Question 1
What will be the maximum sum of 44, 42, 40, ...... ?
A
502
B
504
C
506
D
500
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Question 1 Explanation: 
This is a decreasing arithmetic progression with difference as 2. The series is 44, 42, 40 ...... 0, -2, -4...... The sum would be maximum if we consider the series till 0 or 2. So sum would be 506 using the AP Sum formula given here
Question 2
Find the sum of the expression gatecs201321
A
7
B
8
C
9
D
10
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Question 2 Explanation: 
The Series can be re-written as (√2-√1)/(√2+√1)(√2-√1) + (√3-√2)/(√2+√2)(√3-√2) + .......... which simplifies to (√2-√1) + (√3-√2) + ..... (√81-√80) which again simplifies to √81 - √1 which is 8
Question 3
A tourist covers half of his journey by train at 60 km/h, half of the remainder by bus at 30 km/h and the rest by cycle at 10 km/h. The average speed of the tourist in km/h during his entire journey is
A
36
B
30
C
24
D
18
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Question 3 Explanation: 
Let total distance be D Total Time = D(1/2*60 + 1/4*30 + 1/4*10) = D/24 Average Speed = Total distance / Total time = 24
Question 4
Consider the following logical inferences.
I1: If it rains then the cricket match will not be played.
The cricket match was played.
Inference: There was no rain.
I2: If it rains then the cricket match will not be played.
It did not rain.
Inference: The cricket match was played.
Which of the following is TRUE?
A
Both I1 and I2 are correct inferences
B
I1 is correct but I2 is not a correct inference
C
I1 is not correct but I2 is a correct inference
D
Both I1 and I2 are not correct inferences
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Question 4 Explanation: 
The cricket match may not be played even if doesn't rain.
Question 5
The cost function for a product in a firm is given by 5q2, where q is the amount of production. The firm can sell the product at a market price of Rs 50 per unit. The number of units to be produced by the firm such that the profit is maximized is
A
5
B
10
C
15
D
25
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Question 5 Explanation: 
Profit = Price - Cost
       = 50q - 5q2
The value of above expression is maximum at q = 5. 
Question 6
A political party orders an arch for the entrance to the ground in which the annual convention is being held. The profile of the arch follows the equation y = 2x – 0.1x2 where y is the height of the arch in meters. The maximum possible height of the arch is
A
8 meters
B
10 meters
C
12 meters
D
14 meters
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Question 6 Explanation: 
y = 2x – 0.1x2 dy/dx = 2 - 0.2x So the value maximizes at 2 - 0.2x = 0 => x = 10 => y = 20 - 10 = 10 meters
Question 7
An automobile plant contracted to buy shock absorbers from two suppliers X and Y. X supplies 60% and Y supplies 40% of the shock absorbers. All shock absorbers are subjected to a quality test. The ones that pass the quality test are considered reliable. Of X’s shock absorbers, 96% are reliable. Of Y’s shock absorbers, 72% are reliable. The probability that a randomly chosen shock absorber, which is found to be reliable, is made by Y is
A
0.288
B
0.334
C
0.667
D
0.720
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Question 7 Explanation: 
Probability that the absorber is reliable = 0.96*0.6 + 0.72*0.4 
                                          = 0.576 + 0.288


Probability that  the absorber is from y and reliable = 
            (Probability that is made by Y)  X (Probability that it is reliable)
           = 0.4 * 0.72 
           = 0.288

The probability that randomly picked reliable absorber is from y = 
    (Probability that  the absorber is from y and reliable) / (>Probability that the absorber is reliable )
   = (0.288)/ (0.576 + 0.288) 
   =  0.334 
Question 8
Which of the following assertions are CORRECT? P: Adding 7 to each entry in a list adds 7 to the mean of the list Q: Adding 7 to each entry in a list adds 7 to the standard deviation of the list R: Doubling each entry in a list doubles the mean of the list S: Doubling each entry in a list leaves the standard deviation of the list unchanged
A
P, Q
B
Q, R
C
P, R
D
R, S
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Question 8 Explanation: 
Mean is average.
Let us consider below example
[Tex] 2,\ 4,\ 4,\ 4,\ 5,\ 5,\ 7,\ 9 [/Tex]

These eight data points have the mean (average) of 5:
[Tex] \frac{2 + 4 + 4 + 4 + 5 + 5 + 7 + 9}{8} = 5. [/Tex]

When we add 7 to all numbers, mean becomes 12 so P is TRUE.

If we double all numbers mean becomes double, so R is also
TRUE.

Standard Deviation is square root of variance.
Variance is sum of squares of differences between all numbers
and means.

Deviation for above example
First, calculate the deviations of each data point from the mean, 
and square the result of each:

[Tex] \begin{array}{lll} (2-5)^2 = (-3)^2 = 9 && (5-5)^2 = 0^2 = 0 \\ (4-5)^2 = (-1)^2 = 1 && (5-5)^2 = 0^2 = 0 \\ (4-5)^2 = (-1)^2 = 1 && (7-5)^2 = 2^2 = 4 \\ (4-5)^2 = (-1)^2 = 1 && (9-5)^2 = 4^2 = 16. \\ \end{array} [/Tex]

[Tex]variance = \frac{9 + 1 + 1 + 1 + 0 + 0 + 4 + 16}{8} = 4. [/Tex]

[Tex]standard deviation = \sqrt{ 4 } = 2 [/Tex]

If we add 7 to all numbers, standard deviation won't change 
as 7 is added to mean also. So Q is FALSE.

If we double all entries, standard deviation also becomes 
double.  So S is false. 
References: https://en.wikipedia.org/wiki/Standard_deviation http://staff.argyll.epsb.ca/jreed/math30p/statistics/standardDeviation.htm
Question 9
Given the sequence of terms, AD CG FK JP, the next term is
A
OV
B
OW
C
PV
D
PW
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Question 9 Explanation: 
Here 1st letter of each term in order are: A C F J Now In alphabets, A and C have a difference of 1 alphabet, C and F have a difference of 2, and F and J have a difference of 3. Hence next term here should contain its 1st letter as an alphabet with a difference of 4 after J, i.e O. Similarly, 2nd letter of each term in order are: D G K P Now In alphabets, D and G have a difference of 2 alphabets, G and K have a difference of 3, and K and P have a difference of 4. Hence next term here should contain its 2nd letter as an alphabet with a difference of 5 after P, i.e V.
Question 10
If Log(P) = (1/2)Log(Q) = (1/3)Log(R), then which of the following options is TRUE?
A
P2 = Q3R2
B
Q2 = PR
C
Q2 = R3P2
D
R = P2Q2
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Question 10 Explanation: 
It is given that Log(P) = (1/2)Log(Q) = (1/3)Log(R)

Let Log(P) = (1/2)Log(Q) = (1/3)Log(R) = C

Let the base of log be B

P = BC
Q = B2C
R = B3C

Which means Q2 = PR
Question 11
P, Q, R and S are four types of dangerous microbes recently found in a human habitat. The area of each circle with its diameter printed in brackets represents the growth of a single microbe surviving human immunity system within 24 hours of entering the body. The danger to human beings varies proportionately with the toxicity, potency and growth attributed to a microbe shown in the figure below: ME_2011_63 A pharmaceutical company is contemplating the development of a vaccine against the most dangerous microbe. Which microbe should the company target in its first attempt?
A
P
B
Q
C
R
D
S
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Question 11 Explanation: 
Answer should be A **The danger to human beings varies proportionately with the toxicity, potency and growth attributed to a microbe**
P = 800*0.4*50 = 16000
Q = 600*0.5*40 = 12000
R = 300*0.4*30 = 3600
S = 200*0.8*20 = 3200
Question 12
The variable cost (V) of manufacturing a product varies according to the equation V = 4q, where q is the quantity produced. The fixed cost (F) of production of same product reduces with q according to the equation F = 100/q.How many units should be produced to minimize the total cost (V+F)?
A
5
B
4
C
7
D
6
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Question 12 Explanation: 
The value of V+F is 4q + 100/q We can try all possible options and see that q = 5 gives the minimum value
Question 13
A transporter receives the same number of orders each day. Currently, he has some pending orders (backlog) to be shipped. If he uses 7 trucks, then at the end of the 4th day he can clear all the orders. Alternatively, if he uses only 3 trucks, then all the orders are cleared at the end of the 10th day. What is the minimum number of trucks required so that there will be no pending order at the end of the 5th day?
A
4
B
5
C
6
D
7
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Question 13 Explanation: 
Let each truck can take at most x units.  Let the daily order be y and let backlog be z.

7*4*x = 4y + z
3*10*x = 10y + z

We need value of (5y + z)/5 in terms of x.

We can get value of y by subtracting first from second
6y = 2x
y = x/3

We can get value of z by substituting  value of y in first equation
4y + z = 28x
4(x/3) + z = 28x
z = (80/3)x

So the value of (5y + z)/5 is 5*(x/3) + (80/3)x  which is 17/3

So almost 6 days needed.
Question 14
A container originally contains 10 litres of pure spirit. From this container 1 litre of spirit is replaced with 1 litre of water. Subsequently, 1 litre of the mixture is again replaced with 1 litre of'water and this process is repeated one more time. How much spirit is now left in the container?
A
7.58 litres
B
7.84 litres
C
7 litres
D
7.29 litres
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Question 14 Explanation: 
spirit left after first replacement = 9 litre spirit left after second replacement = 9 * (9/10) spirit left after third replacement = 9 * (9/10) * (9/10) = 7.29
Question 15
The weight of a sequence a0, a1, ..., an-1 of real numbers is defined as a0+a1/2+...+ aa-1/2n-1. A subsequence of a sequence is obtained by deleting some elements from the sequence, keeping the order of the remaining elements the same. Let X denote the maximum possible weight of a subsequence of a0, a1, ...,an-1 and Y the maximum possible weight of a subsequence of a1, a2, ...,an-1. Then X is equal to
A
max(Y, a0+Y)
B
max(Y, a0+Y/2)
C
max(Y, a0+2Y)
D
a0+Y/2
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Question 15 Explanation: 
Using concepts of Dynamic Programming, to find the maximum possible weight of a subsequence of X, we will have two alternatives: 1. Do not include a0 in the subsequence: then the maximum possible weight will be equal to maximum possible weight of a subsequence of {a1, a2,....an} which is represented by Y 2. Include a0: then maximum possible weight will be equal to a0 + (each number picked in Y will get divided by 2) <=> a0 + Y/2. Here you can note that Y will itself pick optimal subsequence to maximize the weight. Final answer will be Max(Case1, Case2) i.e. Max(Y, a0 + Y/2). Hence B).
Question 16
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 football is:
A
2
B
17
C
13
D
3
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Question 16 Explanation: 
25 - (15+ 17-10)
Question 17
Hari(H), Gita(G), Irfan(I) and Saira(S) are siblings (i.e., brothers and sisters). All were born on 1st January. The age difference between any two successive siblings (that is born one after another) is less than 3 years. Given the following facts:
i.  Hari's age + Gita's age > Irfan's age + Saira's age 
ii. The age difference between Gita and Saira is 1 year. However Gita is not
    the oldest and Saira is not the youngest. 
iii. There are no twins. 
In what order were they born (oldest first)?
A
HSIG
B
SGHI
C
IGSH
D
IHSG
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Question 17 Explanation: 
H + G > I + S G - S = 1 OR S - G = 1 G is not the oldest and S is not the youngest. We need to try all options one by one.
Question 18
If 137 + 276 = 435 how much is 731 + 672?
A
534
B
1403
C
1623
D
1513
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Question 18 Explanation: 
If we try adding the numbers directly (i.e. considering decimal)
 
  1 
  137
 +276 
  ---  
    3
Since 7+6=13 and the given answer 435 has 5 in the one's place therefore the numbers are in base 8; Because 13 will correspond to 15 (7+8) in base 8 system. As shown: base Now converting 731 and 672 in decimal 7x8^2 + 3x8^1 + 1x8^0 = 473 6x8^2 + 7x8^1 + 2x8^0 = 442 Adding 473 + 442 = 915 Converting 915 into base 8 = 1623 base1 This explanation has been contributed by Kriti Kushwaha. More questions at: number-representation
Question 19
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-skilled and 5 unskilled workers, how long will it take to build the wall?
A
20
B
10
C
16
D
15
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Question 19 Explanation: 
5 skilled workers can build a wall in 20 days 1 skilled worker can build the same wall in 100 days Capacity of each skilled worker is 1/100 8 semi-skilled workers can build a wall in 25 days 1 semi-skilled worker can build the same wall in 200 days Capacity of each semi-skilled worker is 1/200 Capacity of 1 unskilled worker is 1/300 Capacity of 2 skilled + 6 semi-skilled + 5 unskilled workers is 2(1/100) + 6(1/200) + 5/300 = 1/15
Question 20
Given digits 2, 2, 3, 3, 3, 4, 4, 4, 4 how many distinct 4 digit numbers greater than 3000 can be formed?
A
50
B
51
C
52
D
54
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Question 20 Explanation: 
First digit is either 3 or 4. We'll consider each case separately: (1) First digit is 3: Then the rest of the numbers must come from the list: 2, 2, 3, 3, 4, 4, 4, 4 Therefore we may choose any 3-digit sequence except 222 and 333 for the rest of the digits. This shows there are 3*3*3 - 2 = 25 numbers in this case. (2) First digit is 4: Then the rest of the numbers must come from the list 2, 2, 3, 3, 3, 4, 4, 4 Therefore we may choose any 3-digit sequence except 222 for the rest of the digits. This shows there are 3*3*3 - 1 = 26 numbers in this case. Now, the total number is just 25 + 26 = 51. Source: http://in.answers.yahoo.com/question/index?qid=20100216113008AANZGwP
Question 21
IF (z + 1/z)2 = 98, compute (z2 + 1/z2)
A
96
B
99
C
100
D
94
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Question 21 Explanation: 
(z + 1/z)2 = (z2 + 1/z2) + 2*z*1/z (z2 + 1/z2) = (z + 1/z)2 - 2 = 98 - 2 = 96
Question 22
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
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Question 22 Explanation: 
  • A says that strategies are now available for eliminating psychiatric illnesses but it is mentioned in the very first line that the geneticists are very close but the strategy is not available till now. So, A is incorrect.
  • The given data says that the geneticists are working on the genetic roots of psychiatric illnesses such as depression and schizophrenia, which implies that these two diseases have genetic basis. Thus, B is the correct option.
  • C says that all human diseases can be traced back to genes and how they are expressed, but the data given in the question talks about psychiatric illnesses such as depression and schizophrenia only. So, C is also incorrect.
  • D says that in future, genetics will be the only relevant field for identifying psychiatric illnesses, which cannot be inferred from the given data. So, D is also incorrect.
So, B is the correct option  
Question 23
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 _________.
A
850
B
900
C
800
D
1000
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Question 23 Explanation: 
One way single person fare is 100. Therefore 2 way
is 200.

For 5 persons it is 200 x 5 = 1000

Now 1st discount is of 10 % on total fare, which is
100( 10 % of 1000). And as the group is of more than 4, 
an additional discount of 5 % on total fare, which is 
50( 5 % of 1000).

Hence total discount is equal to 100 + 50 = 150.

Therefore tickets are charged at Rs 1000 - 150 = 850. 
Question 24
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. The irresponses are tabulated below. GATECS2014Q9 What percent of respondents do not own a scooter?
A
48
B
40
C
50
D
45
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Question 24 Explanation: 
No. of respondents do not own scooter = 
                        No. of persons who have car alone + 
                        No. of persons who don't have both.
In men, 40 + 20 = 60 and
In women 34 + 50 = 84.
Total 60 + 84 = 144 .
Now the percentage is, (144/300) *100 = 48
Question 25
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? _____________
A
6
B
8
C
4
D
10
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Question 25 Explanation: 
The Tetrahedron has 4 triangular surfaces with 4 vertices/corners ( say A,B,C and D) as can be seen here. http://www.sjsu.edu/faculty/wa... Now if you take a point inside a tetrahedron (suppose O) and connect it with any two of its corners which are nothing but vertices( suppose A and B), you will get 1 internal plane as OAB. So we can see from here that, no of new internal planes = no of different pair of corners or vertices Similarly you can take any other 2 corners like (A,C) or (A,D) or (B,C) or (B,D) or (C,D), hence total possible pair of corners are 6. Therefore 6 new internal planes possible. We could also calculate the possible corners by using combinations formula, which is nCr, i.e. no of ways to select a combination of r things from a given set of n things. here n = 4 ( as total 4 vertices, A,B,C and D) and r =2 ( as we need two corners at a time) Thus, 4C2 = 6.
Question 26
There are 5 bags labeled 1 to 5. All the coins in a given bag have the same weight. Some bags have coins of weight 10 gm, others have coins of weight 11 gm. I pick 1, 2, 4, 8, 16 coins respectively from bags 1 to 5. Their total weight comes out to 323 gm. Then the product of the labels of the bags having 11 gm coins is ___.
A
15
B
12
C
8
D
1
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Question 26 Explanation: 
There are 5 bags numbered 1 to 5.

We don't know how many bags contain 10 gm and 
11 gm coins.

We only know that the total weights of coins is 323.

Now the idea here is to get 3 in the place of total 
sum's unit digit.

Mark no 1 bag as having 11 gm coins.
Mark no 2 bag as having 10 gm coins.
Mark no 3 bag as having 11 gm coins.
Mark no 4 bag as having 11 gm coins.
Mark no 5 bag as having 10 gm coins.

Note: The above marking is done after getting false 
results for some different permutations, the permutations
which were giving 3 in the unit place of the total sum.

Now, we have picked 1, 2, 4, 8, 16 coins respectively
from bags 1 to 5.

Hence total sum coming from each bag from 1 to 5 is 11,
20, 44, 88, 160 gm respectively.

For the above combination we are getting 3 as unit digit
in sum.

Lets find out the total sum, it's 11 + 20 + 44 + 88 + 160 = 323.

So it's coming right.

Now 11 gm coins containing bags are 1, 3 and 4.
Hence, the product is : 1 x 3 x 4 = 12. 
Question 27
What is the average of all multiples of 10 from 2 to 198?
A
90
B
100
C
110
D
120
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Question 27 Explanation: 
From 2 to 198 there are 19 multiples of 10.

These are 10,20,30.....180,190.

This is an A.P series, whose sum is (n/2{a1 + aN}), 
where a1 and aN are the 1st and last terms respectively.

Putting in the formula,

a1 = 10, aN = 190.

Sum = Sn = (19/2{10 + 190 }) = 1900

Average = Sum / Total number = 1900 / 19 = 100. 
Question 28
GATECS2014Q5
A
3.464
B
3.932
C
4.000
D
4.444
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Question 28 Explanation: 
let x = the given expression.
Now squaring both sides.

(x)^2 = 12 + x
(x)^2 - x - 12 = 0

Now solve this quadratic equation for finding the 
roots(value of x, or this expression).
(x-4)(x+3) = 0

hence x = 4.
Question 29
If x is real and |x2 - 2x + 3| = 11, then possible values of |- x3 + x2 - x| include
A
2, 4
B
2, 14
C
4, 52
D
14, 52
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Question 29 Explanation: 
Here we use the modulus property, which says:

|x| = x when x >= 0

|x| = -x when x < 0

i.e. range of a modulus function is always positive.

Now, given that |x^2 – 2x + 3| = 11, we can say that

x^2 – 2x + 3 = +11 ----------------(1)

and

x2 – 2x + 3 = -11------------------(2)

Solving 1st equation, we get real roots as 4 and -2.

Solving 2nd eq, we get imaginary roots, hence we ignore them.

Now, for eq |- x^3 + x^2 – x|, we put 4 and -2 in place of x.

putting x = 4, we get |-4^3 + 4^2-4| = |-64+16-4| =  52

putting x = -2 we get |-(-2)^3 + (-2)^2 - (-2)| = 14

so |- x^3 + x^2 – x| has possible values as 52 and 14 
Question 30
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 doubled in 2009, by what percent did the number of male students increase in 2009? GATECS2014Q92
A
120
B
140
C
160
D
180
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Question 30 Explanation: 
Let x represent the males and y represent the females.

In 2008.
x / y = 2.5 -----------(1)

In 2009.
M / 2y = 3-------------(2)

where M is the total number of males in 2009.

Now x = 2.5y (from (1))
and M = 6y ( from (2))

hence increased number of males in 2009 are 
M - x = 6y - 2.5y = 3.5y

Now the increase in % of males =

(change in no of males / initial number)*100

= (3.5y / x )*100 = (3.5 / 2.5)*100 = 140 
                                 (given x/y = 2.5)

Hence, B is the right option.
Question 31
At what time between 6 a.m. and 7 a.m. will the minute hand and hour hand of a clock make an angle closest to 60o
A
6:22 am
B
6:27 am
C
6:38 am
D
6:45 am
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Question 31 Explanation: 
Speed of the Hour hand = ( 360 degree ) / ( 12 * 60 minutes ) 
                       = 0.5 degree / minute.
Speed of the minute hand = ( 360 degree ) / ( 60 minutes ) 
                         = 6 degree / minute.
At 6 am, hour hand will point vertically downward to 6 in the clock, and minute hand will point vertically upward to 12 in the clock. ( Hence they are opposite with a gap of 180 degree between them). Now after t minutes , The angle between these two hands will be either of the below two:

(180 - 6t) + 0.5t, when the minute hand is 
                   behind the hour hand or,

6t - (180 + 0.5t), when the minute hand is 
                    ahead of hour hand,

Now the the question asks for angle of 60 degree.

Hence, 
(180 - 6t) + 0.5t = 60 , we get t = 21.8 minute
and
6t - ( 180 + 0.5t ) = 60, we get t = 48 minutess
Hence the closest to answer is 22 minutes, i.e. 6.22 am. Hence answer is A.
Question 32
The number of distinct positive integral factors of 2014 is _________________________
A
7
B
8
C
9
D
10
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Question 32 Explanation: 
the factors are 1, 2, 19, 38, 53, 106, 107 and 2014. So the total makes it 8 number of integral factors.
Question 33
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
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Question 33 Explanation: 
Given series is 2,5,10,17,26,37,50,64.

Here total number of terms are 8..i.e. A(1) to A(8).

For the 1st 7 terms, you can observe the relationship 
between the terms which is 
A(n) = [ A(n-1) - {A(n-1) + A(n-2)} + 2 ] where n >= 3

Now for the 8th term i.e. A(8), this relationship violates.
According to the relationship,
A(8) = [A(7) + {A(7) - A(6)} + 2 ]
= [50 + {50 - 37} + 2 ]
= 50 + 13 + 2
= 65.
But in the series it is 64. Hence 64 doesn't belong to 
the series. 
Question 34
The table below has question-wise data on the performance of students in an examination. The marks for each question are also listed. There is no negative or partial marking in the examination. GATECS2014Q5 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
General Aptitude    GATE-CS-2014-(Set-3)    
Discuss it


Question 34 Explanation: 
As you can see from each row that the total number of
students in the class are 44.

Now we have to find the total number of marks obtained
by the class.

Marks are given for correct answers only. 
No negative or partial marking.

For 1st question total marks obtained are : 2*21 = 42
For 2nd question total marks obtained are : 3*15 = 45
For 3rd question total marks obtained are : 2*23 = 46

hence total marks obtained by the class are = 42+45+46 = 133

Now, Average marks obtained = Total Marks/Total no of students
= 133/44
= 3.02
Hence C is the answer.
Question 35
A dance programme is scheduled for 10.00 a.m. Some students are participating in the programme and they need to come an hour earlier than the start of the event. These students should be accompanied by a parent. Other students and parents should come in time for the programme. The instruction you think that is appropriate for this is
A
Students should come at 9.00 a.m. and parents should come at 10.00 a.m.
B
Participating students should come at 9.00 a.m. accompanied by a parent, and other parents and students should come by 10.00 a.m.
C
Students who are not participating should come by 10.00 a.m. and they should not bring their parents. Participating students should come at 9.00 a.m.
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.
General Aptitude    GATE-CS-2014-(Set-3)    
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Question 35 Explanation: 
  • A is not the appropriate instruction as only the participating students and their parents have to come at 9.00 a.m. and other students along with their parents have to come at 10.00 a.m., while the statement in A says that all students should come at 9.00 a.m. and all the parents should come at 10.00 a.m.
  • B is the appropriate instruction and covers all the aspects of the information to be conveyed.
  • C is not the appropriate instruction as the non participating students have to come at 10.00 a.m. with their parents, while the statement in B says that these students have to come without their parents.
  • D is not the appropriate instruction as it states that the participating students have to come before 9.00 a.m. whereas they have to come at 9.00 a.m.
So B is Correct option.
Question 36
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 
A
(i), (ii) and (iv)
B
(iii) only
C
(i) and (iv)
D
(iv) only
General Aptitude    GATE-CS-2014-(Set-3)    
Discuss it


Question 36 Explanation: 
Paradigm shift means a fundamental change in approach to something or change in the underlying assumptions in relation to something. This change, as per the question, was verified with the experimental measurements of the position of a star that was behind the sun. (i) is incorrect as it generalizes the experimental evidence of the star and assumes it to be always true, which may not be the case every time. (ii) is also incorrect. If there was a paradigm shift at the beginning of the 20th century, it does not necessarily means that all paradigm shifts usually occur at the beginning of centuries. (iii) is incorrect as it again generalizes an experimental statement. Stars proved to be important in the given case does not necessarily imply that they would be important every time. (iv) is correct as it is clearly understood from the given case conditions that this experimental measurements provided a clinching (solid/concrete) evidence to our understanding of the universe.   So, D is the correct choice as only (iv) is the correct statement.   Please comment below if you find anything wrong in the above post.
Question 37
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%
General Aptitude    GATE-CS-2014-(Set-3)    
Discuss it


Question 37 Explanation: 
Suppose original GDP was x then its international
value is x/50. 

Now GDP becomes 107*x/100 and its international 
value becomes (107x/100)/60= 107x/6000.

The value has decreased by (x/50)-(107x/6000).  
Percentage approx 10.8% = 11%
Question 38
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? GATECS2014Q9
A
1:1
B
2:1
C
1.5:1
D
2.5:1
General Aptitude    GATE-CS-2014-(Set-3)    
Discuss it


Question 38 Explanation: 
Number of female students in 2011 and 2012 are equal.
Suppose they are x.

Now,
Males students in 2011 = Female students in 2011 
                       = x (as the ratio is 1)

And in 2012, Male students / Female students = 
                                       1.5(Given)

Hence Male students in 2012 = 1.5 * Female students 
                            = 1.5 * x

Now ratio of Male students in 2012 to Male students
in 2011 = ( 1.5 * x ) / x
        = 1.5 / 1
i.e. 1.5 : 1

Hence C is the answer. 
Question 39
Consider the equation: (7526)8 − (Y)8 = (4364)8 , where (X)N stands for X to the base N. Find Y.
A
1634
B
1737
C
3142
D
3162
General Aptitude    GATE-CS-2014-(Set-3)    
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Question 39 Explanation: 
(X)N stands for X to the base N. 7526(8) - Y(8) = 4364(Y) Base 8(Octal) uses digits 0 to 7. Now Y(8) = 7526(8) - 4364(8) The subtraction of octal numbers follows the same rules as the subtraction of numbers in any other number system. The only variation is in borrowed number. In the decimal system, you borrow a group of 10(10). In the binary system, you borrow a group of 2(10). In the octal system you borrow a group of 8(10). Reference: http://www.tpub.com/neets/book13/53f.htm
Question 40
Consider the following statements:
  P: Good mobile phones are not cheap
  Q: Cheap mobile phones are not good

  L: P implies Q
  M: Q implies P
  N: P is equivalent to Q 
Which one of the following about L, M, and N is CORRECT?
A
Only L is TRUE.
B
Only M is TRUE.
C
Only N is TRUE.
D
L, M and N are TRUE
General Aptitude    GATE-CS-2014-(Set-3)    
Discuss it


Question 40 Explanation: 
Let a and b be two proposition
a: Good Mobile phones.
b: Cheap Mobile Phones.

P and Q can be written in logic as
P: a-->~b
Q: b-->~a.

Truth Table
a   b   ~a  ~b   P   Q
T   T   F    F   F   F
T   F   F    T   T   T
F   T   T    F   T   T
F   F   T    T   T   T

it clearly shows P and Q are equivalent.
so option D is Correct
Question 41
The minimum number of cards to be dealt from an arbitrarily shuffled deck of 52 cards to guarantee that three cards are from some same suit is
A
3
B
8
C
9
D
12
General Aptitude    GATE-CS-2000    
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Question 41 Explanation: 
Total number of suits is 4 We need minimum 9 cards to make sure that there are 3 cards of same suit. For example, With 8 cards, we can have 2 cards of each suit.
Question 42
Based on the given statements, select the most appropriate option to solve the given question. If two floors in a certain building are 9 feet apart, how many steps are there in a set of stairs that extends from the first floor to the second floor of the building?  
Statements:
1. Each step is 3/4 foot high.
2. Each step is 1 foot wide.
A
Statement 1 alone is sufficient, but statement 2 alone is not sufficient
B
Statement 2 alone is sufficient, but statement 1 alone is not sufficient
C
Both statement together are sufficient, but neither statement alone is sufficient
D
Statement 1 and 2 together are not sufficient
General Aptitude    GATE-CS-2015 (Set 1)    
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Question 42 Explanation: 
When we climb from one floor to other, it is the height that matters and not the width of the staircase.Therefore, From statement 1 only, we can figure out that 9 / (3/4) or 12 steps are required.
Question 43
The number of students in a class who have answered correctly, wrongly, or not attempted each question in an exam, are listed in the table below. The marks for each question are also listed. There is no negative or partial marking.
Q.No. Marks Answered-Correctly Answered-Wrongly Not-Attempted
 1      2         21                17               6 
 2      3         15                27               2    
 3      1         11                29               4
 4      2         23                18               3
 5      5         31                12               1 
What is the average of the marks obtained by the class in the examination?
A
2.290
B
2.970
C
6.795
D
8.795
General Aptitude    GATE-CS-2015 (Set 1)    
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Question 43 Explanation: 
There are total 44 students. This count can be obtained by adding last 3 entries of any row of given total.
Total marks = 2*21 + 3*15 + 1*11 + 2*23  + 5*31
            = 299
Average marks =  299/44 = 6.795 
Question 44
The given statement is following by some courses of action. Assuming the statement to be true, decide the correct option.
Statement: 
There has been a significant drop in the water level 
in the lakes supplying water to the city.

Course of action:
1. The water supply authority should impose a partial 
   cut in supply to tackle the situation.
2. The government should appeal to all the residents 
   through mass media for minimal use of water.
3. The government should ban the water supply in lower 
   areas
A
Statement 1 and 2 follow
B
Statement 1 and 3 follow
C
Statement 2 and 3 follow
D
All statements follow
General Aptitude    GATE-CS-2015 (Set 1)    
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Question 44 Explanation: 
3rd course of action is not correct. Banning water supply can not solve the problem.
Question 45
The pie chart below has the breakup of the number of students, from different departments in an engineering college for the year 2012. The proportion of male to female students in each department is 5 : 4. There are 40 males in Electrical Engineering. What is the different between the numbers of female students in the Civil department and the female students in the Mechanical department? Q9
A
32
B
16
C
48
D
8
General Aptitude    GATE-CS-2015 (Set 1)    
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Question 45 Explanation: 
Total male students in Electrical = 40 Total female in Electrical = (40 * 4)/5 = 32 Total female in Mechanical = 32/2 = 16 Total female in Civil = [(30 + 42)*3/2]*4/9 = = 72 * 2/3 = 48 The difference is 32.
Question 46
Based on the given statements, select the most appropriate option to solve the given question. What will be the total weight of 10 poles each of same weight?
Statements: 
  (I) One fourth of the weight of a pole is 5 kg
  (II) The total weight of these poles is 160 kg more
       than the total weight of two poles.
A
Statement II alone is not sufficient
B
Statement II alone is not sufficient
C
Either I or II alone is sufficient
D
Both statements I and II together are not sufficient.
General Aptitude    GATE-CS-2015 (Set 2)    
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Question 46 Explanation: 
(I) is sufficient. We can determine total weight of 1o
   poles as 10 * 4 * 5 = 200 Kg

(II) is also sufficient, we can determine the weight.
  Let x be the weight of 1 pole.
  10*x - 2*x = 160 Kg
  x = 20 Kg
  10x = 200 Kg 
Question 47
If the list of letters, P, R, S, T, U is an arithmetic sequence, which of the following are also in arithmetic sequence?
1. 2P, 2R, 2S, 2T, 2U
2. P–3, R–3, S–3, T–3, U–3
3. P2, R2, S2, T2, U2
A
1 only
B
1 and 2
C
2 and 3
D
1 and 3
General Aptitude    GATE-CS-2015 (Set 2)    
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Question 47 Explanation: 
1 is AP with common difference as double of that of original series. 2 is AP with common difference as same as original series.
Question 48
Four branches of a company are located at M, N, O and P. M is north of N at a distance of 4 km; P is south of O at a distance of 2 km; N is southeast of O by 1 km. What is the distance between M and P in km?
A
5.34
B
6.74
C
28.5
D
45.49
General Aptitude    GATE-CS-2015 (Set 2)    
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Question 48 Explanation: 
Q8
Question 49
In a triangle PQR, PS is the angle bisector of ∠ QPR and ∠ QPS = 60°. What is the length of PS? Q9 Q91
A
a
B
b
C
c
D
d
General Aptitude    GATE-CS-2015 (Set 2)    
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Question 49 Explanation: 
Area of a Δ = 1/2 * ac sinB 
            = 1/2 * bc sinA 
            = 1/2 ab sinC

Here area (ΔPQR) = area (ΔPQS) + area (ΔPRS)

1/2 rq sin120 = 1/2 PS * r sin60 + 1/2 PS * q sin60

=> PS = rq/(r+q)
There seems to be something wrong with question as it says ∠ QPS = 60°. The question is same on GATE official site paper.
Question 50
If p, q, r, s are distinct integers such that:
f(p, q, r, s) = max (p, q, r, s)
g(p, q, r, s) = min (p, q, r, s)
h(p, q, r, s) = remainder of (p × q) / (r × s)  if (p × q) > (r × s) OR 
                remainder of (r × s) / (p × q) if (r × s) > (p × q)
Also a function fgh (p, q, r, s) =
                f(p, q, r, s) × g(p, q, r, s) × h(p, q, r, s).
Also the same operation are valid with two variable functions 
of the form f(p, q).

