Applied-Mathematics PYQ — Page 4

Out of 1000 employees, 100 have to be selected for a survey . After being arranged in the alphabetical order each one is assigned a number from 1 to 1000. A number 4 is selected and then every 10th person is selected (i.e 4 , 14, 24 ... ) . Which form of sampling is this an example of ?

From the data given below the Laspeyre's price index for the year 2016 with year 2010 as base year is | Commodity | Price year 2010 | Price year 2016 | Quantity Year 2010 | Quantity Year 2016 | |---|---|---|---|---| | A | 1 | 2 | 10 | 13 | | B | 5 | 10 | 12 | 16 | | C | 6 | 10 | 15 | 18 |

In the formula for Z-test statistic $Z = \frac{\bar{x} - \mu_0}{\frac{\sigma}{\sqrt{n}}}$, mark the incorrect statement.

If the objective function for an L.P.P. is $z = 3x + 4y$ and the corner points for unbounded feasible region are (9, 0), (4, 3), (2, 5) and (0, 8), then the minimum value of $z$ occurs at :

A dishonest delivery man purchases 20 liters of pure milk and dilutes it by adding 4 liters of water. If he sells the diluted milk at Rs.50/L, then what is the cost price of pure milk?

If $x = 3at^2$, $y = 3at^4$ then $\frac{dy}{dx}$ is :

A monopolist's Demand function is $x = 70 - \frac{P}{2}$, the revenue at $x = 5$ will be :

A carpenter earns a profit of ₹ 50 and ₹ 80 on one chair and one table respectively. The requirement and availability of wood and labour are tabled as : | Required | Chair | Table | Available quantity | |----------|-------|-------|--------------------| | Wood | 3 | 5 | 150 | | Labour | 1 | 2 | 56 | The number of chairs and tables in appropriate units to be manufactured for maximum profit are, respectively :

If the cost function and the profit function for a company is given by $C = 10 - 0.3x^2$ and $P = 0.3x^2 + 2x - 10$ respectively , where X represent units of output, then the revenue function is given by :

The wholesale price index (or price relative) of rice in 2018 compared to 2014 is 150. If the cost of rice was Rs. 16 per kg in 2014, then per kg cost of rice in 2018 is :

The prices and the quantities of three commodities are given are : | Commodity | Price (₹) in Year 2006 | Price (₹) in Year 2009 | Quantities in Year 2006 | Quantities in Year 2009 | |-----------|------------------------|------------------------|--------------------------|--------------------------| | P | 100 | 90 | 12 | 10 | | Q | 80 | $x$ | 8 | 7 | | R | 60 | 50 | 4 | 6 | The Laspeyre's price index number for year 2009 with year 2006 as base is 200. The value of $x$ is :

The probability distribution of a random variable X is given below : | X | 0 | 1 | 2 | 3 | 4 | |---|---|---|---|---|---| | P(X) | 0.1 | 0.25 | 0.3 | 0.2 | 0.15 | Then, $\text{Var}\left(\frac{X}{2}\right)$ is :

A consumer in 2015, paid Rs 20 per kg for a particular variety of rice. The wholesale price index number for this variety of rice for the year 2018, with the year 2015 as the base year is 125. Then the cost per kg of rice in the year 2018 will be:

If $y = \log_3(\log_3 x)$, then $\frac{dy}{dx}$

If $x = at^2$ and $y = a^3 t^3$, then $\frac{d^2 y}{dx^2}$ will be :

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

If $57 \equiv x (\bmod 5)$, then the least positive value of $x$ is:

Mr. X invested Rs.20,000 in year 2022 for 5 years. If Compound annual growth rate for that investment turned out to be 12%, the end value of the investment will be : {Use $(1.12)^5 = 1.76$}

Which of the following is not a statistic ?

If the probability distribution of a random variable X is given as | $x_i$ | 0 | 1 | 2 | 3 | |---|---|---|---|---| | $p_i$ | $2k^2$ | $k^2$ | $3k^2$ | $k$ | Then the mean of X is

For the data : | Variable | Price - Base year | Price - Current year | Weights | |---|---|---|---| | X | 50 | 60 | 5 | | Y | 20 | 25 | 7 | | Z | 30 | 40 | 4 | The weighted aggregative index number is :

If the objective function $Z = px + qy$ ($p, q > 0$) of an LPP has minimum value 7p, at the corner points (2, 3) and (7, 0), then

Let us consider an annuity whose periodic payment is Rs. R payable at the end of each payment period for 'n' periods, interest paid r% per period or $i = \frac{r}{100}$, so the amount of obligation can be given as _______.

The price index of sugar in 2019 compared to 2016 is 120. If the cost of sugar was Rs.25 per kg in 2016 then the cost in 2019 is: