List of practice Questions

Let $f$ be a function defined on $\left(-\dfrac{\pi}{2}, \dfrac{\pi}{2}\right)$ as \[ f(x) = \frac{\cos\left(\dfrac{\pi}{2} + |x|\right)}{\sin\left(\dfrac{\pi}{2} - |x|\right)}. \] Then,

The net inflow of foreign currency into a country on current account and capital account combined is negative in a particular year. The country could be following a fixed or a flexible exchange rate regime. Which of the following scenarios is/are possible for the country’s economy in that year?

If the number of employed workers in a country increases while its population does not change, then the unemployment rate in the country

The workforce participation rate of a country is 60%. This country has a population of 100 million, of which 6 million are unemployed. The unemployment rate for this country is

According to John Maynard Keynes, which one of the following statements is correct for a closed economy operating at less than the full employment level of output?

A monopolist is facing a downward sloping linear market demand. His variable cost of production is zero. The profit maximizing price will

X pays Rs. 5 lakhs to a person to transport fake currency worth Rs. 50 lakhs. The Police department pays Rs. 5 lakhs to a detective to investigate the crime. The detective’s income is taxed at 10%. If the above transactions happen in the same year and within the boundary of a country, the contribution of these transactions to GDP (in Rs. lakhs) is

An amateur singer has just recorded his first music album with a recording company. The demand for his album is given by $Q = 40000 - 800P$, where $Q$ is the number of albums sold and $P$ is the price of each album. Furthermore, per unit cost of producing each album is given by Rs. 8. A profit maximizing recording company has offered the following contract options to the singer
(i) 20% of the revenue from the sales of the album;
(ii) Rs. 2 per album sold;
(iii) A fixed fee of Rs. 32,000
Which of the following is/are correct?

Which one of the following statements is NOT correct in the context of economic planning in India?

There are only two firms in an industry producing a homogeneous product and having identical production technology. The cost function of firm $i$ is \[ C_i(q_i) = q_i^2, \quad \text{for } i = 1,2; \] where $q_i$ is the quantity produced by firm $i$. The market demand for the product is $p = 100 - q$, where $p$ is the unit price and $q = q_1 + q_2$ is the aggregate quantity. Assuming the firms are price takers, the competitive equilibrium solution of $p$ and $q$ in this market is

An upstream paper mill dumps effluents in a river. The total benefit and total cost to the mill are $TB = 120Q - Q^2$ and $TC = 20Q$, respectively, where $Q$ is the amount of output it produces. The environmental cost due to the negative externality is $EC = Q^2$. The government wants to impose a production tax of $t$ per unit of output on the mill. The value of $t$ to achieve the socially optimal level of production is

Which one of the following statements is NOT correct regarding changes in the occupational structure of the workforce between 1951 and 1991 in India?

Which one of the following statements is correct?

A monopoly canteen serves packed meals to two groups of consumers, group $X$ and group $Y$. The demand for packed meals for $X$ and $Y$ are given by, \[ Q_X = 200 - 4P \quad \text{and} \quad Q_Y = 300 - P, \] where $P$ is the uniform price per unit. The unit cost of producing each meal is Rs. 50. The value of $P$ (in Rs.) that maximizes the canteen’s profit is

The utility from wealth $(w)$ for an individual is given by $u(w) = \sqrt{w$. The individual owns a risky asset that is equally likely to yield either Rs. 400 or Rs. 900. The risk premium of the asset (in Rs.) is}

Let $\{x_1, x_2, \ldots, x_n\$ be the realization of a randomly drawn sample of size $n$ with sample mean $\bar{x}$, and let $k$ be a real number other than $\bar{x}$. Let $S_1$ and $S_2$ be the sums of squared deviations defined as} \[ S_1 = \sum_{i=1}^{n} (x_i - \bar{x})^2 \quad \text{and} \quad S_2 = \sum_{i=1}^{n} (x_i - k)^2 \] Then,

You have a budget of Rs. 4000 and would like to purchase LPG cylinders from a local seller who charges Rs. 50 per cylinder. The seller has a subsidy scheme by which if you return the empty cylinder purchased from him, you will get a refund of Rs. 20 per cylinder. You cannot borrow money from anyone. The maximum number of cylinders you can purchase is

Which one of the following is NOT a feature of the New Industrial Policy, 1991?

Which one of the following is a possible reason for underestimation of the official poverty ratio in India?

Which one of the following committees is NOT associated with financial sector reforms in India?

The differential equation \[ (3x^2y + y^3)\,dx + (x^3 + 3xy^2)\,dy = 0 \] is

When the expected future marginal product of capital increases, then the IS curve

An unanticipated inflation would cause

For the reaction, \[ \mathrm{Q + R \xrightleftharpoons[k_{-1}]{k_1} X \xrightarrow{k_2} P} \] Given: $k_1 = 2.5 \times 10^5$ L mol$^{-1}$ s$^{-1}$, $k_{-1} = 1.0 \times 10^4$ s$^{-1}$, and $k_2 = 10$ s$^{-1}$. Under steady-state approximation, the rate constant for the overall reaction in L mol$^{-1}$ s$^{-1}$ (rounded off to the nearest integer) is ________.

The mean ionic activity coefficient of 0.004 molal CaCl$_2$ in water at 298 K (rounded off to three decimal places) is ________. (Given: Debye–Hückel constant for an aqueous solution at 298 K is 0.509 kg$^{1/2}$ mol$^{-1/2}$)