List of top Questions asked in GATE XH-C1

Consider the Solow growth model in which output (Y) is determined by the production function Y_t = 0.2K_t + 0.8L_t, where K and L denote capital and labour used in the production process, and t depicts time. The depreciation is given by δK_t, where δ = 0.2. Saving is given by sY_t, where s = 0.5. Assume that the population does not grow with time. The steady state capital per unit of labour is ______ (in integer).

The following table provides different statistical model specifications along with the elasticity of y_t with respect to x_t. Which one of the following options is correct ?

Row	Statistical Model	Elasticity
1	\(y_t=β_1+β_2\frac{1}{x_t}\epsilon_t\)	\(-\frac{β_2}{x^2_t}\)
2	\(y_t=β_1-β_2\text{ln}(x_t)+\epsilon_t\)	\(-\frac{β_2}{x^2_t}\)
3	ln(yt) = β1 + β2 ln(xt) + εt	β2
4	ln(yt) = β1 + β2xt + εt	β2xt
5	ln(yt) = β1 + β2 ln(xt) + εt	β2 exp(xt)
6	ln(yt) = β1 + β2xt + εt	\(β_2\frac{1}{\text{exp}(x_t)}\)

Based on the table given below, the current account deficit in nominal terms as a percentage of GDP during 2012-13 will be _______ (rounded off to three decimal places).

Expenditure on Gross Domestic Product (Rupees in Crores)
At Current Prices		2009-10	2010-11	2011-12	2012-13
1.	Final Consumption Expenditures	448	525	617	696
2.	Gross Fixed Capital Formation	206	241	286	307
3.	Change in Inventory Stocks	18	27	17	17
4.	Exports of Goods & Services	130	171	215	243
5.	Imports of Goods & Services	165	205	272	311
At Constant 2004-05 Prices		2009-10	2010-11	2011-12	2012-13
1.	Final Consumption Expenditures	340	368	400	421
2.	Gross Fixed Capital Formation	159	117	199	200
3.	Change in Inventory Stocks	14	21	12	11
4.	Exports of Goods & Services	100	120	138	145
5.	Imports of Goods & Services	133	154	187	199

For the function \(F: \R^2 → \R\) specified as F(x, y) = x³ - y³ + 9xy, which of the following options is/are correct

Let x and y be two dummy variables that take the values of either 0 or 1, and follow the bivariate frequency distribution as given below. If a logit regression is estimated with y as the dependent variable and x as the independent variable, then the estimated coefficient of x is _____ (rounded off to two decimal places)

x	0	1	Total
y
0	6	11	17
1	6	7	13
Total	12	18	30

A decrease in the income tax rate has a ________ effect on the labour supply if the ________ effect dominates.

If a discrete random variable X follows the uniform distribution and assumes only the values 8, 9, 11, 15, 18, and 20, then P(|X -14| < 5) is

Assume the following probabilities for two events, A and B: P(A) = 0.50,P(B) = 0.50, and P(A ∪ B) = 0.85. Then we can conclude that

If X and Y are two random variables with the joint probability density function
\(f(x,y)=\left\{ \begin{array}{l} \frac{2}{3}(x+2y);\ \text{for}\ 0\lt x, y\lt 1 \\ 0;\ \ \ \ \ \ \ \ \ \ \text{otherwise} \end{array} \right.\)
then \(E[X|Y=\frac{1}{2}]\) will be

Two friends Aditi and Raju are deciding independently whether to watch a movie or go to a music concert that evening. Both friends would prefer to spend the evening together than apart. Aditi would prefer that they watch a movie together, while Raju would prefer that they go to the concert together. The payoff matrix arising from their actions is presented below. p and (1 - p) are the probabilities that Aditi will decide in favour of the movie and concert, respectively. Similarly, q and (1 - q) are the probabilities that Raju will decide in favour of the movie and concert, respectively. Which one of the following options correctly contains all the Nash Equilibria ?

		Raju
Aditi		Movie	Concert
	Movie	2,1	0,0
	Concert	0,0	1,2

For a given foreign currency, if the forward exchange rate of delivery is 20 and the current value of spot exchange rate is 8, then the forward premium will be _________ (rounded off to two decimal places).

Consider a simple pooled regression model: y_it = β₀ + β₁x_it + vit where v_it = μ_i + ∈_it and Cov(x_it, μ_i) ≠ 0. Here, μ_i captures the unknown individual specific effects and it is the idiosyncratic error uncorrelated with both x_it and μ_i. If the parameters of this model are estimated using the ordinary least squares (OLS) method, then the estimated slope coefficient will be

A six-face fair die is rolled once, with X being the number that appeared on the uppermost surface. Then the variance of X is ________ (rounded off to three decimal places).

Which of the following factor(s) do NOT affect output and employment in the classical macroeconomic model ?

For the following function f(x) to be a probability density function, the value of c will be ____________ (rounded off to two decimal places).
\(f(x)=\left\{ \begin{array}{l}\frac{c}{\sqrt{x}};0\lt x\lt 4\ \text{and}\ c\gt0 \\ 0;\ \ \text{otherwise} \end{array} \right.\)

Let x₁, x₂ ….. x_n be an independently, and identically distributed (iid) random sample drawn from a population that follows the Normal Distribution N(μ, σ²), where both the mean (μ) and variance (σ²) are unknown. Let \(\bar{x}\) be the sample mean. The maximum likelihood estimator (MLE) of the variance (\(\hat{\sigma}^2_{MLE}\)) is/are then characterized by

When transfer of income happens from the "not richer" individual to the "not poorer" individual, then such a transfer is known as

Which one of the following is NOT a source of finance of the Government of India ?

In an economy, the dependency ratio is the ratio of

In the context of the Harris-Todaro model of rural-urban migration, which one of the following is TRUE ?

Read the passage and identify the statement(s) which follow(s) from it :
The purpose of this work is to inform educators about the brain science related to emotion and learning, and, more important, to offer strategies to apply these understandings to their own teaching. Although many of the approaches I describe will be familiar, integrating the lens of emotion and the brain may be a new concept. As an educator I had been trained in how to deliver content and organize my lessons, but I had not been taught how to design learning experiences that support emotions for learning.

If A says that his mother is the daughter of B's mother, then how is B related to A ?

If the difference between actual GDP and the trend output varies inversely with the difference between actual unemployment rate and the natural rate of unemployment, then such a relationship is called the

Which one of the following measures in the Keynesian framework is adopted to tame inflation in an economy ?

Which of the following recommended action(s) seem to be appropriate with the stated problem ?
Stated problem : Many students at educational institutes do not attend classes in the post-pandemic scenario.