CAT 1998 Question Paper

This percentage is maximum in February in J&K; where the percentage is $$\frac{11183}{11285}=99.09$$%

From the table it is clear that the state which supplied the most number of apples is either HP or J&K.; UP and Cold Storage supplied less than a thousand apples in total.

The total number of apples supplied by HP is 231,028
The total number of apples supplied by J&K; is 262,735

Hence, the correct answer is J&K;

The answer to this question is the same as the state which supplied the maximum number of apples.

We can rule out UP and Cold Storage as they supplied significantly less than the other two.
Among the other two states,

The total number of apples supplied by HP is 231,028
The total number of apples supplied by J&K; is 262,735

Hence, the correct answer is J&K;

The supply is greater than or equal to demand if the cold storage number is zero.

This is the case between the months May-September.

Hence, the correct option is option (c)

To calculate the number of trees required, let us calculate the total number of tonnes supplied.

The total number of tonnes supplied equals 494,525.

One tree supplies 40 kilograms.

Hence, the number of trees required is $$\frac{494525*1000}{40} \approx 12.5$$ million trees

In the earlier question, we determined that we needed 12.36 million trees per year.
Each hectare has 250 trees.

So, number of hectares of land used is $$\frac{12.36*1000000}{250} \approx 49450$$

Percentage growth of all households South region showed the maximum increase in all households in the given period. (100% + 340%+ 425% = 865%)

We don't know the number of households in the upper-middle income class for Northern region and hence can't calculate the total household income for the same.

The answer is provided by the bar chart.
Look at the graph named North and the bar colored Orange.
This shows the percentage increase in the upper middle class households from the year 1987-88 to 1994-95 and it equals 200%

The answer to this question is provided in the table.
The average income of middle income category is 30,000
The average income of upper-middle income category is 50,000 and
The average income of high income category is 75,000

Hence, the correct answer is 75,000

Since we do not know the region-wise population of 1987-1988, we cannot find the increase in the number of households.
Hence, we cannot find the total income for the year 1995-96.
So the ratio cannot be determined.

Since we do not know the distribution of households in each region, we cannot determine the average income.

Let the amounts paid by Gopal and Ram to Krishna be 2X and 3X.
Gopal invested 2 lakhs additionally.
So, the total amount spent by him is 2X+2.
As the total amounts spent by the two of them are equal, it implies that 2X+2 = 3X or X = 2
Hence, the cost of the land is 2X+3X = 5X = 10 lakhs.
Total investment by the two of them is 10+2 = 12 lakhs

Hence, the total revenue generated is 12*25% = 3 lakhs.
The revenue generated by coconuts is $$3*\frac{3}{3+2} = 3*\frac{3}{5} = 1.8$$ lakhs

Cost of a coconut is Rs. 5

Hence, the total output of coconuts is $$\frac{180000}{5} = 36,000$$

Let the amounts paid by Gopal and Ram to Krishna be 2X and 3X.

Gopal invested 2 lakhs additionally.
So, the total amount spent by him is 2X+2.
As the total amounts spent by the two of them are equal, it implies that 2X+2 = 3X or X = 2
Hence, the cost of the land is 2X+3X = 5X = 10 lakhs.
Total investment by the two of them is 10+2 = 12 lakhs

Hence, the total revenue generated is 12*25% = 3 lakhs.
The revenue generated by lemons is $$3*\frac{2}{3+2} = 3*\frac{2}{5} = 1.2$$ lakhs

Total land used to cultivate lemons is 5 acres.

So, revenue generated by the lemons per acre is $$\frac{1.2}{5} = 0.24$$ lakhs per acre

Let the amounts paid by Gopal and Ram to Krishna be 2X and 3X.

Gopal invested 2 lakhs additionally.
So, the total amount spent by him is 2X+2.
As the total amounts spent by the two of them are equal, it implies that 2X+2 = 3X or X = 2
Hence, the cost of the land is 2X+3X = 5X = 10 lakhs.
Total investment by the two of them is 10+2 = 12 lakhs

Hence, the total revenue generated is 12*25% = 3 lakhs.
As the revenue is split equally, Gopal's share in the revenue is $$3*\frac{1}{2} = 1.5$$ lakhs

Let the amounts paid by Gopal and Ram to Krishna be 2X and 3X.

Gopal invested 2 lakhs additionally.
So, the total amount spent by him is 2X+2.
As the total amounts spent by the two of them are equal, it implies that 2X+2 = 3X or X = 2
Hence, the cost of the land is 2X+3X = 5X = 10 lakhs.
Total investment by the two of them is 10+2 = 12 lakhs

Hence, the total revenue generated is 12*25% = 3 lakhs.
The revenue generated by coconuts is $$3*\frac{3}{3+2} = 3*\frac{3}{5} = 1.8$$ lakhs

The number of coconut trees is 5 times the number of lemon trees = 100*5 = 500
So, the value of output per trees for coconuts is $$\frac{180000}{500} = 360$$

We know the total revenue generated by coconuts and lemons respectively.
We also know the price of a coconut and can thus calculate the total number of coconuts produced per acre.
We don't know the price of a lemon and thus can't calculate the total number of lemons produced per acre.

So, the answer can't be determined.

The revenue of 50 units is 1000. So, the revenue per unit is 20.
The variable cost of 50 units is 700. So, the variable cost per unit is 14.
Let the minimum number of units that are needed to be produced to ensure that there is no loss be X.

So, 20X > 14X + 50
Or X > 8
So, the least possible number of units to be produced is 9.

The revenue of 50 units is 1000. So, the revenue per unit is 20.
The variable cost of 50 units is 700. So, the variable cost per unit is 14.

Let the minimum number of units that are needed to be produced to ensure that there is a profit of at least 50.
So, total revenue is 20X and total cost is 14X+50.
So, Profit is 20X - (14X+50) = 6X-50 > 50
Hence, 6X > 100
Or X > 16
So, the least possible number of units to be produced is 17.

Till 34 units, the fixed cost is constant and the revenue increasing per every unit made.
So, to calculate the number of units that need to be produced to maximize the profit, we have to check only at two points: 34 units and 40 units.

The revenue of 50 units is 1000. So, the revenue per unit is 20.
The variable cost of 50 units is 700. So, the variable cost per unit is 14.

If number of units produced is 34,
Fixed cost is 50
Variable cost is 14*34 = 476
Revenue is 20*34 = 680.
So, profit is 680-476-50 = 154

If number of units produced is 40,
Fixed cost is 100
Variable cost is 14*40 = 560
Revenue is 20*40 = 800.
So, profit is 800-560-100 = 140

So, the profit is maximized when the number of units produced is 34

Till 34 units, the fixed cost is constant and the revenue increasing per every unit made.

So, to calculate the number of units that need to be produced to maximize the profit, we have to check only at two points: 34 units and 45 units.

The revenue of 50 units is 1000. So, the revenue per unit is 20.
The variable cost of 50 units is 700. So, the variable cost per unit is 14.

If number of units produced is 34,
Fixed cost is 50
Variable cost is 14*34 = 476
Revenue is 20*34 = 680.
So, profit is 680-476-50 = 154

If number of units produced is 45,
Fixed cost is 100
Variable cost is 14*45 = 630
Revenue is 20*45 = 900.
So, profit is 900-630-100 = 170

So, the profit per unit is maximized when the number of units produced is 34

The revenue of 50 units is 1000. So, the revenue per unit is 20.
The variable cost of 50 units is 700. So, the variable cost per unit is 14.
As fixed cost went up by 40 units, the total fixed cost (when number of units is less than 34) is 50+40 = 90
Let the minimum number of units that are needed to be produced to ensure that there is no loss be X.
So, 20X $$\leq$$ 14X + 90
Or X $$\leq$$ 15
So, the least possible number of units to be produced to ensure no loss is 15.

The maximum percentage increase in price of logs happened in the year 1991 (compared to 1990) and equaled 18/15 - 1 = 20%
The maximum percentage increase in price of plywood happened in the year 1992 (compared to 1991) and equaled 6/4 - 1 = 50%
The maximum percentage increase in price of sawtimber happened in the year 1993 (compared to 1992) and equaled 20/15 - 1 = 33.33%
Hence, the correct answer is 50%

The percentage increase in price of logs over the period of time equals 20/15-1 = 33.33%
The percentage increase in price of plywood over the period of time equals 7/3 - 1 = 133.33%
The percentage increase in price of sawtimber over the period of time equals 200/100 - 1 = 100%

Hence, the maximum percentage increase in price over the period of time happened with plywood.

After an increase by 33%, the difference in the prices of one tonne of saw timber and one cubic metre of logs is given below according to the respective years.

The difference in 1987 is 15 - 10*133.33% = 1.67
The difference in 1988 is 16 - 10*133.33% = 2.67
The difference in 1989 is 17.5 - 12*133.33% = 1.5
The difference in 1990 is 15 - 10*133.33% = 1.67
The difference in 1991 is 17.5 - 12.5*133.33% = 0.833
The difference in 1992 is 18 - 15*133.33% = -2
The difference in 1993 is 20 - 20*133.33% = -6.67

Hence, the difference is least in the year 1991.

From the above diagram, we can say that difference is highest in 1992.

In 1993, price of logs = Rs. 20 per cubic metre.

volume sales of plywood, saw timber and logs were 40%, 30% and 30% 

In 1993, price of plywood = Rs. 7 per tonne

In 1993, price of plywood = Rs. 20 per tonne

Weight of one cubic metre of saw dust and plywood both = 800 kg

1 tonne=1000kg

Price of 1000kg of plywood= Rs 7

Price of 800kg( 1 m$$^3$$)= 7 x 0.8 = Rs 5.6 per cubic metre. 

Price of saw timber = 20 x 0.8 = Rs 16 per cubic metre.

We know that the sales volume of plywood, saw timber and logs are in the ratio 4 : 3 : 3.
Thus, the average realization must be the weighted avg of these three-
$$\frac{(4\times 5.6)+(3 \times 16)+(3 \times 20)}{4+3+3}$$
=13.1
= Rs. 13 (Approximately)

In this case the average realization will be-

$$\frac{(4\times 5.26 \times 1.05)+(3 \times 14.28 \times 1.01)+(3 \times 20 \times 1.1)}{4+3+3} \approx 13.15$$

Only statement A: Angles OAC, ACB, CBO are right angles => OACB is a rectangle. OC = AB and OC is radius => AB is equal to radius. Hence, we can find the answer using statement A only.

Only statement B: The point B can change even though the point A s fixed at a distance of 5 units on x-axis from origin. Hence, length of AB changes => We cannot find the answer using statement B only.

Let's consider the statements one by one.

Statement 1: n is a multiple of HCF(3,5,7,9) = 315. Hence, n can be 315, 630, 945 .... Hence we cannot say if n is odd or even.

Statement 2: 0<n<400, we cannot say if n is odd or even.

Taking both statements together, n=315. Hence, it is odd.

Thus the question can be answered using both statements together.

The definition of the given function is expressed in statement 2, where  $$a \circledast b=\frac{a+b}{a}$$

Hence $$2\circledast3=\frac{2+3}{2}$$.

Hence the answer can be determined by b alone. A does not give any releant information.

Let the total questions be x and the questions solved by Radha and Rani be y and z respectively.

According to the first statement, y+z = 20% of x

Accoding to the second statement, y = 5/3rd of z

There are 2 equations and three variables. Hence the solution cannot be determined.

Let price of tea be t, coffee be c and cold drink be d.

Statement 1: c=t+5, we cannot infer value of t from this information

Statement 2: c=d-5 and d=3t, we cannot infer the value of t from this information

Using the statements together, c=t+5 and c=3t-5.

=>t+5=3t-5

=>2t=10

=> t=5

Hence, we can answer the questions using both statements together.

We cannot uniquely determine a value for a using either statement alone.

Using both statements together, we get an inconsistent set of equations. Hence, there is no solution using both statements together.

Thus, the question cannot be answered using both statements together.

Let the number of girls be g and boys be b. Hence, b+g=150

Statement 1: 50g+25b=4900 => 2g+b=196. Solving the two equations, g=46. Hence, answer can be obtained using statement 1 alone.

Statement 2: 30b+30g=4500 => b+g=150. As both the equations are equal, we cannot find a unique solution.

Thus, the question can be answered using one of the statements alone and not the other.

From the statements we need to infer which envelope contains L2.

From statement 1, we know that C2 should open E1.

From statement 2, we cannot tell which envelope contains L2.

Hence, the question can be answered using one of the statements alone and not the other.

Let's take the two statements individually:

Statement 1: If the second book is in Rack 3, then the fourth book must be in the only remaining odd numbered rack i.e. rack 1. Hence, we can infer the position of book 4 using the first statement.

Statement 2: If the third book is in Rack 2, then the first book must be in Rack 4. However, we don't know anything about the position of Book 4. Hence, we cannot infer the position of book 4 using the second statement.

Hence, the question can be answered using one of the statements but not the other.

Statement 1: a = (X+Y)/2 and $$a^2 = XY$$. Hence, $$a=(X+a^2/X)/2$$. Hence, we can re-arrange the equation to represent X in terms of a

Statement 2: There is no relation given between X and a. Hence, we cannot find value of X in terms of a.

Hence, the question can be answered by one statement alone and not the other.

We know that r1>r2.

Statement 1: $$2\pi(r1-r2) $$ = k. We cannot determine r1 from this information

Statement 2: $$\pi(r1^2-r2^2)$$ = m. We cannot determine r1 from this information.

Using both statements together, (r1+r2)/2 = m/k. We now have two linear equations with two variables. Hence, we can determine the value of r1 in terms of m and k.

Hence, the answer can be found using both statements together.

As the circle circumscribes the square, diameter of the circle= diagonal of the square. Let the side of the circle be s. If we can determine the value of s, then we can find the area of the square $$s^2$$.

Statement 1: Let the radius be r. 2r = $$s \sqrt{2}$$. Hence, s = $$r\sqrt{2}$$. Thus, we can find the area of the circle using this information.

Statement 2: This scenario can be drawn as shown below:

A line drawn from the center of the circle intersects the tangent at an angle of 90°. Hence, the triangle formed is a right-angled triangle with the hypotenuse of 5 cm, one side equal to the radius of the circle and second side equal to the length of the tangent. If the length of the tangent is known then we can calculate the radius using Pythogoras theorem. If the radius is known, the area of the square can be calculated as shown above.

If they work together, then total work done in single day = $$\frac{1}{3} + \frac{1}{4} + \frac{1}{6} = \frac{9}{12}$$
So $$\frac{9}{12}$$ work is done in 1 day
Hence unit work will be done in $$\frac{12}{9}$$ or $$\frac{4}{3}$$ days.
 

if $$n^3$$ is odd then $$n$$ will be odd. let's say it is $$2k+1$$
then $$n^2$$ will be = $$(4k^2 + 4k + 1)$$ which will be odd
Hence answer will be C.

The truck should be sent on a day on which maximum number of units can be sent. It happens on 2nd, 4th, 5th and 7th day. Hence the answer is b.

If the truck is hired only for the 7th day, the cost will be (150*6 + 180*5 + 120*4 + 250*3 + 160*2 + 120)*0.8 = 2776
So, total cost incurred = 2776 + 1000 = 3776

If a truck is hired on 4th day and 7th day, the cost incurred will be (150*3 + 180*2 + 120)*0.8 + 1000 + (160*2 + 120)*0.8 + 1000 = 3096

So, a truck should be hired on the 4th and 7th day.

let's say x is the initial number of bacterias :
So in 2nd generation no. of bacterias = $$\frac{8x}{2} = 4x$$
In 3rd generation, it will be = 16x
4th gen. = 64x
5th gen. = 256x
6th gen. = 1024x
7th gen. = 4096x 
Hence x = 1 million

As radius of circle is 20, lengths of PR, QR and PQ will be (15+5+15) , (10+10+10) , (8+12+8) respectively.
So perimeter will be = 28 + 30 + 35 = 93

$$2\#1 = 2+1 = 3$$

$$1 \triangledown 2 = (1 \times 2)^(1+2) = 2^3$$

So answer will be $$\frac{3}{8}$$

$$((1\#1) \# 2) = 2 \# 2 = 4$$

$$\log_{10} 0.1$$ = $$\log_{10} 10^{-1}$$ = -1

As $$(10^{1.3} \times -1)$$ is not positive, $$(10^{1.3} \triangledown \log_{10}{0.1})$$ = 1

$$1 \triangledown 2$$ = $$(1x2)^{(1+2)}$$ = $$2^3$$ = 8

Hence, the fraction is (4-1)/8 = 3/8

A digit number when squared produces a 3 digit number. This means that the number ranges from [10, 31].
First digit of $$BE^2$$ should be unit digit of $$E^2$$. But unit digit of $$E^2$$ is B. Look at the numbers and the unit digit of their square.

0-0, 1-1, 2-4, 3-9, 4-6, 5-5, 6-6, 7-9, 8-4, 9-1. Only 2-4, 3-9, 4-6, 7-9, 8-4 and 9-1 are kind of pairs we are looking after.But all the pairs except 9-1 produce a number greater than 31. Now, the number we can form from 9-1 is 19 whose square is 361 which satisfies all the condition we are looking for. This is the only such number.

Maximum five digit number which can be formed by using numbers is 43210
And minimum five digit number = 10234
Difference = 43210 - 10234 = 32976

Possible numbers with unit's place as 5 = $$4 \times 3 \times 2 \times 1 = 24$$

Possible numbers with unit's place as 4 and ten's place 3,2,1 = $$3 \times 3 \times 2 \times 1 = 18$$

Possible numbers with unit's place as 3 and ten's place 2,1 = $$2 \times 3 \times 2 \times 1 = 12$$

Possible numbers with unit's place as 3 and ten's place 1 = $$1 \times 3 \times 2 \times 1 = 6$$

Total possible values = 24+18+12+6 = 60

In the first hour, they cover 6km. In the second hour they cover 6.5km. In the third hour, they cover 7km and so on.

Finally, they cover 72km in 9 hours.

Distance covered by A in 9 hours = 4*9 = 36km

=> They meet mid-way between A and B.

Options B,C and D are given vice-versa to given statements which is not necessarily true.

But according to option A, P is true, then Q and R will be true too but S will be false as for S, either Q or R should be false.

So answer will be A.

Area grazed by cow will be = Area of the larger circle - Sector APQ + Sector PBS + Sector CQR

Area of larger circle - Sector APQ = $$\pi r^2 - \frac{\pi r^2}{12}$$ = $$132 \pi$$

Sectors PBS and CQR are symmetrical and hence will have equal area.

In triangle ABC, AB = AC => ABC is isosceles triangle.

As A = 30° => B = C =75°

Hence, angle PBS = 180-75 = 105°

Hence, Area of sector PBS = 105/360 * $$\pi * 2^2$$ = $$ 7 \pi / 6$$

Thus area that can be grazed by the cow = $$132 \pi + 2*7 \pi /6$$ = $$403\pi /3$$

Among all positions for A, if it has first position then either B will be at the 3rd position or C and D will be together which is not possible Hence answer will be A) .

If A is not at the third place, then it has only two choices either 2nd or 4th position
So if A is at 2nd position, then B has only fourth position as choice and C can have either first or third position.
And if A is at 4th position, then B has only 2nd position and again C can have either first or third position.
Hence answer will be C.

If A and B are together, then it can't be at first and second place as C and D will be together which is not possible.
Now if A can be at third place and B is at second place then C and D can be placed accordingly.
Answer will be B).

Let's say price of turban is x.

So total price for 12 months will be = $$90+x$$

total price for 9 months = $$\frac{(90+x) \times 9}{12} = (65+x) $$

By solving above equation, we will get value of x= 10.

$$\frac{(\pi r^2)}{2 \pi r}$$ = $$\frac{2 \pi r}{ \pi r^2}$$
So r = 2
Hence required area = (Area of square) - (Area of 4 circles)
= $$(8^2) - (4 \pi (2^2))$$ (As side of square will be 4*2 = 8)
= $$16 (4- \pi)$$

The intended diagram can be drawn as follows:

ABCD is the square and the coins are placed (numbered 1,2,3,4)

The first wheel completes a revolution in $$\frac{60}{60}=1$$ second
The second wheel completes a revolution in $$\frac{60}{36}=1\frac{2}{3}$$ second
The third wheel completes a revolution in $$\frac{60}{24}=2\frac{1}{2}$$ second

The three wheels touch the ground simultaneously at time which are multiples of the above three times.
Hence, the required number is $$LCM(1,\frac{5}{3},\frac{5}{2}) = 5$$ seconds.

So, the correct option is option (c)

Let's say N is our number
N = (899K + 63) or N = ($$29 \times 31$$K) + 63
So when it is divided by 29, remainder will be $$\frac{63}{29}$$ = 5

Let the number 'n' belong to the set A.
Hence, the remainder when n is divided by 2 is 1
The remainder when n is divided by 3 is 2
The remainder when n is divided by 4 is 3
The remainder when n is divided by 5 is 4 and 
The remainder when n is divided by 6 is 5

So, when (n+1) is divisible by 2,3,4,5 and 6.
Hence, (n+1) is of the form 60k for some natural number k.
And n is of the form 60k-1

Between numbers 0 and 100, only 59 is of the form above and hence the correct answer is 1

As least number of coin, one can have is 10
And no two of them possess same number of coins, hence for having maximum number of coins to one person, the distribution of coins will be = 10,12,14,64
maximum no. of coins = 64

If A collected 54 coins, remaining will be 46.
Now B,C,D must have atleast 10,12,14 coins 
So remaining coins will be 10
So difference between maximum and second maximum should be least when second highest will be as maximum as possible.
I.e. difference = 54- (14+10) = 30

Number of coins with A = 54

Number of coins with B = 2x+2

Number of coins with C = x

Number of coins with D = y

54+3x+2+y = 100

3x+y = 44

If 2x+2 = 28, then x = 13 and y = 5 which is not possible.

If 2x+2 = 20, then x = 9 which is not possible.

If 2x+2 = 26, then x = 12 and y = 8 which is not possible

If 2x+2 = 22, then x = 10 and y = 14 which is feasible

Akbar can wear either red or blue.
Anthony can wear either red or green.
So when both of them wear same colour that has to be red.
And Amar can wear either blue or green.
Hence our answer will be A.

The different possible cases are:

From the table we can see among all of the statements, only fourth statement is false, as if amar wears green, anthony has to wear green.

As we can see here that total number of students are = 60+84+108 = 252

Now given condition is that in one room only the students of the same subject can be there and the number of rooms should be minimum that means the number of students in a particular room will be maximum.

This Maximum number of students will be HCF (Highest common factor) of 60, 84 and 108 and that will be 12

Hence, number of rooms will be = 252/12 = 21

As we know for a number to be divisible by 125, its last three digits should be divisible by 125
So for a five digit number, with digits 2,3,8,7,5 its last three digits should be 875 and 375
Hence only 4 numbers are possible with its three digits as 875 and 375
I.e. 23875, 32875, 28375, 82375
 

Let's say number of rubbies are x and emeralds are y.
So 0.3x + 0.4y = 12
And total wealth = 4x+5y
Now putting value of x from eq.1 to eq.2 
i.e. total wealth = 4(12-0.4y)/0.3 + 5y
Now for maximizing total wealth y should be equal to zero.
Hence x = 40

Let's say number of coins are 2.5x , 3x and 4x
So total amount will be = 2.5x + 3x(0.5) + 4x(0.25) = 210
So x = 42
And number of 1 rs. coins = 2.5x = 105

When numbers of chocolates, biscuits and apples are integers.
Now let's say number of chocolates taken 1 , then biscuits will be 2 and apples can be 4,5,6,7
Hence minimum money that should be spent = 1+1+8 = 10 (Hence option C is cancelled)
Now when number of chocolates are 4
Biscuits will be 8
And apples can be 13,14,15....
Now total money spent can be 4+4+26 = 34 and more of it.
Hence answer will be A

Let the total production cost be 100.
Hence, selling price is 120.
Price of German component A is 30 and the price of the US component B is 50

After change in exchange rate, price of German component is 30*1.3 = 39
and price of US component is 50*1.22=61

Total increase equals 39+61-30-50 = 20
Hence, the minimum production cost is 100+20=120
The maximum possible selling price is 120*110% = 132.

So, maximum possible gain is (132-120)/120 = 10%

Let the total production cost be 100.
Hence, selling price is 120.
Price of German component A is 30 and the price of the US component B is 50

After change in exchange rate, price of German component is 30*1.2 = 36
and price of US component is 50*0.88=44

Total increase equals (36+44)-(30+50) = 0
Hence, the total production cost did not change.
As the selling price also did not change, the gain percentage equals 20%

Since the people wearing yellow saree and the white saree were at the ends, Ms West Bengal was not sitting at one of the ends and was not a runner up, the arrangement is as shown below:

Since the people wearing yellow saree and the white saree were at the ends, Ms West Bengal was not sitting at one of the ends and was not a runner up, the arrangement is as shown below:

Since the people wearing yellow saree and the white saree were at the ends, Ms West Bengal was not sitting at one of the ends and was not a runner up, the arrangement is as shown below:

Since the people wearing yellow saree and the white saree were at the ends, Ms West Bengal was not sitting at one of the ends and was not a runner up, the arrangement is as shown below:

The total time taken for both the journeys is the same. So, a) is incorrect. If he goes with the same speed both ways, he would've been at the same point at noon on both days. So, d) is incorrect. If he does not travel with the same speed in both the directions, he need not be at the same spot at noon. So, option b) is incorrect. Option c) is the correct answer.

The last digit of powers of 2 follow a pattern as given below.

The last digit of $$2^1$$ is 2
The last digit of $$2^2$$ is 4
The last digit of $$2^3$$ is 8
The last digit of $$2^4$$ is 6

The last digit of $$2^5$$ is 2
The last digit of $$2^6$$ is 4
The last digit of $$2^7$$ is 8
The last digit of $$2^8$$ is 6

Hence, the last digit of $$2^{51}$$ is 8

Let the volume of the cup be V.
Hence, after removing three cups of alcohol from the first container,

Volume of alcohol in the first container is 500-3V
Volume of water in the second container is 500 and volume of alcohol in the second container is 3V.
So, in each cup, the amount of water contained is $$\frac{500}{500+3V}*V$$

Hence, after adding back 3 cups of the mixture, amount of water in the first container is $$0+\frac{1500V}{500+3V} $$
Amount of alcohol contained in the second container is $$3V - \frac{9V^2}{500+3V} = \frac{1500V}{500+3V}$$

So, the required proportion of water in the first container and alcohol in the second container are equal.

For a number to be divisible by 8, last 3 digits must be divisible by 8.

Last 3 digits of this number are 354.

354 mod 8 = 2

Hence, 2 is the remainder.

The ranking list would be in the order A, B, C, D......., X, Y, Z. Now the A wins all his 25 matches, B wins 24 matches and lost to A. C wins 23 matches and lost to A and B. In this way N 12 matches and looses 13 matches to A,B,C,D....,M

The best word to use for "links" is "forging".

Hence, "focusing on forging European links" is the correct phrase.

Bank deposits are countable. So they swell. They don't flourish. "To flourish" means to develop. The correct answer is option b.

There is no error in the given sentence. "An inexplicable phenomenon" means a phenomenon which cannot be explained. So the usage is contextually as well as grammatically correct.

"cannot scold freely" means "cannot scold whenever the management want". This can be replaced by "cannot scold at will."

Option C and Option D are incorrect as the author talks about writing without affectation i.e. writing without any pretension. Hence, it can be mistaken for writing without consideration or care and not writing fast. 

Between options A and B, A contains the correct phrase 'at random'. The phrase means without a care and in a disorderly manner. "Writing  randomly" does not carry the same implication. Also, here the modifier 'random' is a misplaced modifier. It is modifying the way of writing instead of modifying what is written. 

Lukewarm is the correct usage in the first blank as it means not entusiastic. "Electifies" correctly matches the second blank. Hence the correct option is B.

Option A is incorrect as in the usage of "these areas", things cannot be used. Similarly option C is incorrect. Option B is incorrect because"basis of proper emotional reaction" is an incorrect usage.

Audible means which can be heard. Audible sounds means the sounds which can be heard..

The two set of words must be opposite to each other. Option A and D are correct in this case. But option A is contextually incorrec as learning cannot be fun if its is fast. The correct answer is D.

Option D is incorrect as it contradicts the statements as "rulers do not get ruled." Option A is contextually incorrect as it does not make any sense. Option B is incorrect as powerfully corrupt is grammatically incorrect. Option C is the best match.

Option C is incorrect as impracticality and knowledge cannot be related because they are totally different.

Option B is incorrect as improvisation means to perform spontaneously and improving means to get better which are not related.

Option D is contextually incorrect. Option A is correct as it talks about imitation and invention which are related terms.

Farmers face problems due to the spiralling prices. So they protest in order to make their pleas head. "Virility" means manliness which has no context in this passage. The protest need not curb the prices. It will make their pleas heard. "Topple the government" is an extreme form which does not demand merit in this passage. Option B is the correct answer.

Option A is incorrect as principally is an incorrect usage. Principal means a chief which does not go in this context. Hencee C is incorrect. Among B and D, B is more suitable as in principle means in primary rule which goes with the tone of the passage.

Options B and C are incorrect as desires cannot convince or categorise people. Between options A and D, "actuated" which means motivated is a better fit as "led" is generally used for other people and not inanimate objects like "desires".

Swindle means to use deception to deprive someone's possession. It means that you have an unequal exchange where you didn't give much of your possession and you robbed the other person of his/her possession. Option C summarises it correctly. 

Sentence C is the starting sentence as it talks about the as salvation. Sentence B is the next sentence as it mentions the traditions of christanity. A and D differentiates the Buddhism from Christanity. The correct order is CBAD.

Statement A highlights the additional issue. Statement B substantiates A. Option C  highlights the issues facing indian agriculture as mentioned in B. Option D is the last sentence as in 6, "it" refers to rural class.

The first sentence talks about magazines. The same idea is continued in sentence B. Hence, B follows the first sentence.

CD is a pair because the "number of editors" concept is introduced in C and then an example is taken in D. 

Hence, BCDA is the answer.

The pronoun "it" in statement B refers to the media attention mentioned in statement 1. Hence, 1-B are a pair. Statements A and D describe the NRIs introduced in B and hence should come after B. As A concludes from the outward characteristics mentioned in D, it should follow D. C mentions the gap in information provided about NRIs and 6 mentions how the film festival is filling those gaps. Hence, C-6 are a pair. Hence, the order is 1BDAC6.

C and B forms a pair as they illustrate simultaneous happenings- one where Western dealers began to look and East and their Indian counterpart discarded synthetic sarees and plastic furniture. Only C has both these sentences together. Thus, C is the correct answer.

The opening sentence is B - it introduces the character the rest of the paragraph is talking about. This is followed by A, which describes the person. The next sentence is D, which talks about the reaction of Annette. The last sentence is C. So, the correct order of sentences is BADC. Option b) is the correct answer.

Sentences A and B start with conjunctions. So, they cannot be used to open a paragraph. The best opening sentence is C. This is immediately followed by A, which gives a contradictory opinion to the one in C. A is followed by D which further explores the idea in A. The last sentence is B. So, option a) is the correct answer.

B is the best opening sentence - it talks about the setting of the scene. This is followed by D, which talks about what happened when they reached the field. This is then followed by C, which talks more about the person introduced in sentence D. The closing sentence is A. So, the correct order of sentences is BDCA. Option b) is the correct answer.

The first sentence is A - it introduces the main character in the paragraph. This is followed by C, which gives a background about that person. B and D is a pair. 'This illusion' in D refers to Alex not being happy about his Indian origins - sentence B. So, the correct order of sentences is ACBD. Option c) is the correct answer.

B is the first sentence of the paragraph. It introduces the subject of the paragraph - the influence of Indian wear on the west. This is then followed by A, which talks about where the maximum influence is. D, which further elaborates the idea, follows A. The concluding sentence is C. Option a) is the correct answer.

CA is a pair. The 'policy' in A refers to the condemnation of the states that do not follow a particular religion. The opening sentence of the paragraph is D and this is immediately followed by B. So, the order of sentences is DBCA. Option b) is the correct answer.

C is thee starting of the sentencee where the author talks about the situation of man and his appearence. Option A continues the tone of the appearence. Option B mentions the time due to which his heart thumped as mentioned in option D. Hence the sequence is CABD.

AC is a pair. 'Him' in C refers to 'the director' in A. BD is also a pair. 'He' in D refers to 'Mitch' in B. Also, A is the best opening sentence. So, the correct order of sentences is ACBD. Option a) is the correct answer.

Option A is the starting sentence where the author focuses on the start f hostility between Germany and USA. Option D continues the tone by stating the consequences. CB are mandatory pair if we look at the word "Neutrality". ADCB is the correct sequence. 

A is the opening sentence. This is followed by B, which describes why the essay talked about in A appeals to the intellect. D should follow C. C talks about studies and D talks about 'excess' study. So, the correct order of sentences is ABCD. Option b) is the correct answer.

C is the best opening sentence. It introduces the topic of the paragraph - logic. This is followed by A, which goes on to explain the meaning of reasoning. This is then followed by B, which explains 'logical reasoning'. The concluding sentence is D. The correct order of sentences is CABD. Option b) is the correct answer.

Either Sita is sick or she is careless => Sita is sick or she is careless.

Consider the pair AD. A says "Sita is not sick". So, it implies that she is careless, which is what is mentioned in statement D. So, AD relate to the original sentence.

The statement can be written as follows:

Ram eats a hamburger => Ram get a swollen nose

Ram did not get a swollen nose => Ram did not eat a hamburger

Option d) is the correct answer.

The members are either hostile or have no confidence.

Consider the pair of sentences CB.

C says the members have confidence in the management. So, they do not have 'no confidence' => The members should be hostile in nature, which is what statement B says. So, option b) is the correct answer.

The sentence can be written as follows:

Ram reads late into the night => His father beats him

Ram's father did not beat him => Ram did not read late into the night

So, none of the pairs given in the options follow from the statement.

The statement can be written as follows:

Children do not cavort => Irresponsible parents shout

Irresponsible parents did not shout => Children cavorted

So, AB follows from the statement.

Statement A: There need not be an intersection between the sets Xs and Ys.

Statement B: There need not be an intersection between the sets Sonas and Crazy.

Statement D: Third statement follows only from the second statement.

The third statement in C follows from its first two statements.

Option b) is the correct answer.

Statement A: Since all cycles are men and some iciles are cycles, it follows that some iciles are definitely men.

Statement B: Girls is a subset of Teeth. There is no intersection between the sets Teeth and Yellow. So, there is no intersection between the sets Girls and Yellow.

The third sentences in C and D need not necessarily follow from the respective first two statements. Option b) is the correct answer.

Statement A: No sun is not white => All Sun is white. So, Sun is a subset of white. All moon is sun => Moon is a subset of Sun. So moon is a subset of white.

In none of the other three statements do the third sentences follow from the respective first two statements.

Option a) is the correct answer.

In both A and C the third statement is logically concuded. The reasoning is if A = B, B = C then A = C.

Similarly T's = Square,  Square = Rectangle then T's = Rectangle.

Idiots = Bumblers, Bumblers = Fumble then Idiots = Fumble 

The author is of the opinion that one cannot limit efficiency to just work. It tends to affect a person's non-work life as well. In other words, efficiency can become all-pervading. Option a) is the correct answer.

Option A cannot be inferred as it is nowhere mentioned. Option B is not necessarily true. The two groups may not agree to each others plans even if they are friendly with each other. Thus, just from the fact that they opposed each others plans we cannot infer that there is contention between the two groups. From the paragraph, we can infer that neither of the two groups can proceed i.e. neither the traffic planners nor the transport planners can move ahead with any plan. Thus, both the parties are dead-locked. Hence, we can infer option C.

From the argument, we understand the following points: 1. The company is trying to instill the spirit of dialogue in its employees. 2. This dialogue is agnostic of position or title of the employee.

So, we can infer that the company believes in fostering the spirit of dialogue without degenerating it into a positioning based debate. Option B is the correct answer.

In option C, there is an assumption that the company had some inter-personal problems in the past. However, there is no such information in the passage from which we can infer the assumption. Also, we have to choose the answer according to the contents of the given paragraph. Therefore, option C is incorrect.

Option b) is incorrect because it says 'only' India is not proud of its culture, which is incorrect.

Option c) is incorrect because we cannot infer if 'most' Indian families have sold off their heirlooms.

Option d) is incorrect because the market is US and Europe and not India. India is the souce.

Option a) can be inferred.

According to the paragraph, the moral police thinks that the movies are bound to affect the judgment of Indian audience and hence they need to censor the movie in order to preserve their already existing judgment and protect them from the influence of such a work.

Option B correctly summarizes the inference.

The sentence is option b) is opposite to what the argument is conveying.

Option a) can be inferred. According to the argument, a lot of aggression has stemmed because the rich want to defend themselves against the poor. In other words, the aggression has stemmed from the desire of the haves to defend themselves against the have-nots.

According to the passage, the latter kind of travelers only visit such monuments as the time they have at their disposal allows them to contemplate without irreverent haste.

A is incorrect as the preference of the writer is not the main subject of focus.
B is way too harsh. This cannot be inferred from the passage.
C correctly describes the second kind of travelers.

Thus, C is the correct answer.

Option a) is incorrect because we cannot infer that the speaker is a colonist. The speaker could be a neutral observer. So, we cannot say that he has the good of the nation at heard. English is not an issue that is related only to the colonial empire. We cannot infer the statement in option c) also.

Option d) is the correct answer.

Option a) is incorrect because 'translating from real life to reel' is the opinion of the author of the paragraph and not necessarily the opinion of the director. Similarly, option b) also cannot be inferred. There is nothing in the paragraph from which we can infer whether the movie was a success or a failure. Option d) is the correct answer.

There is nothing in the passage to suggest that the Indian middle class has been transformed to a 'pampered' middle class. Options b) and c) are incorrect. However, the paragraph strongly suggests that the Indian middle class has been the focus of the economic policies of the Government for a long time now. So, option a) can be inferred.

The answer to this question can be referred from the given lines:"And to that extent that is true now, if someone was born today, they would be born into a very different set of cultural assumptions and hopes than somebody born 50 years ago. We were entirely sold on the Nehru-Gandhi kind of plan." Here the author says that they were inspired from the idea of Nehru-Gandhi ideology.

Refer to the following sentences: "Where Naipaul is right, although I don't share his conclusions about it, but I think where he is right, is in saying that this is a great historical moment". So, the writer does not share Naipaul's conclusion on the 50th anniversary being a historical moment. Option c) is the correct answer.

Refer to the following lines:"If you ask people in general, they would have absolutely no problem with the idea of India at all. I think, in a way the strength of the nationalist idea is shown by its ability to survive the extraordinary stresses that it was placed under" This quality is resilience where we can endure more stress and still emerge victorious.

Both the options can be inferred from the given lines:"Anybody who knows anything about these countries, and I do know something about these countries, knows that every cheap politician can put a demonstration in the street in five minutes. That doesn't represent in any sense the people's will." 

The given passage is based on the experience of the author. Here the author states the democratic credentials of India and highlights the resilience of Indians.In the last line of the passage, the author mentions about his life experience specifically. Hence the answer is a.

The answer can be interpreted from the following lines:"One of the things that I remember very vividly, being there 10 years ago at about the time of the killings that took place in Assam, is discussing this with good friends and fellow writers. And I remember somebody said to me, until we understand that we are capable of these things, we can't begin to move beyond them." Here the author's friend says that we can move beyond some things after we are capable to do those things.

Refer to the following sentence: "The civilizing influence is what prevents most of us from giving vent to those terrible urges". This idea is mentioned in option d). Option d) is the correct answer.

Refer to the following sentences: "I think corruption ..... to call itself a democracy.". From these sentences, we can infer that the author fears the long-term damage to democracy which corruption can bring about. Hence, option b) is the correct answer.

The answer can be deduced directly from the given lines:" It creates backlashes, it creates polarisation, and it creates the risk of more upheaval. Partly, I am saying this as a kind of objective observer, but nobody is an objective observer."

Refer to the following sentences: "The thing that became independent had never previously existed, except that there had been an area... was an invention". So, the writer is questioning the existence of a political entity called India prior to independence. Option a) is the correct answer.

Refer to the following lines in which the author clearly mentions that the creation of Pakistan was under-imagines:"The history of India is a history of independent nation-states. It is a history of Oudh or Bengal or Maratha kingdoms. All those independent histories agreed to collectivise themselves into the idea of the nation of India. In the case of Pakistan, it was less successful. Pakistan was under-imagined. It did not survive as a nation-state."

Refer to the following two sentences in the passage: "I think, in a way the strength of the nationalist idea is shown by its ability to survive", "But that it does exist and that it is something to which people feel they belong". The secret of India's survival, according to the author, lies in its ability to fight back stress and strains and a sense of belonging that people feel for it. Option d) is the correct answer.

Refer to the first sentence of the passage: "In Western civilization is in a state of permanent crisis, it is not far-fetched to suggest that there maybe something wrong with its education". So, the writer's contention is that the crisis in the Western civilization can be explained by the presence of some flaws in its education. Option a) is the correct answer.

Refer to the following sentences: "Lord Snow, it will be recalled, talked about 'The Two Cultures'...at the other the scientists". So, according to Lord Snow, the intellectual life of the Western society is split between the scientists and literary intellectuals". