[2013 : 2 Marks]
Question1.36: Find the sum of the expression 1/(√1+√2) + 1/(√2+√3) + 1/(√3+√4) + ….. + 1/(√80+√81)
Options: (a) 7 (b) 8 (c) 9 (d) 10
Answer: (b) 8
Reason: Rationalize karo: 1/(√n+√(n+1)) = √(n+1)-√n. Telescoping sum = √81-√1 = 9-1 = 8.
[2013 : 2 Marks]
Question1.37: Out of all the 2-digit integers between 1 and 100, a 2-digit number has to be selected at random. What is the probability that the selected number is not divisible by 7?
Options: (a) 13/90 (b) 12/90 (c) 78/90 (d) 77/90
Answer: (d) 77/90
Reason: 2-digit numbers total 90 (10 se 99). 7 se divisible 13 numbers hai (14,21…98). Not divisible = 90-13=77. Probability=77/90.
[2013 : 2 Marks]
Question1.38: After several defeats in wars, Robert Bruce went in exile and wanted to commit suicide. Just before committing suicide, he came across a spider attempting tirelessly to have its net. Time and again, the spider failed but did not deter it to refrain from making attempts. Such attempts by the spider made Bruce curious. Thus, Bruce started observing the near-impossible goal of the spider to have the net. Ultimately, the spider succeeded in having its net despite several failures. Such act of the spider encouraged Bruce not to commit suicide. And then, Bruce went back again and won many a battle, and the rest is history. Which one of the following assertions is best supported by the above information? (a) Failure is the pillar of success (b) Honesty is the best policy (c) Life begins and ends with adventures (d) No adversity justifies giving up hope
Answer: (d) No adversity justifies giving up hope
Reason: Story ka moral hai mushkilo me himmat na harna. Spider fail hoke bhi try karta raha, Bruce ne bhi hope nahi chodi.
[2013 : 2 Marks]
Question1.39: The current erection cost of a structure is Rs. 13,200. If the labour wages per day increase by 1/5 of the current wages and the working hours decrease by 1/24 of the current period, then the new cost of erection in Rs., is
Options: (a) 16,500 (b) 15,180 (c) 11,000 (d) 10,120
Answer: (b) 15,180
Reason: New = (6/5 Wage)*(23/24 Hours) = 138/120 *13200 = 1.15*13200=15180.
[2013 : 2 Marks]
Question1.41: Which of the following options is the closest in meaning to the phrase underlined in the sentence below? It is fascinating to see life forms cope with varied environmental conditions.
Options: (a) adopt to (b) adapt to (c) adept in (d) accept with
Answer: (b) adapt to
Reason: cope with = adapt to = mahaul ke hisab se dhal jana.
[2014 (Set-1) : 1 Mark]
Question1.42: Choose the most appropriate word to complete the sentence: He could not understand the judges awarding her the first prize, because he thought that her performance was quite __.
Options: (a) superb (b) medium (c) mediocre (d) exhilarating
Answer: (c) mediocre
Reason: Judge ne prize diya par usko laga performance achi nahi thi, to mediocre (average/bekar) aayega.
[2014 (Set-1) : 1 Mark]
Question1.43: In a press meet on the recent scam, the minister said, “The buck stops here”. What did the minister convey by the statement?
Options: (a) He wants all the money (b) He will return the money (c) He will assume final responsibility (d) He will resist all enquiries
Answer: (c) He will assume final responsibility
Reason: Idiom hai “buck stops here” = zimmedari mai leta hu, ab aage nahi jayegi.
[2014 (Set-1) : 1 Mark]
Question1.44: If (z + 1/z)^2 = 98, compute (z^2 + 1/z^2).
Answer: 96
Reason: (z+1/z)^2 = z^2+1/z^2+2 =98 => z^2+1/z^2=96.
[2014 (Set-1) : 2 Marks]
Question1.46: The Palghat Gap (or Palakkad Gap), a region about 30 km wide in the southern part of the Western Ghats in India, is lower than the hilly terrain to its north and south. The exact reasons for the formation of this gap are not clear. It results in the neighbouring regions of Tamil Nadu getting more rainfall from the South West monsoon and the neighbouring regions of Kerala having higher summer temperatures. What can be inferred from this passage? (a) The Palghat gap is caused by high rainfall and high temperatures in southern Tamil Nadu and Kerala (b) The regions in Tamil Nadu and Kerala that are near the Palghat Gap are low-lying (c) The low terrain of the Palghat Gap has a significant impact on weather patterns in neighbouring parts of Tamil Nadu and Kerala (d) Higher summer temperatures result in higher rainfall near the Palghat Gap area
Answer: (c) The low terrain of the Palghat Gap has a significant impact on weather patterns in neighbouring parts of Tamil Nadu and Kerala
Reason: Passage bol raha hai gap neeche hone ki wajah se Tamil Nadu me jyada barish aur Kerala me garmi badhti hai. Matlab low terrain ka weather pe impact hai. (a) ulta reason de raha hai, isliye galat.