What is the value of fg(h(2, 5, 7, 3), 4, 6, 8)? 
A
6
B
7
C
8
D
9
General Aptitude    GATE-CS-2015 (Set 2)    
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Question 50 Explanation: 
The question asks value of fg (h(2, 5, 7, 3), 4, 6, 8)

We need to first find value of h(2, 5, 7, 3) 

h is defined as 
h(p, q, r, s) = remainder of (p × q) / (r × s)  if (p × q) > (r × s)
                remainder of (r × s) / (r × q)  if (r × s) > (p × q)

h(2, 5, 7, 3) = remainder of (7 * 3) / (2 * 5)  since 7*3 > 2*5
              = 1

fg(1, 4, 6, 8) = f(1, 4, 6, 8) * g(1, 4, 6, 8)
               = max(1, 4, 6, 8) * min(1, 4, 6, 8)
               = 8 * 1
               = 8
Question 51
The number of divisors of 2100 is _________.
A
42
B
36
C
78
D
72
General Aptitude    GATE-CS-2015 (Set 2)    
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Question 51 Explanation: 
2100  =  22 * 31 * 52 * 71

There are 3 choices for powers of 2,  the choices are 0, 1, 2
Similarly, there are 2 choices for powers of 3,  3 choices for power of 5
and 2 choices for power of 7.

So total number of divisors is 3 * 2 * 3  * 2 = 36 
Question 52
If ROAD is written as URDG, then SWAN should be written as:
A
VXDQ
B
VZDQ
C
VZDP
D
UXDQ
General Aptitude    GATE-CS-2015 (Set 3)    
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Question 52 Explanation: 
In ROAD to URDG transformation, every character is replaced by next third character in alphabetic sequence. (R by U, O by R, A by D and D by G) Applying same, SWAN becomes VZDQ
Question 53
A function f(x) is linear and has a value of 29 at x = –2 and 39 at x = 3. Find its value at x = 5.
A
59
B
45
C
43
D
35
General Aptitude    GATE-CS-2015 (Set 3)    
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Question 53 Explanation: 
f(x) = 2x+33
Question 54
Alexander turned his attention towards India, since he had conquered Persia. Which one of the statements below is logically valid and can be inferred from the above sentence?
A
Alexander would not have turned his attention towards India had he not conquered Persia
B
Alexander was not ready to rest on his laurels, and wanted to march to India
C
Alexander was completely in control of his army and could command it to move towards India.
D
Since Alexander’s kingdom extended to India borders after the conquest of Persia, he was keen to move further
General Aptitude    GATE-CS-2015 (Set 3)    
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Question 54 Explanation: 
Conquering Persia was the reason for Alexander turning his attention towards India
Question 55
The head of a newly formed government desires to appoint five of the six selected members P, Q, R, S, T and U to portfolios of Home, Power, Defence, Telecom, and Finance. U does not want any portfolio if S gets one of the five. R wants either Home or Finance or no portfolio. Q says that if S gets either Power of telecom, then she must get the other one. T insists on a portfolio if P gets one Which is the valid distribution of portfolios?
A
P-Home, Q-Power, R-Defence, S-Telecom, T-Finance
B
R-Home, S-Power, P-Defence, Q-Telecom, T-Finance
C
P-Home, Q-Power, T-Defence, S-Telecom, U-Finance
D
Q-Home, U-Power, T-Defence, R-Telecom, P-Finance
General Aptitude    GATE-CS-2015 (Set 3)    
Discuss it


Question 55 Explanation: 
Six selected members are P, Q, R, S, T and U

Portfolios are Home, Power, Defence, Telecom, and Finance. 

U does not want any portfolio if S gets one of the five. 

R wants either Home or Finance or no portfolio. 

Q says that if S gets either Power of telecom, then she must 
get the other one.

T insists on a portfolio if P gets one Which is the valid 
distribution of portfolios?

A) P-Home, Q-Power, R-Defence, S-Telecom, T-Finance
Not valid as R doesn't get home or finance here

R-Home, S-Power, P-Defence, Q-Telecom, T-Finance
Is valid and satisfies all conditions.

C) P-Home, Q-Power, T-Defence, S-Telecom, U-Finance
Not valid as U is not satisfied. Condition for U is, S should not
get any portfolio.

D) Q-Home, U-Power, T-Defence, R-Telecom, P-Finance
Like A, not valid as R doesn't get home or finance here

Question 56
Choose the most appropriate equation for the function drawn as a thick line, in the plot below. Q10
A
A
B
B
C
C
D
D
General Aptitude    GATE-CS-2015 (Set 3)    
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Question 56 Explanation: 
The problem can be easily solved by trying point (2, -1) 
on thick line, i.e., x = 2, y = -1.

None of the options except (B) satisfy above values. 
Question 57
Most experts feel that in spite of possessing all the technical skills required to be a batsman of the highest order, he is unlikely to be so due to lack of requisite temperament. He was guilty of throwing away his wicket several times after working hard to lay a strong foundation. His critics pointed out that until he addressed this problem, success at the highest level will continue to elude him. Which of the statements(s) below is/are logically valid and can be inferred from the above passage?
(i) He was already a successful batsman at the highest level.
(ii) He has to improve his temperament in order to become a great batsman.
(iii) He failed to make many of his good starts count.
(iv) Improving his technical skills will guarantee success.
A
(iii) and (iv)
B
(ii) and (iii)
C
(i), (ii) and (iii)
D
(ii) only
General Aptitude    GATE-CS-2015 (Set 3)    
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Question 57 Explanation: 
(i) is incorrect "He was guilty of throwing away his wicket several times after working hard to lay a strong foundation. " (ii) is correct, "His critics pointed out that until he addressed this problem, success at the highest level will continue to elude him." (iii) is correct, "His critics pointed out that until he addressed this problem, success at the highest level will continue to elude him." (iv) is incorrect "Temperament is also required"
Question 58
The exports and imports (in crores of Rs.) of a country from the year 2000 to 2007 are given in the following bar chart. In which year is the combined percentage increase in imports and exports the highest?
Q11
A
2004
B
2005
C
2006
D
2007
General Aptitude    GATE-CS-2015 (Set 3)    
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Question 58 Explanation: 
In 2006 export increased from 70 yo 100 and import increased from 90 to 120.

% increase in import = 30/70 = 42.8 %
% increase in export = 30/90 = 33.33 %

Combined % increase in 2006 is more than any other year.  
Question 59
In a population of N families, 50% of the families have three children, 30% of the families have two children and the remaining families have one child. What is the probability that a randomly picked child belongs to a family with two children?
A
3/23
B
6/23
C
3/10
D
3/5
General Aptitude    GATE-IT-2004    
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Question 59 Explanation: 
x- total families. Given:
  • 50% -3 Children -> (5*x/10) * 3=(1*x/2)*3
  • 30% -2 Children-> (3*x /10) * 2
  • Rear 20%- 1child -> (2*x/10)*1 =1*x/5
Probability = No of ways it can happen/Total Outcomes =( (3/10)*2 ) / ( (1/2)*3 + (3/10)*2 +1/5 ) = 6/23 So Answer is B
Question 60
In a class of 200 students, 125 students have taken Programming Language course, 85 students have taken Data Structures course, 65 students have taken Computer Organization course; 50 students have taken both Programming Language and Data Structures, 35 students have taken both Data Structures and Computer Organization; 30 students have taken both Data Structures and Computer Organization, 15 students have taken all the three courses.How many students have not taken any of the three courses?
 
