List of top Questions asked in GATE AR

Consider performing depth-first search (DFS) on an undirected and unweighted graph G starting at vertex s. For any vertex u in G, d[u] is the length of the shortest path from s to u. Let (u, v) be an edge in G such that d[u] < d[v]. If the edge (u, v) is explored first in the direction from u to v during the above DFS, then (u, v) becomes a _____ edge.
For any twice differentiable function ƒ: R → R, if at some x* ∈ R, f'(x*) = 0 and f'(x*) > 0, then the function f necessarily has a ______ at x = x*.
Note : R denotes the set of real numbers.
Match the items in Column 1 with the items in Column 2 in the following table :
Column 1Column 2
(p)First In First Out(i)Stacks
(q)Lookup Operation(ii)Queues
(r)Last In First Out(iii)Hash Tables
Match the items in Column 1 with the items in Column 2 in the following table :
Column 1Column 2
(p)Principal Component Analysis(i)Discriminative Model
(q)Naïve Bayes Classification(ii)Dimensionality Reduction
(r)Logistic Regression(iii)Generative Model
Euclidean distance based k-means clustering algorithm was run on a dataset of 100 points with k = 3. If the points \(\begin{bmatrix} 1 \\ 1 \end{bmatrix}\) and \(\begin{bmatrix} -1 \\ 1 \end{bmatrix}\) are both part of cluster 3, then which ONE of the following points is necessarily also part of cluster 3 ?
Consider the following statements :
(i) The mean and variance of a Poisson random variable are equal.
(ii) For a standard normal random variable, the mean is zero and the variance is one.
Which ONE of the following options is correct ?
Three fair coins are tossed independently. T is the event that two or more tosses result in heads. S is the event that two or more tosses result in tails. What is the probability of the event T ∩ S?
Consider the matrix \(M=\begin{bmatrix} 2 & -1 \\ 3 & 1 \end{bmatrix}\).
Which ONE of the following statements is TRUE ?
In a one-way single lane traffic stream, the observed average time headway is 2.5 seconds. The traffic flow of the above mentioned lane, in vehicle/hr, is _______ (in integer).
The demand of a EcoCity theme park is estimated as P = 1500 7.5Q, where P (in Indian Rupees) is the price of a ticket for single entry, and Q (in integer) is the number of tickets sold per hour. The maximum revenue per hour along the demand curve, in Indian Rupees, is _______ (in integer)
A city with a present population of 1,75,000 is expecting an annual population growth rate of 0.85%. In a traffic assessment study, the trip generation model has been developed as Y = 142 +0.675X, where Y is the number of daily trips generated within the city and X is the population of the city. The number of daily trips to be generated within the city after 10 years is _______(in integer).
A 2 TR window air-conditioner of Energy Efficiency Ratio (EER) 3.1 is catering to a room of volume 40 \(m^3\). The air-conditioner is operational for 600 hours during summer on cooling mode. The compressor is also operational for the complete duration. The total energy consumption of the air-conditioner during the above mentioned period, in kWh, is _________(rounded off to nearest integer).
The network diagram of a construction project is shown in the following Figure. The duration of each activity, in days, and the early start time of the project are denoted in the diagram. The total project duration along the critical path, in days, is _____(in integer).
The network diagram of a construction project is shown in the following Figure. The duration of each activity,
A real estate developer is developing a township on a PPP mode. The total area of the site is 2.672 hectares with an allowable FAR of 2.25, of which 20% is earmarked for MIG category. The gross area of each MIG unit including common areas and services is 72 \(m^2\). Assuming super built up area to be same as FAR, the maximum number of MIG apartments that can be constructed _______(in integer).
A municipal town requires a volume of 70,000 \(m^3\) compacted solid waste to fill a low lying land. The city has a total of 10,000 households.
Type of HousePercentage of HouseholdsEquivalent volume of compacted solid waste generated/ household/ day
LIG30%0.10 \(m^3\)
MIG60%0.15 \(m^3\)
HIG10%0.20 \(m^3\)

Using the information as shown in the Table above, the estimated minimum number of days required to fill the low lying land is _______ (in integer).
At present, the cost of a new office equipment is 50,000 (in Indian Rupees). It has 15% salvage value after a useful life of 5 years. Using straight line method of depreciation, the book value of the equipment 3 years from now, in Indian Rupees, will be ______ (in integer).
Match the terminologies in Group-I with their descriptions in Group-II.
Group IGroup II
(P)   Edge City  (1) Rapid expansion of geographical areas of towns or cities
(Q)    Synekism (2) Violence against the city 
(R)    Urbicide (3) A secondary CBD on the edge of the city 
(S)    Urban Sprawl (4) Rebuilding core city area 
 (5) Union of several small urban settlements under one rule 
R(UVWXYZ)
Which FD can be determined from the above FD Set
Which FD can be determined from the above FD Set?

Match the items in Group-I with the most appropriate stages of travel demand modelling in Group-II. 

\[\begin{array}{|c|c|} \hline \textbf{Group I} & \textbf{Group II} \\ \hline (P)\ \text{US-EPA's MOVES} & (1)\ \text{Trip Assignment} \\ (Q)\ \text{Fratar Model} & (2)\ \text{Trip Production} \\ (R)\ \text{Growth Factor Model} & (3)\ \text{Trip Distribution} \\ (S)\ \text{User Equilibrium} & (4)\ \text{Mobile source emission estimation} \\ & (5)\ \text{Destination Choice} \\ \hline \end{array} \]
 

Match the Acts in Group-I with the corresponding organizations empowered by the Act in Group-II. 

\[\begin{array}{|c|c|} \hline \textbf{Group I} & \textbf{Group II} \\ \hline (P)\ \text{RERA 2016} & (1)\ \text{Chief Information Commission} \\ (Q)\ \text{RTI Act 2005} & (2)\ \text{Land Registration Board} \\ (R)\ \text{Town and Country Planning Act} & (3)\ \text{Real Estate Regulatory Authority} \\ (S)\ \text{Municipal Act} & (4)\ \text{Development Authority} \\ & (5)\ \text{Board of Councillors} \\ \hline \end{array} \]
 

As per URDPFI Guidelines (2015), match the following settlement types in Group-I to their population range in Group-II.

\[ \begin{array}{|c|c|} \hline \textbf{Group I} & \textbf{Group II} \\ \hline (P)\ \text{Large city} & (1)\ 50,000 \text{ to } 1 \,\text{lakh} \\ (Q)\ \text{Metropolitan city II} & (2)\ 50 \,\text{lakh to } 1 \,\text{crore} \\ (R)\ \text{Small town II} & (3)\ 20,000 \text{ to } 50,000 \\ (S)\ \text{Medium town I} & (4)\ \text{More than 1 crore} \\ & (5)\ 5 \,\text{lakh to } 10 \,\text{lakh} \\ \hline \end{array} \]

Match the application areas in Group I with the Satellites/Satellite sensors in Group II. 

Group IGroup II 
(P) Cyclone prediction(1) IRNSS 11 
(Q) Communication(2) HySIS 
 (R) High resolution mapping(3) GSAT 30
(S) Navigation(4) CARTOSAT 3
 (5) SCATSAT 1

 

Select the institution(s) that are mandated as per the 73rd Constitutional Amendment Act, 1992 of India.
Select the method(s) that can be used for landuse classification based on satellite images.
The figure below shows a contour diagram and two points (A \& B) on the continuously ascending surface. The horizontal projection of AB is 200 m long, and the gradient of AB is 1 in 25. The constant contour interval (in m) is \underline{\hspace{1cm}} [in integer]. \begin{center} \includegraphics[width=0.5\textwidth]{09.jpeg} \end{center}