[2014 (Set-1) : 2 Marks]
Question1.47: Geneticists say that they are very close to confirming the genetic roots of psychiatric illnesses such as depression and schizophrenia, and consequently, that doctors will be able to eradicate these diseases through early identification and gene therapy. On which of the following assumptions does the statement above rely? (a) Strategies are now available for eliminating psychiatric illnesses (b) Certain psychiatric illnesses have a genetic basis (c) All human diseases can be traced back to genes and how they are expressed (d) In the future, genetics will become the only relevant field for identifying psychiatric illnesses
Answer: (b) Certain psychiatric illnesses have a genetic basis
Reason: Agar genetic root hai tabhi gene therapy se eradicate kar payenge. To assumption yahi hai ki in bimariyo ka genetic basis hai.
[2014 (Set-1) : 2 Marks]
Question1.48: Round-trip tickets to a tourist destination are eligible for a discount of 10% on the total fare. In addition, groups of 4 or more get a discount of 5% on the total fare. If the one way single person fare is Rs 100, a group of 5 tourists purchasing round-trip tickets will be charged Rs __.
Answer: 850
Reason: One way 100, round trip per person 200. 5 ka total 1000. 10% discount=100 + 5% group discount=50, Total discount 150. 1000-150=850. Agar successive discount lo to 855 aayega.
[2014 (Set-1) : 2 Marks]
Question1.49: In a survey, 300 respondents were asked whether they own a vehicle or not. If yes, they were further asked to mention whether they own a car or scooter or both. Their responses are tabulated below. What percent of respondents do not own a scooter? Table: Own vehicle Car Men 40 Women 34, Scooter Men 30 Women 20, Both Men 60 Women 46, Do not own vehicle Men 20 Women 50.
Answer: 48%
Reason: Scooter own karne wale = Only Scooter + Both = (30+60)=90 Men + (20+46)=66 Women =156. Total 300. Not owning scooter =300-156=144. 144/300=48%.
[2014 (Set-1) : 2 Marks]
Question1.50: When a point inside of a tetrahedron (a solid with four triangular surfaces) is connected by straight lines to its corners, how many (new) internal planes are created with these lines? __.
Answer: 6
Reason: Tetrahedron ke 6 edges hote hai. Har edge + andar wala point ek naya internal plane banata hai. Total 6 planes.
[2014 (Set-2) : 1 Mark]
Question1.51: Choose the most appropriate phrase to complete the sentence: India is a post-colonial country because (a) it was a former British colony (b) Indian IT professionals have colonized the world (c) India does not follow any colonial practices (d) India has helped other countries gain freedom
Answer: (a) it was a former British colony
Reason: Post-colonial matlab pehle colony tha, ab aazad hai.
[2014 (Set-2) : 1 Mark]
Question1.52: Who __ was coming to see us this evening? (a) you said (b) did you say (c) did you say that (d) had you said
Answer: (a) you said
Reason: Correct reported speech structure: “Who you said was coming…”
[2014 (Set-2) : 1 Mark]
Question1.53: Match the columns: Column 1 (1) eradicate (2) distort (3) saturate (4) utilize Column 2 (P) misrepresent (Q) soak completely (R) use (S) destroy utterly Codes: (a) 1:S, 2:P, 3:Q, 4:R (b) 1:P, 2:Q, 3:R, 4:S (c) 1:Q, 2:R, 3:S, 4:P (d) 1:S, 2:P, 3:R, 4:Q
Answer: (a) 1:S, 2:P, 3:Q, 4:R
Reason: eradicate=destroy utterly, distort=misrepresent, saturate=soak completely, utilize=use.
[2014 (Set-2) : 1 Mark]
Question1.54: What is the average of all multiples of 10 from 2 to 198? (a) 90 (b) 100 (c) 110 (d) 120
Answer: (b) 100
Reason: 10,20,…190. Total 19 numbers. Average = (10+190)/2 =100.
[2014 (Set-2) : 1 Mark]
Question1.55: The value of √(12 + √(12 + √(12 + …))) is (a) 3.464 (b) 3.932 (c) 4.000 (d) 4.444
Answer: (c) 4.000
Reason: x=√(12+x) => x^2=12+x => x^2-x-12=0 => x=4.
[2014 (Set-2) : 2 Marks]
Question1.56: The old city of Koenigsberg, which had a German majority population before World War 2, is now called Kaliningrad. After the events of the war, Kaliningrad is now a Russian territory and has a predominantly Russian population. It is bordered by the Baltic Sea on the north and the countries of Poland to the south and west and Lithuania to the east respectively. Which of the statements below can be inferred from this passage? (a) Kaliningrad was historically Russian in its ethnic make up (b) Kaliningrad is a part of Russia despite it not being contiguous with the rest of Russia (c) Koenigsberg was renamed Kaliningrad, as that was its original Russian name (d) Poland and Lithuania are on the route from Kaliningrad to the rest of Russia
Answer: (b) Kaliningrad is a part of Russia despite it not being contiguous with the rest of Russia
Reason: Passage se clear hai ab Russian hai par Poland/Lithuania se ghira hai, matlab mainland Russia se contiguous nahi hai.
[2014 (Set-2) : 2 Marks]
Question1.57: The number of people diagnosed with dengue fever (contracted from the bite of a mosquito) in north India is twice the number diagnosed last year. Municipal authorities have concluded that measures to control the mosquito population have failed in this region. Which one of the following statements, if true, does not contradict this conclusion? (a) A high proportion of the affected population has returned from neighbouring countries where dengue is prevalent (b) More cases of dengue are now reported because of an increase in the Municipal Office’s administrative efficiency (c) Many more cases of dengue are being diagnosed this year since the introduction of a new and effective diagnostic test (d) The number of people with malarial fever (also contracted from mosquito bites) has increased this year
Answer: (d) The number of people with malarial fever (also contracted from mosquito bites) has increased this year
Reason: Malaria bhi mosquito se hota hai, uska badhna matlab mosquito control fail hua hai. Ye conclusion ko support karta hai, contradict nahi karta. Baaki a,b,c me increase ka reason dusra hai, jo failure conclusion ko contradict karta hai.
[2014 (Set-2) : 2 Marks]
Question1.58: If x is real and |x^2 – 2x + 3| = 11, then possible values of |-x^3 + x^2 – x| include
Options: (a) 2, 4 (b) 2, 14 (c) 4, 52 (d) 14, 52
Answer: (d) 14, 52
Reason: x^2-2x+3 = (x-1)^2+2 hamesha positive, to =11 => x^2-2x-8=0 => x=4, -2. x=4 pe value |-64+16-4|=52, x=-2 pe |8+4+2|=14.
[2014 (Set-2) : 2 Marks]
Question1.59: The ratio of male to female students in a college for five years is plotted in the graph. If the number of female students doubled in 2009, by what percent did the number of male students increase in 2009? [Graph: 2008~2.5, 2009~3.0]
Answer: 140% to 200% (Exact graph ke hisab se) [Official GATE me graph se: 2008=2.5, 2009=3 => Increase = (3*2-2.5)/2.5=140%]
Reason: M = Ratio * F. F09=2F08. %inc = (R092 – R08)/R08 *100.
[2014 (Set-2) : 2 Marks]
Question1.60: At what time between 6 a.m. and 7 a.m. will the angle closest to 60°? (a) 6:22 a.m. (b) 6:27 a.m. (c) 6:38 a.m. (d) 6:45 a.m.
Answer: (a) 6:22 a.m.
Reason: Angle = |180 – 5.5M| =60 => M=21.81 min. 6:22 sabse close.
[2014 (Set-3) : 1 Mark]
Question1.61: While trying to collect (I) an envelope from under the table (II), Mr. X fell down (III) and was losing consciousness (IV). Which underlined part is NOT appropriate?
Options: (a) I (b) II (c) III (d) IV
Answer: (d) IV
Reason: was losing consciousness galat hai, simple past ‘lost consciousness’ ya ‘was losing’ ke jagah ‘lost’ hona chahiye. Sequence me fall ke baad lost.
[2014 (Set-3) : 1 Mark]
Question1.62: If she _ how to calibrate the instrument, she _ done the experiment. (a) knows, will have (b) knew, had (c) had known, could have (d) should have known, would have
Answer: (c) had known, could have
Reason: Past unreal conditional – If + past perfect, could/would have + V3.
[2014 (Set-3) : 1 Mark]
Question1.63: Choose the word that is opposite in meaning to the word “coherent”. (a) sticky (b) well-connected (c) rambling (d) friendly
Answer: (c) rambling
Reason: coherent = logical, connected. Opposite = rambling = bina logic ke bhatakna.
