List of top Questions asked in GATE XH-C1

An economy is characterized by the following production function: \[ Y = A K^{0.25} L^{0.75} \] where \(K\) denotes capital, \(L\) denotes labour, \(A\) denotes the total factor productivity, and \(Y\) denotes output produced. All capital and labour are fully employed. Suppose that the growth rate of labour is 1%, the growth rate of capital is 4%, and the growth rate of output is 4%. The growth rate of total factor productivity \(A\) is:

Okun’s law says that a 1% increase in unemployment for one year is associated with a 2% decrease in GDP growth. Suppose an economy has the following expectations augmented Phillips curve: \[ \pi = \pi^e - \beta (U - U^N), \quad \beta>0 \] where \( \pi \) and \( \pi^e \) are the inflation and expected inflation rates, respectively. \( U \) and \( U^N \) are the unemployment and natural rate of unemployment, respectively. \( \beta \) measures sensitivity of inflation to unemployment gap. When \( \beta = 2 \), by what percentage does output fall short of full-employment given that the inflation rate, expected inflation rate, and natural rate of unemployment are 8%, 10%, and 6%, respectively?

Which one of the following is a test of heteroscedasticity?

As per recent Economic Survey, how many states and Union Territories (UTs) are driven by services sector in India?

What is the user cost of capital for a firm when the rate of depreciation of machine is 20% and the cost of financial capital is 15%?

Which of the following committees was set-up to address issues related to capital account convertibility in India?

Bretton Woods agreement gave birth to the following organization:

Which among the following Gini coefficients exhibits the highest equality?

IndiaSMart is a retail shop that accepts either a Rupay credit card, or a Visa credit card. 31 percent of IndiaSMart’s customers carry a Rupay credit card, 44 percent of its customers carry a Visa credit card, while 18 percent of its customers carry a Rupay credit card as well as a Visa credit card. What is the probability that a customer carries at least one of the two, i.e. either a Rupay or a Visa credit card?

Let \( f(x, y) \) be a continuously differentiable homogeneous function of degree 4. Which of the following is necessarily true?

The demand curve for tea in Borduria is given by \[ D(P) = 40 - 2P \] and the domestic supply curve of tea in Borduria is given by \[ S(P) = \frac{2}{3}P \] Here \(D(P)\) denotes quantity demanded when price is \(P\) and \(S(P)\) is quantity supplied by domestic producers at price \(P\). Tea is traded in a competitive world market and imported into Borduria at a price of 9 per unit. Initially there was no restriction on trade. However, as a result of lobbying by the domestic suppliers, the Bordurian government imposes a tariff of 3 per unit on each unit imported. As a result of the tariff, import of tea decreased by how many units?

Consider the following system of equations in three variables \(x, y, z\): \[ -x - y - z = 3 \] \[ x + y + z = 10 \] \[ 2x - 3y = 6 \] This system of equations has

Which of the following models appropriately explains the fluctuations in potential output and long-run aggregate supply by understanding the shocks to productivity or the willingness of the worker?

The change in equilibrium output for an equal amount of change in government expenditure and tax revenue is linked to which one of the following multipliers?

Solaris is a firm that can install solar panels at an airport to generate electricity for the airport’s usage. The company claims that in 70 percent of all airports where its solar panels are installed, an airport’s electricity bill is reduced by at least 40 percent. The probability that an airport’s electricity bill is reduced by at least 40 percent, in seven out of ten airports where the company’s solar panels are installed, equals approximately:

The Human Development Index (HDI), as reported by the United Nations Development Program, is based on three components. Two of these components are per-capita income and a measure of educational attainment of society. The third component is

Suppose we estimate the following regression equation: \[ \ln(x_t) = \alpha_0 + \alpha_1 \ln(y_t) + \epsilon_t, \quad \alpha_0, \alpha_1>0 \] where \(x_t\) and \(y_t\) are some variables, \(\alpha_0\) and \(\alpha_1\) are the intercept and the slope, respectively, and \(\epsilon_t\) is the residual term. What is the interpretation of the coefficient \(\alpha_1\)?

Suppose that a firm has a technology represented by the following production function: \[ Y(K, L) = K^x L^y \] where \( K \) denotes capital, \( L \) denotes labour, \( Y \) denotes the maximum output that is possible to produce using capital \( K \) and labour \( L \). \( x \) and \( y \) are two positive real numbers. It is also known that the production function satisfies constant returns to scale. Then which of the following is true?

Cholera, typhoid, diphtheria and tuberculosis cause huge number of deaths. Poor quality drinking water has always been the world’s greatest single carrier of sickness. Disease is transmitted when sewage and drinking water come into contact. Children are particularly vulnerable. In some of the poorest countries the infant mortality rate is high. The separation of sewage and the supply of clean drinking water are the domain of civil engineers, and their work makes a significant contribution to public health. That contribution was recognized when public sanitation was voted the greatest medical breakthrough, beating the discoveries including antibiotics and vaccines in a poll organized by the British Medical Journal. Identify the statement(s), which is/are NOT TRUE according to the passage.

Shark’s teeth have evolved to correspond to the diet of each particular species of shark. Consequently, the teeth of the great white shark bear little resemblance to those of the bull shark or nurse shark. There were essentially four different shark diets and thus four varieties of shark teeth. Sharks that feed on fish have needle-like teeth, perfect for spearing and ripping. Sharks that eat mammals such as seals and sea lions have heavy, serrated teeth, typically triangular on the upper jaw and pointed on the lower jaw. Shark that feed in the benthic zone of the ocean have flattened teeth for crushing the shell of the creatures they find scuttling in the sand or clinging to rocks. Sharks that bask have teeth that are largely non-functional; these sharks filter food from the water by passing it through their gills.
Which of the following is/are the CORRECT inference(s) as per the passage?

A particular school management wants to contact all parents, all businessmen and all engineers. The following statistics are available with the school.
Businessmen = 50
Engineers = 25
Parents = 2500
Businessmen who are engineers = 0
Businessmen who are parents = 25
Engineers who are parents = 15
The number of people who need to be contacted are _________.

Six examinations are required to be conducted in a week starting from Sunday to Saturday. Hindi is not scheduled on the first day and English is not scheduled before Hindi. Mathematics is scheduled one day after Physics. Biology is scheduled two days after Hindi. One day prior to Chemistry, there is no examination. Only one examination can be scheduled on a single day and Sunday is not an off day. What are the subjects scheduled on first and the last days?

Vinod has a pre-determined route. Each morning he delivers 37 newspapers to customers in his neighborhood. It takes Vinod 50 minutes to deliver all the papers. When Vinod was sick or had other engagements, his friend Tarun, who lives on the same street delivered the papers on his behalf. Find the statement(s) that must be TRUE according to the given information.

For a painting to succeed, it is essential that the painter and his public agree about what is significant. The subject of the painting may have a personal meaning for the painter or a common person; but there can also be the possibility of their agreement on its general meaning. It is at this point that the culture of the society and the period in question precedes the artists and her/his art. Renaissance art would have meant nothing to the Aztecs, and vice versa. If, to some extent, a few intellectuals can appreciate them both today, it is because their culture is a historical one. Its inspiration is history and all known developments to date. According to the passage, which of the following is/are NOT necessarily among the attributes needed for a painter to succeed?

Park street is parallel to Rock street. Garden street is perpendicular (90°) to Lake street. Lake street is parallel to Rock street. For the situation described above, the TRUE statement is