List of top Questions asked in GATE XH-C1

The table lists the top 5 nations according to the number of gold medals won in a tournament; also included are the number of silver and the bronze medals won by them. Based only on the data provided in the table, which one of the following statements is INCORRECT?


 

Eight students (P, Q, R, S, T, U, V, and W) are playing musical chairs. The figure indicates their order of position at the start of the game. They play the game by moving forward in a circle in the clockwise direction.
After the 1st round, the 4th student behind P leaves the game.
After the 2nd round, the 5th student behind Q leaves the game.
After the 3rd round, the 3rd student behind V leaves the game.
After the 4th round, the 4th student behind U leaves the game.

Who all are left in the game after the 4th round?

A stick of length one meter is broken at two locations at distances of \( b_1 \) and \( b_2 \) from the origin (0), as shown in the figure. Note that \( 0<b_1<b_2<1 \). Which one of the following is NOT a necessary condition for forming a triangle using the three pieces? 
Note: All lengths are in meter. The figure shown is representative. 


 

Identify the option that has the most appropriate sequence such that a coherent paragraph is formed:
P: Over time, such adaptations lead to significant evolutionary changes with the potential to shape the development of new species.
Q: In natural world, organisms constantly adapt to their environments in response to challenges and opportunities.
R: This process of adaptation is driven by the principle of natural selection, where favorable traits increase an organism’s chances of survival and reproduction.
S: As environments change, organisms that can adapt their behavior, structure, and physiology to such changes are more likely to survive.
Which one of the following plots represents \( f(x) = -\frac{|x|}{x} \), where \( x \) is a non-zero real number?
Note: The figures shown are representative.

The following figures show three curves generated using an iterative algorithm. The total length of the curve generated after 'Iteration n' is: 


 

Meaning of 'Human Development':
Defend or refute the following statements with valid arguments:
"The policy of protectionism encouraged the growth of domestic industries, but at the same time proved to be an impediment."
Explain the need and type of land reforms implemented in the agriculture sector.
The Minimum Support Prices in India are notified based on the recommendations of which one among the following Commissions ?
In the Keynesian closed economy IS-LM model, where interest rate is plotted along the vertical axis and output is plotted along the horizontal axis, the product market schedule will be
In the Keynesian system, the speculative demand for money arises because of
Which of the following statements is/are TRUE ?
Consider a Cobb-Douglas utility function given as U(H) = (24 - H)1-a (wH)a, where H is the number of hours spent working per day, and w is the wage rate per hour. If \(a=\frac{1}{2}\) then the corresponding labour supply (in hours) is _______( in integer).
A dual economy consisting of a manufacturing sector (M) and an agricultural sector (A) is depicted in the figure below. OMOA is the total labour available in the economy of which OMLSM is the labour supply in the manufacturing sector before any migration was allowed among the labourers. The vertical axis in the left (right) side measures the wage in the manufacturing, WM (agricultural, WA) sector. LDM (LDA) is the demand of labour in the manufacturing (agricultural) sector with respect to OM(OA) as the origin. If wages are flexible, and labour is allowed to migrate between these two sectors, then it will be TRUE that
Graph of economy
An incumbent firm (I) faces the possibility of entry by a challenger firm (C). If C enters, I may either accommodate or fight. If C does not enter, its payoff is 1, while I's payoff is 2. If C enters, and I accommodates, their payoffs are 2 and 1, respectively. However, if C's entry is met with a fight by I, their payoffs are 0 and 1, respectively. Which one of the following is a subgame perfect Nash equilibrium (SPNE) under perfect information ?
Which of the following statements is/are FALSE ?
Suppose XYZ Corp. is totally financed by equity; it is earning Rs. 2.50 per share; its capitalization rate is 20%. There are 10,000 shares outstanding, and the replacement cost of the firm's real assets is Rs. 1,25,000. XYZ Corp.'s value of Tobin's q is _______ (in integer).
An industry comprising only two firms produces a homogenous product where the market demand function is given by P = 200 – 2(q1 +q2) where q1 and q2 are the output levels of firm 1 and firm 2, respectively. The individual firm's cost functions are TC1 = 4q1 and TC2 = 4q2, where TC1 and TC2 are total costs of firm 1 and 2, respectively. If firm 2 is a Stackelberg Leader, and firm 1 is a Follower, then the profit of the Stackelberg Leader will be ________ (rounded off to two decimal places).
In an economy, the effort level of a worker in firm i is denoted by e; and depends on the wage Wi received by the worker from the firm, and the minimum wage Wo is set by the government. The effort function is given by
\(e_i(W_iW_0)=\sqrt{W_i-W_0}\)
If the firm employs Ni unit of workers, then the efficiency unit of labour employed by the firm is eiNi. The production is based on only the efficiency unit of labour, and the production function is given by
\(F(e_iN_i) = \log e (e_iN_i)\)
If the minimum wage set by the government is 10, and the profit maximizing firms sell the good in a competitive market at price P by choosing Wi and N¡, then the profit maximizing wage set by the firm will be _______ (rounded off to one decimal place).
Consider an industry with six firms. An analyst collated the data for this industry as given below. The Herfindahl-Hirschman Index (HHI) for this industry will be ________ (in integer).
FirmMarket Share
F130%
F220%
F315%
F415%
F510%
F610%
Amma's tone in the context of the given passage is that of :
For Amma, the difference between men and women was a kind of discrimination and inequality; she felt strongly about women's rights but was not familiar with concepts like gender and patriarchy. She would have dismissed Betty Friedan because she was predominantly dealing with the problems of white middle-class women in the United States. Amma, and women of her generation, could de-link the oppression of women from the wider struggle for the liberation of human beings from class exploitation and imperialism. So Amma continued to play her role as mother and wife, but would often complain: 'I am a doormat on which everyone wipes their emotional dirt off".
Fill in the blanks by choosing the correct sequence for the following passage:
I am wearing for the first time some (i)_____ that I have never been able to wear for long at a time, as they are horribly tight. I usually put them on just before giving a lecture. The painful pressure they exert on my feet goads my oratorical capacities to their utmost. This sharp and overwhelming pain makes me sing like a nightingale or like one of those Neapolitan singers who also wear (ii)_______ that are too tight. The visceral physical longing, the overwhelming torture provoked by my (iii)_______ forces me to extract from words distilled and sublime truths, generalized by the supreme inquisition of the pain my (iv)_______ suffer.
The appropriate synonym for the word ‘ignite' in the following passage will be :
Spirituality must be integrated with education. Self-realization is the focus. Each one of us must become aware of our higher self. We are links of a great past to a grand future. We should ignite our dormant inner energy and let it guide our lives. The radiance of such minds embarked on constructive endeavor will bring peace, prosperity and bliss to this nation.
Which of the following sentences is punctuated correctly ?