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GATE Electronics & Communication · Analogy · 2010-2026
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Rosen — Discrete Mathematics and Its Applications
Discrete structures, counting, relations, graph theory
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Had I learnt acting as a child, I__________a famous film star. Select the most appropriate option to complete the above sentence.
An organization allows its employees to work independently on consultancy projects but charges an overhead on the consulting fee. The overhead is 20\% of the consulting fee, if the...
The 12 musical notes are given as $C, C^{\#}, D, D^{\#}, E, F, F^{\#}, G, G^{\#}, A, A^{\#}$. Frequency of each note is $\sqrt[12]{2}$ times the frequency of the previous note. If...
Five years ago, the ratio of Aman’s age to his father’s age was 1:4, and five years from now, the ratio will be 2:5. What was his father’s age when Aman was born?
The greatest prime factor of $(3^{199} - 3^{196})$ is
Two identical sheets A and B, of dimensions 24 cm × 16 cm, can be folded into half using two distinct operations, FO1 or FO2. In FO1, the axis of folding remains parallel to the in...
"I cannot support this proposal. My __________ will not permit it."
Courts : __________ : : Parliament : Legislature (By word meaning)
What is the smallest number with distinct digits whose digits add up to 45?
In a class of 100 students, (i) there are 30 students who neither like romantic movies nor comedy movies, (ii) the number of students who like romantic movies is twice the number o...
Out of 1000 individuals in a town, 100 unidentified individuals are covid positive. Due to lack of adequate covid-testing kits, the health authorities of the town devised a strateg...
A 100 cm $$\times$$ 32 cm rectangular sheet is folded 5 times. Each time the sheet is folded, the long edge aligns with its opposite side. Eventually, the folded sheet is a rectang...
Mr. X speaks ____________ Japanese ___________ Chinese.
A sum of money is to be distributed among P, Q, R, and S in the proportion 5 : 2 : 4 : 3, respectively. If R gets Rs. 1000 more than S, what is the share of Q (in Rs.) ?
A trapezium has vertices marked as P, Q, R and S (in that order anticlockwise). The side PQ is parallel to side SR. Further, it is given that, PQ = 11 cm, QR = 4 cm, RS = 6 cm and...
Mosquitoes pose a threat to human health. Controlling mosquitoes using chemicals may have undesired consequences. In Florida, authorities have used genetically modified mosquitoes...
Consider the following inequalities. (i) 2x $$-$$ 1 > 7 (ii) 2x $$-$$ 9 Which one of the following expressions below satisfies the above two inequalities?
In a class of five students P, Q, R, S and T, only one student is known to have copied in the exam. The disciplinary committee has investigated the situation and recorded the state...
Consider a square sheet of side 1 unit. In the first step, it is cut along the main diagonal to get two triangles. In the next step, one of the cut triangles is revolved about its...
Given below are two statements and two conclusions. Statement 1 : All purple are green Statement 2 : All black are green Conclusion I : Some black are purple. Conclusion II : No bl...
Computers are ubiquitous. They are used to improve efficiency in almost all fields from agriculture to space exploration. Artificial intelligence (AI) is currently a hot topic AI e...
p and q are positive integers and $${p \over q} + {q \over p} = 3$$, then $${{{p^2}} \over {{q^2}}} + {{{q^2}} \over {{p^2}}}$$ =
The current population of a city is 11,02,500. If it has been increasing at the rate of 5% per annum, what was its population 2 yeas ago?
He was not only accused of theft $\_\_\_\_$ of conspiracy.
It is quarter past three in your watch. The angle between the hour hand and the minute hand is $\_\_\_\_$ .
Five different books (P, Q, R, S, T) are to be arranged on a shelf. The books R and S are to be arranged first and second respectively from right side of the shelf. The number of d...
Two design consultants, P and Q, started working from 8 AM for a client. The client budgeted a total of USD 3000 for the consultants. P stopped working when hour hand moved by 210...
It would take one machine 4 hours to complete a production order and another machine 2 hours to complete the same order. If both machine work simultaneously at their respective con...
"Even though there is a vast scope for its __________, tourism has remained a/an _________ area." The words that best fill the blanks in the above sentence are
A coastal region with unparalleled beauty is home to many species of animals. It is dotted with coral reefs and unspoilt white sandy beaches. It has remained inaccessible to touris...
A 1.5 m tall person is standing at a distance of 3 m from a lamp post. The light from the lamp at the top of the post casts her shadow. The length of the shadow is twice her height...
What is the value of $$1 + {1 \over 4} + {1 \over {16}} + {1 \over {64}} + {1 \over {256}} + ......$$?
Leila aspires to buy a car worth Rs. 10,00,000 after 5 years. What is the minimum amount in Rupees that she should deposit now in a bank which offers 10% annual rate of interest, i...
1200 men and 500 women can build a bridge in 2 weeks. 900 men and 250 women will take 3 weeks to build the same bridge. How many men will be needed to build the bridge in one week?
In the summer, water consumption is known to decrease overall by 25%. A water Board official states that in the summer household consumption decreases by 20%, while other consumpti...
40% of deaths on city roads may be attributed to drunken driving. The number of degrees needed to represent this as a slice of a pie chart is
A rule states that in order to drink beer one must be over 18 years old. In a bar, there are 4 people. P is 16 years old, Q is 25 years old, R is drinking milkshake and S is drinki...