[2014 (Set-3) : 1 Mark]
Question1.64: Which number does not belong in the series below? 2, 5, 10, 17, 26, 37, 50, 64 (a) 17 (b) 37 (c) 64 (d) 26
Answer: (c) 64
Reason: Series n^2+1 hai, 8^2+1=65 hona chahiye, 64 galat hai.
[2014 (Set-3) : 1 Mark]
Question1.65:Table: Q.No Marks Answered Correctly Answered Wrongly Not Attempted – Q1 2 21 17 6, Q2 3 15 27 2, Q3 2 23 18 3. What is the average of the marks obtained by the class in the examination? (a) 1.34 (b) 1.74 (c) 3.02 (d) 3.91
Answer: (c) 3.02
Reason: Total students=44. Total marks=212+153+23*2=42+45+46=133. Avg=133/44=3.022.
[2014 (Set-3) : 2 Marks]
Question1.66: A dance programme is scheduled for 10.00 a.m. Some students are participating and they need to come an hour earlier than the start. These students should be accompanied by a parent. Other students and parents should come in time. Which instruction is appropriate?
Answer: (d) Participating students should come before 9.00 a.m. Parents who accompany them should come at 9.00 a.m. All others should come at 10.00 a.m.
Reason: Participating wale 1 hr pehle = 9 baje se pehle, unke parents exactly 9 baje, baaki sab 10 baje programme time pe.
[2014 (Set-3) : 2 Marks]
Question1.67: By the beginning of the 20th century, several hypotheses were being proposed, suggesting a paradigm shift in our understanding of the universe. However, the clinching evidence was provided by experimental measurements of the position of a star which was directly behind our sun. Which of the following inference(s) may be drawn from the above passage? (i) Our understanding of the universe changes based on the positions of stars (ii) Paradigm shifts usually occur at the beginning of centuries (iii) Stars are important objects in the universe (iv) Experimental evidence was important in confirming this paradigm shift Options: (a) (i),(ii) and (iv) (b) (iii) only (c) (i) and (iv) (d) (iv) only
Answer: (c) (i) and (iv)
Reason: Passage me star ki position se universe ki understanding badli aur experimental evidence se confirm hua. Isliye (i) aur (iv) sahi hai. (ii) me ‘usually’ galat hai, sirf ek baar ka example hai.
[2014 (Set-3) : 2 Marks]
Question1.68: The Gross Domestic Product (GDP) in Rupees grew at 7% during 2012-2013. For international comparison, the GDP is compared in US Dollars (USD) after conversion based on the market exchange rate. During the period 2012-2013 the exchange rate for the USD increased from Rs. 50/ USD to Rs. 60/ USD. India’s GDP in USD during the period 2012-2013 (a) increased by 5% (b) decreased by 13% (c) decreased by 20% (d) decreased by 11%
Answer: (d) decreased by 11%
Reason: Maan lo 2012 GDP =100 Rs =2 USD (50 rate). 2013 GDP =107 Rs =107/60=1.783 USD. %change = (1.783-2)/2 = -10.83% ~ -11%.
[2014 (Set-3) : 2 Marks]
Question1.69: The ratio of male to female students in a college for five years is plotted in the following line graph. If the number of female students in 2011 and 2012 is equal, what is the ratio of male students in 2012 to male students in 2011? Graph: 2008=2.4, 2009=2.8, 2010=1.7, 2011=0.5, 2012=1.0 Options: (a) 1:1 (b) 2:1 (c) 1.5:1 (d) 2.5:1
Answer: (b) 2:1 [Graph ke exact value ke hisab se 1.5:1 bhi mana jata hai]
Reason: Female same hai F11=F12. Male = Ratio * Female. M12/M11 = Ratio12/Ratio11 = 1.0/0.5 =2 => 2:1. Agar book me Ratio11=0.66 dikhaya hai to 1/0.66=1.5:1 aayega. Tere photo me 2011 ka point 0.5 pe hai to answer 2:1.
[2014 (Set-3) : 2 Marks]
Question1.70: Consider the equation: (7526)_8 – (Y)_8 = (4364)_8, where (X)_N stands for X to the base N. Find Y.
Options: (a) 1634 (b) 1737 (c) 3142 (d) 3162
Answer: (c) 3142
Reason: Octal me ghatao: 7526-4364=3142. Decimal check: 7526_8=3926, 4364_8=2292, diff=1634 decimal jo octal me 3142 hota hai.