List of top Questions asked in GATE XH-C1

A passage consists of 6 sentences. The first and sixth sentences of the passage are at their correct positions, while the middle four sentences (represented by P, Q, R, and S) are jumbled up. First sentence: Smoke oozed up between the planks. P: Passengers were told to be ready to quit the ship.
Q: The rising gale fanned the smouldering fire.
R: Everyone now knew there was fire onboard.
S: Flames broke out here and there.
Sixth sentence: Most people bore the shock bravely. The most logically CORRECT order for the given jumbled up sentences is

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?

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.

The Arecibo telescope does not resemble what most of us think of when we hear the word telescope. Its reflective surface covers an area of 20 acres, which is quite remarkable. Dangling above it are towers and cables, sub-reflectors and antennas, all of which can be positioned using 26 motors to transmit radio waves and receive echoes with astonishing precision. From the passage, it can be inferred that most telescopes

Tailgating another vehicle is unsafe and illegal. Many rear-end collisions are caused by drivers following too closely to the vehicle in front of them. The rules state that a driver must keep significant distance from the vehicle in front in order to stop safely and avoid a collision. Drivers should allow a minimum two seconds gap between their vehicle and the one ahead. At 60 km per hour, this equates to a gap of 33 meters; at 100 km per hour, it equates to a gap of 55 meters. More distance is needed to safely stop in rain or poor visibility, as during rain slippery roads reduce the effectiveness of braking. Which of the following statement(s) can be inferred from the above passage?

There are three separate, but equal-sized boxes. Inside each box, there are two separate small boxes. Inside each of the small boxes, there are four even smaller boxes. The total number of boxes will be _________.

In a specific language, \( \text{xer dan} \) means "big horse", \( \text{liro cas} \) means "red tomato", and \( \text{dum cas dan} \) means "big red barn".
The equivalent word for \textit{barn} in this language is

A relationship is expressed as Iodine : Goitre. The pair(s) of words showing SIMILAR relationship is/are

Three individuals are named P, Q, and R. Together they have a total of fifteen children, of which nine are boys. P has three girls and Q has the same number of boys. Q has one more child than P, who has four children. R has four more boys than the number of girls of P. The number of girls of R is equal to the number of boys of P. How many boys do R and P have?

Now, it is clear that the decline of a language must ultimately have political and economic causes: it is not due simply to the bad influence of this or that individual writer. But an effect can become a cause, reinforcing the original cause and producing the same effect in an intensified form, and so on indefinitely. A man may take to drink because he feels himself to be a failure, and then fail all the more completely because he drinks. It is rather the same thing that is happening to the English language. It becomes ugly and inaccurate because our thoughts are foolish, but the slovenliness of our language makes it easier for us to have foolish thoughts. (Adapted from Politics and the English Language by George Orwell.) The illustration of the man who takes to drink is used to underscore which of the following ideas in the passage above?

Given below is an inter-industry transactions matrix. If final demand for the agriculture sector changes from 150 units to 300 units and for the manufacturing sector changes from 120 units to 200 units, then the output of the agriculture sector should be _________ units (in integer).

Consider the following Table.

Based on the given data, the average Broad Money Multiplier for the period April - June is _________ (round off to three decimal places).

Two farmers, Rohit and Harish, graze their animals on a common land. They can choose to use this common resource ‘lightly’ or ‘heavily’ and the resulting strategic interaction may be described as a simultaneous-move game. The payoff matrix is given below:

The minimum value of the discount rate (where the discount rate is less than one) under infinite repetition of the game where the threat strategy (“Graze lightly if the opponent also grazes lightly, whereas, if the opponent reneges then always graze heavily in all the future periods”), is a Sub-game Perfect Nash Equilibrium (SPNE) and, both the farmers graze their animals lightly is _________ (round off to one decimal place).

Consider an intersection of roads without any traffic light. Two cars A and B approach an intersection and they want to proceed as indicated by respective arrows in the following diagram. If both proceed without stopping and there is an accident, then A would have a payoff of -100 and B would have a payoff of -500 (since B is responsible for the accident). If one stops, and the other proceeds then the payoff is: -5 and 10, respectively. If both of them stop, then it takes a little longer to reach their respective destinations, they have a payoff of -5 each. Find the Pure Strategy Nash Equilibrium (PSNE) of the players (Car drivers).

Let A and B be two events with probabilities \( P(A) = \frac{3}{4} \) and \( P(B) = \frac{1}{3} \); then which of the following options is true?

Consider an individual who maximizes her expected utility having Bernoulli utility function

Assuming that external economies exist, when demand increases in a perfectly competitive market, in the long-run, the price of the product:

Consider a regression model \( y = \beta_0 + \beta x + u \) where the continuous variable \( y \) is regressed on a dummy variable \( x \), which takes the value either 1 or 0. However, the model was estimated using the instrumental variable (IV) estimation method, wherein the indicator variable \( z \) is used as an instrument of \( x \). Let \( \bar{y}_1 \) and \( \bar{y}_0 \) be the sample averages of \( y \) when \( z \) takes the value 1 and 0, respectively. Let \( \bar{x}_1 \) and \( \bar{x}_0 \) be the sample averages of \( x \) when \( z \) takes the value 1 and 0, respectively. Let \( \bar{y}_1 \) and \( \bar{y}_0 \) be the sample averages of \( y \) when \( x \) takes the value 1 and 0, respectively. Let \( \bar{z}_1 \) and \( \bar{z}_0 \) be the sample averages of \( z \) when \( x \) takes the value 1 and 0, respectively. Then the estimated coefficient of \( \beta_{IV} \) is:

Piku faces a lottery with outcomes of ₹24, ₹12, ₹48 and ₹6 given by the following probability distribution:

She is indifferent between the lottery and receiving ₹28 with certainty. Given the information we can conclude that Piku is a

Let the rate of inflation in an economy be 4.2%, the growth rate of velocity of money be 2%, and the growth rate of real GDP be 6%. According to Milton Friedman’s ‘k’ percent rule, the rate of growth of money supply for maintaining stable prices will be _________ (round off to one decimal place).

The long-run cost function of all identical firms in a perfectly competitive industry is given by: \[ C = 25q - 3q^2 + 1.5q^3 \] The market demand function is: \[ P = 2500 - 0.25Q \] The number of firms in the industry at equilibrium is _________ (in integer).

Consider that a sample of size 3 is randomly drawn from a population that takes only two values, equally likely: -1 and 1. Let \( z = \max(x_1, x_2, x_3) \) where \( x_1, x_2, x_3 \) are the sample observations. The expected value of \( z \), \( E(z) \) is _________ (round off to two decimal places).

Suppose Vijay has purchased a high-speed car worth ₹1000000. During the purchase, an Insurance company has shared the latest available road safety survey, wherein it is mentioned that, due to heavy congestion on roads, there is a 40% chance of an accident within the first year of car purchase resulting in loss of the car value by 60%. Vijay’s utility function for wealth (W) is given by \( U(W) = \ln(W) \). If Vijay plans to buy an accident insurance having a premium of 30%, then he will purchase an insurance of ₹_________ (round off to the nearest integer).

Consider two regression models estimated on a sample of 350 observations.
\[ y = \beta_0 + \beta_1 x_1 + \beta_2 x_2 + \beta_3 x_3 + \beta_4 x_4 + \beta_5 x_5 + u \quad \text{--------(1)} \] \[ y = \alpha_0 + \alpha_1 x_1 + \alpha_2 x_2 + v \quad \text{--------(2)} \] The \( R^2 \) in model (1) is \( R^2_1 = 0.3521 \) and in model (2) is \( R^2_2 = 0.2314 \). The value of the test statistic to test the \( H_0: \beta_3 = \beta_4 = \beta_5 = 0 \) is _________ (round off to three decimal places).

Consider a competitive market where the demand and supply functions are given by \( q^d = 12 - 2P \) and \( q^s = 4P \), respectively. The tax rate per unit of output that maximizes the tax yield (revenue) is _________ (in integer).