A
15
B
20
C
25
D
35
General Aptitude    GATE-IT-2004    
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Question 60 Explanation: 
P(AUBUC)=P(A)+P(B)+P(C)- P(A∩B)-P(A∩C)- P(B∩C)+P(A∩B∩C)
125+85+65-503530+15 =175
No of students not taking any courses-> 200175=25 So C is the Answer.
Question 61
If ‘relftaga’ means carefree, ‘otaga’ means careful and ‘fertaga’ means careless, which of the following could mean ‘aftercare’?
A
zentaga
B
tagafer
C
tagazen
D
relffer
General Aptitude    GATE-CS-2016 (Set 1)    
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Question 61 Explanation: 
'taga' and 'care' are a matching pair in every combination. So, 'taga' surely represents 'care'.   Also, note here that the second half of the word in encoded value refers to the first half of the word in the decoded value. So, 'fer' represents 'less', 'relf' represents 'free' and 'o' represents 'full'.   Going by the same logic, the answer would be tagazen, i.e., C.
Question 62
A cube is built using 64 cubic blocks of side one unit. After it is built, one cubic block is removed from every corner of the cube. The resulting surface area of the body (in square units) after the removal is __________.
A
56
B
64
C
72
D
96
General Aptitude    GATE-CS-2016 (Set 1)    
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Question 62 Explanation: 
The surface area of the body will remain unchanged as when a cube is removed, it exposes three faces, which makes the number of exposed faces same as before removal.   So, surface area of the body before removal = surface area of the body after removal = 6 * side * side = 6 * 4 * 4 = 96.   Thus, D is the correct choice.
Question 63
A shaving set company sells 4 different types of razors, Elegance, Smooth, Soft and Executive. Elegance sells at Rs. 48, Smooth at Rs. 63, Soft at Rs. 78 and Executive at Rs. 173 per piece. The table below shows the numbers of each razor sold in each quarter of a year.   GATECS161   Which product contributes the greatest fraction to the revenue of the company in that year?
A
Elegance
B
Executive
C
Smooth
D
Soft
General Aptitude    GATE-CS-2016 (Set 1)    
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Question 63 Explanation: 
Revenue from Elegance = (27300+25222+28976+21012) * Rs. 48 = Rs. 4920480 Revenue from Smooth = (20009+19392+22429+18229) * Rs. 63 = Rs. 5043717 Revenue from Soft = (17602+18445+19544+16595) * Rs. 78 = Rs. 5630508 Revenue from Executive = (9999+8942+10234+10109) * Rs. 173 = Rs. 6796132 Total Revenue = Rs. 22390837   Fraction of Revenue for Elegance = 0.219 Fraction of Revenue for Smooth = 0.225 Fraction of Revenue for Soft = 0.251 Fraction of Revenue for Executive = 0.303   Thus, B (Executive) is the correct answer.
Question 64
Indian currency notes show the denomination indicated in at least seventeen languages. If this is not an indication of the nation’s diversity, nothing else is. Which of the following can be logically inferred from the above sentences?
A
India is a country of exactly seventeen languages.
B
Linguistic pluralism is the only indicator of a nation’s diversity.
C
Indian currency notes have sufficient space for all the Indian languages.
D
Linguistic pluralism is strong evidence of India’s diversity.
General Aptitude    GATE-CS-2016 (Set 1)    
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Question 64 Explanation: 
A is incorrect as it cannot be inferred that exactly 17 languages are there, because the statement says that there are atleast 17 languages on the currency note.   B is incorrect because of the word 'only' in the option, which is too strong to be inferred.   C is incorrect as it says 'space for all Indian languages', but the number of languages in India is not mentioned in the question.   D is correct as it can be easily inferred from the statement.
Question 65
Consider the following statements relating to the level of poker play of four players P, Q, R, and S.
I    P always beats Q
II.  R always beats S
III. S loses to P only sometimes
IV.  R always loses to Q 
Which of the following can be logically inferred from the above statements?
(i) P is likely to beat all the three other players
(ii) S is the absolute worst player in the set 
A
(i) only
B
(ii) only
C
(i) and (ii)
D
neither (i) nor (ii)
General Aptitude    GATE-CS-2016 (Set 1)    
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Question 65 Explanation: 
All three can Beat S, but S loses to P only sometimes. So, (ii) can not be inferred from the given statements. Defeating in Poker is not transitive. P beats Q. Q beats R and R beats S. Yet S loses to P only sometimes, meaning that S mostly wins against P. So we can not logically infer that P is likely to beat R.
Question 66
If f(x) = 2x7 + 3x - 5 Which of the following is a factor of f(x)?
A
(x3 + 8)
B
(x - 1)
C
(2x - 5)
D
(x + 1)
General Aptitude    GATE-CS-2016 (Set 1)    
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Question 66 Explanation: 
f(x) = 2x7 + 3x - 5
     = 2x7 - 2x + 5x - 5
Putting x = 1, we get f(x) = 0. So, x-1 is a factor of f(x).   Thus, B is the correct choice.
Question 67
In a process, the number of cycles to failure decreases exponentially with an increase in load. At a load of 80 units, it takes 100 cycles for failure. When the load is halved, it takes 10000 cycles for failure. The load for which the failure will happen in 5000 cycles is ________.
A
40.00
B
46.02
C
60.01
D
92.02
General Aptitude    GATE-CS-2016 (Set 1)    
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Question 67 Explanation: 
For exponential dependence we must have functions of form
f(x) = a.(k power x) : a,k are constants and f(0)=a

Let us assume: C = cycles for failure ; L = Load; a, k = constants
according to question C is an exponential function of L
Hence we can say,

1) C = a x (k^L) ---- > in case C is increasing exponentially
2) C = a / (k^L) ---- > in case C is decreasing exponentially

we take 2nd equation and apply log to both side we get:

log C + L x (log k) = log a ...... by logarithmic property

given (C=100 for L=80) and (C=10000 for L=40)
apply these to values to above equation, this gives us 2 equations
and 2 variables:

log a = log 100 + (80 x log k)...............(1)
log a = log 10000 + (40 x log k)...........(2)

we have 2 variables and 2 equations hence we find
log a = 6
log k= 1/20

now find, [ L = (log a - log C) / (log k) ] for C=5000 cycles

=> L = (6 - log 5000)*20 = 46.0206 ~ 46.02 => [ANS]
Question 68
The coefficient of x12 in (x3 + x4 + x5 + x6 + ...)3 is. [This Question was originally a Fill-in-the-Blanks question]
A
1
B
2
C
4
D
10
General Aptitude    GATE-CS-2016 (Set 1)    
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Question 68 Explanation: 
The expression can be re-written as: (x3 (1+ x + x2 + x3 + ...))3=x9(1+(x+x2+x3))3 Expanding (1+(x+x2+x3))3 using binomial expansion (1+(x+x2+x3))3 = 1+3(x+x2+x3)+3*2/2((x+x2+x3)2+3*2*1/6(x+x2+x3)3….. The coefficient of x3 will be 10, it is multiplied by x9 outside, so coefficient of x12 is 10.
Question 69
Pick the odd one from the following options.
A
CADBE
B
JHKIL
C
XVYWZ
D
ONPMQ
General Aptitude    GATE-CS-2016 (Set 2)    
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Question 69 Explanation: 
In the given options apart from Option D, characters at odd positions are consecutive alphabets in increasing order and similarly characters at even positions also are consecutive alphabets in increasing order. Option A: CADBE C,D,E(characters at 1st,3rd and 5th positions are consecutive alphabets in increasing order) similarly A,B(characters at 2nd and 4th positions are consecutive alphabets in increasing order). Option D: ONPMQ O,P,Q(characters at 1st,3rd and 5th positions are consecutive alphabets in increasing order) but N,M(characters at 2nd and 4th positions are not increasing order)
Question 70
Among 150 faculty members in an institute, 55 are connected with each other through Facebook ® and 85 are connected through WhatsApp ® . 30 faculty members do not have Facebook ® or WhatsApp ® accounts. The number of faculty members connected only through Facebook ® accounts is ______________.
A
35
B
45
C
65
D
90
General Aptitude    GATE-CS-2016 (Set 2)    
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Question 70 Explanation: 
Suppose n(F) : number of faculty connected through facebook n(W) : number of faculty connected through whatsapp n(F ∪ W) : number of faculty connected through either facebook and whatsapp n(F ∩ W) : number of faculty connected through both facebook and whatsapp n(F ∪ W) = (total faculty - faculty not connected to anything) = (150-30) = 120 From number theory: n(F ∪ W) = n(F) + n(W) - n(F ∩ W) n(F) - n(F ∩ W) = n(F ∪ W) - n(W) n(F) - N(F ∩ W) = (120-85) = 35 n(F)- n(F ∩ W) is the faculty that has only facebook account, Hence answer is 35. This explanation has been contributed by Dharmesh Singh.
Question 71
Computers were invented for performing only high-end useful computations. However, it is no understatement that they have taken over our world today. The internet, for example, is ubiquitous. Many believe that the internet itself is an unintended consequence of the original invention. With the advent of mobile computing on our phones, a whole new dimension is now enabled. One is left wondering if all these developments are good or, more importantly, required. Which of the statement(s) below is/are logically valid and can be inferred from the above paragraph? (i) The author believes that computers are not good for us. (ii) Mobile computers and the internet are both intended inventions
A
(i) only
B
(ii) only
C
both (i) and (ii)
D
neither (i) nor (ii)
General Aptitude    GATE-CS-2016 (Set 2)    
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Question 71 Explanation: 
ubiquitous - everywhere unintended - unplanned
--> Author has not said anything against internet and mobile computing 
but is talking about the surprising usage of these.

"Many believe that the internet itself is an unintended consequence of 
the original invention."
--> The author says that many believe that 'internet itself' is unplanned 
but actually both internet and mobile computers are unplanned(unintended) 
inventions.

Hence, D is the correct option of this answer. This explanation has been contributed by Mohit Gupta.
Question 72
All hill-stations have a lake. Ooty has two lakes. Which of the statement(s) below is/are logically valid and can be inferred from the above sentences?

(i) Ooty is not a hill-station.
(ii) No hill-station can have more than one lake. 
A
(i) only
B
(ii) only
C
both (i) and (ii)
D
neither (i) nor (ii)
General Aptitude    GATE-CS-2016 (Set 2)    
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Question 72 Explanation: 
Given statement doesn't say that - "All hill-stations have a lake" but any place having a lake is surely a hill station. ---> Ooty may or may not be a hill station Hence (i) is false ---> Here, it is not a compulsion that a place need to have exactly one lake to be a hill station. Hence (ii) is also false This explanation has been contributed by Mohit Gupta.
Question 73
In a 2 × 4 rectangle grid shown below, each cell is a rectangle. How many rectangles can be observed in the grid? gt30
A
21
B
27
C
30
D
36
General Aptitude    GATE-CS-2016 (Set 2)    
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Question 73 Explanation: 
5C2 * 3C2
Question 74
The value of the expression 1399(mod 17), in the range 0 to 16, is :   Note : This question was asked as Numerical Answer Type.
A
4
B
13
C
8
D
16
General Aptitude    GATE-CS-2016 (Set 2)    
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Question 74 Explanation: 
We have 13 * 13 * 13 * ... * 13 (total 99 terms)   By remainder theorem, => (-4) * (-4) * ... * (-4) (total 99 terms) => 16 * 16 * ... * 16 * (-4) (total 50 terms, 49 terms for 16 and one term for -4)   Reapplying remainder theorem, => (-1) * (-1) * ... * (-1) * (-4) (total 50 terms, 49 terms for -1 and one term for -4) => (-1) * (-4) => 4   Thus, A is the correct option.
Question 75
For the statement given below, mark the part of the statement that contains an error. If there is no error mark choice d.
From 1982 to 1990 sales of good quality paper (I) have increased between five (II) and ten per cent annually (III)
A
I
B
II
C
III
D
No Error
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Question 75 Explanation: 
Here, focus is on the sales of good quality paper that should be the subject of the sentence. Since the period of time covered began and ended in the past, the verb should be in the simple past tense (increased) and not in present perfect (have increased)
Question 76
Call the doctor at once.

Select the appropriate Passive voice for the above sentence.
A
Doctor be called at once.
B
Let the doctor be called at once.
C
Let us call the doctor at once.
D
At once the doctor be called.
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Question 76 Explanation: 
whenever we are given any imperative sentence, to change it to passive voice we use 'LET' as - Let + Object + Be/Get + Past Participle. i.e. Let + the doctor + be + called at once . Imperative sentences are those sentences that shows command, request, advice or instruction. It typically begins with a verb. As in the given Question - "Call the doctor at once".
Question 77
Suppose there are two teams A and B. Both of them are competing with each other on a racing track of 1 km. But team A has got the advantage of starting the race from 280 m from the starting point. If the ratio of speed of A to B is 3:4.

Select the correct option from the options given below:
A
Team A will win by 20m
B
Team B will win by 20m
C
Team A will win by 40m
D
Team B will win by 40m
General Aptitude    GATE 2017 MOCK II    
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Question 77 Explanation: 
To win the race first, A has to cover (1000 – 280) m = 720m B covers 4 part of distance when A covers 3 part of it. So, if A covers 720m, then B covers (4/3 * 720)m i.e. 960m Hence, A will win the race by 40m.
There are 77 questions to complete.

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