Applied-Mathematics PYQ — Page 7

Pipe A can independently empty a half-filled tank in 3 hours whereas pipe B can alone fill the same tank in 4 hours, when the tank is completely empty. In how much time will the empty tank be completely filled, if both the pipes are opened together?

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:

The feasible region for an LPP is shown in the figure given below: If objective is maximizing $Z = 22x + 18y$ find $(x, y)$ for the optimal $Z$.

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:

If the life expectancy of an asset is 10 years, scrap value Rs.5,000 and annual depreciation of Rs.3000 per annum, then original cost of the asset is:

For a 3 $\times$ 3 matrix A = [a$_{ij}$], whose element a$_{ij}$ is given by $a_{ij} = \sqrt{i^2 + 3j}$ then what is element a$_{31}$?

A runs 5 times faster than B. If A gives B a start of 100 m, how far must the goal be so that A and B reach there at the same time.

In a game of carrom of 100 points, A can give B 20 points and C 40 points, then points B can give C is:

Given $\sum p_0 q_0 = 800$, $\sum p_0 q_1 = 1500$, $\sum p_1 q_1 = 1300$ and $\sum p_1 q_0 = 900$, where subscripts 0 and 1 are used for base year and current year respectively. The Paasche's index number is:

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 :

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

The set of values of $x$ satisfying $26 \equiv 5 \pmod{x}$ 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 $(1.12)^5 = 1.76$}

A swimmer's speed in swimming pool is 6 km/hr. He swims between two points in a river and returns back to the starting point. He took 24 minutes more to cover the distance upstream than downstream. If the speed of the stream is 4 km/hr, then the distance between two points is:

The rise in prices before Christmas is an example of

Three partners Ramesh, Suresh and Mahesh shared the profit in a business in the ratio 5:4:7 respectively, they invested the money for 10 months, 8 months and 6 months respectively then ratio of their investment is :

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

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

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

A simple random sample consists of three observations 1, 3, 5. The point estimate of the population standard deviation is :

The effective rate that is equivalent to a nominal rate of 16% compounded semi-annually is :

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

Area of the region bounded by the curve $x^2 = 4y$, $x$ - axis and $x = 3$ is

The value of the integral $I = \int_{-1}^{1} (x + x^3 + x^5) dx$ is :