List of top Questions asked in GATE XH-C1

Rice, a versatile and inexpensive source of carbohydrate, is a critical component of diet worldwide. Climate change, causing extreme weather, poses a threat to sustained availability of rice. Scientists are working on developing Green Super Rice (GSR), which is resilient under extreme weather conditions yet gives higher yields sustainably. Which one of the following is the CORRECT logical inference based on the information given in the above passage?

Consider the following inequalities.
(i) \( 3p - q<4 \)
(ii) \( 3q - p<12 \)
Which one of the following expressions below satisfies the above two inequalities?

Given below are three statements and four conclusions drawn based on the statements.

Statement 1: Some engineers are writers.
Statement 2: No writer is an actor.
Statement 3: All actors are engineers. Conclusion I: Some writers are engineers.
Conclusion II: All engineers are actors.
Conclusion III: No actor is a writer.
Conclusion IV: Some actors are writers.
Which one of the following options can be logically inferred?

Inhaling the smoke from a burning __________ could __________ you quickly.

In the flexible exchange rate environment with perfect capital mobility, a fiscal stimulus will be linked to which of the following statements?

Consider a lottery with two possible outcomes:

Rupees 100 with probability 0.6
Rupees 50 with probability 0.4 The maximum amount that a risk-neutral person would be willing to pay to play the above lottery equals Rupees _________ (in integer).

Mr. Sharma’s consumption preference for tea (denoted by \( x \)) and sugar (denoted by \( y \)) is given by the utility function \[ U(x,y) = \min(x, 2y) \] The price per unit of tea is 10 and the price per unit of sugar is 10. Mr. Sharma’s total income is 900. The optimum quantity of tea purchased by Mr. Sharma equals _________ (in integer).

Suppose \( \alpha \) is a real number between 0 and 1. Rohit is choosing \( x \) and \( y \) to maximize the following utility function: \[ U(x, y) = x^2 + 2xy + y^2 + 4\alpha^2 + 8\alpha + 10 \] subject to the following constraints: \[ 2x + y = 10, \quad x, y \geq 0. \] Then the optimal value of \( y \) chosen by Rohit is _________ (in integer).

In a competitive market for dry-cleaning, the inverse market demand function is given by: \[ P = 100 - Q \] where \( P \) denotes price and \( Q \) denotes quantity. The (private) marginal cost (MC) of production for all the dry-cleaning firms together is given by: \[ MC = 20 + 2Q \] The market pollution generated by the dry-cleaning processes of all firms creates external damages given by the marginal external cost (MEC): \[ MEC = 2Q. \] The socially efficient output of dry-cleaning is _________ (in integer).

Suppose an investigator has specified the following simultaneous equation model:
\[ y_{1,t} = \alpha_{1,0} + \alpha_{1,2} y_{2,t} + \alpha_{2} M_{t} + \alpha_{3} K_{t} + u_{t} \tag{1} \] \[ y_{2,t} = \alpha_{2,0} + \alpha_{2,1} y_{1,t} + \alpha_{3} I_{t} + v_{t} \tag{2} \] where \( y_{1,t} \) and \( y_{2,t} \) are endogenous variables. \( M_t, K_t, I_t \) are predetermined variables. \( u_t \) and \( v_t \) are residual terms. Based on the order condition of identification, which one of the following statements is correct?

There are two regions in a country. The demand for chocolates in region 1 is given by
\[ Q_1(P) = 100 - P \] and the demand for chocolates in region 2 is given by
\[ Q_2(P) = 200 - P \] where \( Q_1(P) \) and \( Q_2(P) \) denote the demand for chocolates in region 1 and 2 respectively at a price \( P \). There is only one seller who is licensed to sell chocolates in the country. Suppose the seller sets a price of \( P = 125 \). The total demand for chocolates in the country at this price is

A producer manufactures batteries by using techniques I and II. The capacities (in ampere hours) of 12 randomly selected batteries manufactured by using technique I are: 140, 132, 136, 142, 138, 150, 154, 150, 152, 136, 144, and 142. Moreover, the capacities (in ampere hours) of 14 randomly selected batteries manufactured by using technique II are: 144, 134, 132, 130, 136, 146, 140, 128, 131, 128, 150, 137, 130, and 135. Suppose that battery capacities manufactured by using techniques I and II are normally distributed, with unknown means, \( \mu_I \) and \( \mu_{II} \) respectively, and an unknown common variance \( \sigma^2 \). Consider the null hypothesis \( H_0: (\mu_I - \mu_{II}) = \gamma \) ampere hours. For which of the following values of \( \gamma \) should the null hypothesis \( H_0 \) be accepted against the alternative hypothesis \( H_1: (\mu_I - \mu_{II}) \neq \gamma \) ampere hours, at 10% level of significance?

Tom and Jerry both arrive at a petrol pump. Without worrying about price, Tom says, “I want 10 liters of petrol.” Also, without worrying about price, Jerry says, “I want petrol worth 1000 rupees.” The own price elasticities of demand for Tom (denoted by \( \varepsilon_T \)) and Jerry (denoted by \( \varepsilon_J \)) are:

Which of the following variables are pushed upwards by ‘Seigniorage’?

Suppose Raju enters the job market at age 25 and earns annual income of Rs. 6000. He retires at age 65 and his life expectancy is 75 years. He does not own any assets. Assume that Raju consumes annual income uniformly over his lifetime. What will be his average propensity to consume during employment years?

A monopolist faces the following inverse demand function: \[ P = 40 - Q \] where \(P\) denotes price and \(Q\) denotes quantity. The monopolist has zero fixed cost and a marginal cost of 5 per unit of output produced. The monopolist aims to maximize profit. Suppose the government imposes a tax of 5 per unit of output on the monopolist. As a result, the price charged by the profit-maximizing monopolist to the consumer increases by:

Let \( f(x) \) be the probability distribution function of a random variable \( X \), where \[ f(x) = \frac{5x^4}{64} \quad \text{if} \quad -2<x<2 \] \[ = 0 \quad \text{otherwise} \] Let \( | \cdot | \) denote the modulus function. Then, \( P(|X|<1) \) and \( P(X^2<3) \) are given by (respectively):

Liquidity Adjustment Facility (LAF) uses the following instruments:

What is the weightage of manufacturing sector in the Index of Industrial Production (IIP) during 2020-2021? Note: numbers are in approximate values

The curve that explains the relationship between tax rate and tax revenue is known as:

Suppose the estimated consumption equation of an economy is: \[ C = 40 + \beta Y_d \] where \(Y_d\) is the personal disposable income, \(\beta\) is the marginal propensity to consume (MPC). Government expenditure \(G\) is given as 90. Total tax (\(T_x\)) received is \(\delta Y\), where \(Y\) is aggregate output or real income and \(\delta\) is tax to real income proportionality factor. Autonomous investment \(I_A\) is given as 80. What are the tax revenue and budget surplus of the government when \(\beta = 0.75\) and \(\delta = 0.20\)? All units are measured in constant rupees.

Consider a two-period consumption model in which a representative household lives for two periods only. In period 1, he earns income \(y_1\) and consumes \(c_1\). In period 2, he earns \(y_2\) and consumes \(c_2\). He can borrow and lend at the same rate of interest (\(r\)). His lifetime utility function is as follows: \[ U(c_1, c_2) = \ln(c_1) + \beta \ln(c_2) \] where \(\beta>0\) measures the sensitivity of future period’s consumption. What will be the marginal propensity to consume of current consumption, i.e. \(\frac{\partial c_1}{\partial y_1}\)?

Which one of the following is a test of heteroscedasticity?