constraints are (0, 10), (5, 5), (15, 15), (0, 20). Let $Z = ax + by$, where a, b > 0. Condition on a and b so that the maximizing value of Z occurs at both the points (15, 15) and (0, 20) is:

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:

Ravi takes a loan of Rs. 40,000 at an interest of 12% per annum for a period of 4 year, then EMI by using flat method is :

Match List - I with list- II | List-I | List - II | |---|---| | A. the probability distribution is applied for discrete random variable | normal distribution | | B. A normal distribution is symmetric about | standard deviation | | C. this probability distribution is applied for continuous random variable | mean | | D. the shape of normal curve depend upon | Poisson distribution | Choose the correct option below :

The corner points of the feasible region determined by $x + y \leq 8$, $2x + y \geq 8$, $x \geq 0$, $y \geq 0$, are A(0, 8), B(4, 0) and C(8, 0). If the objective function Z = ax + by has its maximum value on the line segment AB, then the relation between a and b is :

A vehicle costing Rs. 10,50,000 has a final scrap value of Rs. 5,25,000. If annual depreciation charge is Rs. 75,000, then useful life of the vehicle is :

If $K \equiv 5 \pmod{11}$, then all the possible non-negative values of K are :

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

A die is rolled thrice. What is the probability of getting a number greater than 4 in the first and the second throw of dice and a number less than 4 in the third throw?

The variance of the Binomial Distribution $B\left(5, \frac{1}{4}\right)$ is:

The value of the integral $\int e^x \left(\frac{1}{x} - \frac{1}{x^2}\right) dx$ is :

The solution set of the inequation $\frac{7+5x}{4} \geq \frac{x}{3} - 10$, $x \in \mathbb{R}$ is :

An asset costing Rs. 50,000 has a useful life of 4 years. The estimated scrap value is Rs. 10,000. By using linear depreciation method, the book value at the end of the second year is :

The cost of type A cement is Rs 100 per kg and that of type B cement is Rs 120 per kg. If both are mixed in the ratio of 2:3, the price of the cement mixer per kg will be

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

Given that p$_0$ and p$_1$ represent base and current prices of a commodity, q$_0$ and q$_1$ refer to the base and current quantities, then the formula used to calculate price relatives is :

If the mean of a binomial distribution is 12 and its standard deviation is 2, then the number of trials is :