Fatima starts from point P, goes North for 3 km, and then East for 4 km to reach point Q. She then turns to face point P and goes 15 km in that direction. She then goes North for 6...
500 students are taking one or more courses out of Chemistry, Physics, and Mathematics. Registration records indicate course enrolment as follows: Chemistry (329), Physics (186), M...
Trucks (10 m long) and cars (5 m long) go on a single lane bridge. There must be a gap of at least 20 m after each truck and a gap of at least 15 m after each car. Trucks and cars...
“If you are looking for a history of India, or for an account of the rise and fall of the British Raj, or for the reason of the cleaving of the subcontinent into two mutually antag...
$$500$$ students are taking one or more courses out of chemistry, physics and Mathematics. Registration records indicate course enrolment as follows: chemistry $$(329)$$, physics $...
The number of 3 digit numbers such that the digit 1 is never to the immediate right of 2 is
Each of P, Q, R, S, W, X, Y and Z has been married at most once. X and Y married and have two children P and Q, Z is grandfather of the daughter ‘S’ of P. Further Z and W married a...
S, T, U, V, W, X, Y and Z are seated around a circular table. T's neighbors are Y and V. Z is seated third to the left of T and second to the right of S. U's neighbors are S and Y:...
In a huge pile of apples and oranges, both ripe and unripe mixed together, 15% are unripe fruits. Of the unripe fruits, 45% are apples. Of the ripe ones, 66% are oranges. If the pi...
S, M, E and F are working in shifts in a team to finish a project. M works with twice the efficiency of others but for half as many days as E worked. S and M have 6 hour shifts in...
The number that least fits this set: (324, 441, 97 and 64) is ________.
It takes 10 s and 15 s, respectively, for two trains traveling at different constant speeds to completely pass a telegraph post. The length of the first train is 120 m and that of...
If $$\log_x\left(\frac57\right)=\frac{-1}3$$, then the value of x is
Operators $$\square$$,◊,$$\rightarrow$$ are defined by : a $$\square$$ b = $$\frac{a-b}{a+b}$$; a ◊ b = $$\frac{a+b}{a-b}$$; a $$\rightarrow$$ b = ab. Find the value of (66 $$\squa...
Ram and Ramesh appeared in an interview for two vacancies in the same department. The probability of Ram’s selection is 1/6 and that of Ramesh is 1/8. What is the probability that...
If x>y>1, which of the following must be true? $$$\begin{array}{l}\mathrm i.\;\ln\left(\mathrm x\right)>\ln\left(\mathrm y\right)\;\;\;\;\;\;\;\;\;\;\mathrm{ii}.\;\;\mathrm e^\math...
Find the missing sequence in the letter series below: A, CD, GHI, ? , UVWXY
In a housing society, half of the families have a single child per family, while the remaining half have two children per family. The probability that a child picked at random, has...
A train that is 280 meters long, traveling at a uniform speed, crosses a platform in 60 seconds and passes a man standing on the platform in 20 seconds. What is the length of the p...
A car travels 8 km in the first quarter of an hour, 6 km in the second quarter and 16 km in the third quarter. The average speed of the car in km per hour over the entire journey i...
Find the sum to n terms of the series 10 + 84 + 734 +.........
What is the chance that a leap year, selected at random, will contain 53 Sundays?
In the summer of 2012, in New Delhi, the mean temperature of Monday to Wednesday was 41ºC and of Tuesday to Thursday was 43ºC. If the temperature on Thursday was 15% higher than th...
Raju has 14 currency notes in his pocket consisting of only Rs. 20 notes and Rs. 10 notes. The total money value of the notes is Rs. 230. The number of Rs. 10 notes that Raju has i...
There are eight bags of rice looking alike, seven of which have equal weight and one is slightly heavier. The weighing balance is of unlimited capacity. Using this balance, the min...
Choose the most appropriate word from the options given below to complete the following sentence: Given the seriousness of the situation that he had to face, his ________ was impre...
There are two candidates P and Q in an election. During the campaign, 40% of the voters promised to vote for P, and rest for Q. However, on the day of election 15% of the voters we...
Three friends, R, S and T shared toffee from a bowl. R took 1/3 rd of the toffees, but returned four to the bowl. S took 1/4 rd of what was left but returned three toffees to the b...
Given that f(y) = |y| / y, and q is any non-zero real number, the value of | f(q) - f(-q) | is
The sum of n terms of the series 4 + 44 + 444 +.... is
Choose the most appropriate word from the options given below to complete the following sentence: It was her view that the country's problems had been_________ by foreign technocra...
25 persons are in a room. 15 of them play hockey, 17 of them play football and 10 of them play both hockey and football. Then the number of persons playing neither hockey nor footb...
Hari (H), Gita (G), Irfan (I) and Saira (S) are siblings (i.e. brothers and sisters). All were born on 1 st January. The age difference between any two successive siblings (that is...
5 skilled workers can build a wall in 20 days; 8 semi-skilled workers can build a wall in 25 days; 10 unskilled workers can build a wall in 30 days. If a team has 2 skilled, 6 semi...
Which of the following options is the closest in meaning to the world below: Circuitous
The question below consists of a pair of related of related words followed by four pairs of words. Select the pair that best expresses the relation in the original pair. Unemployed...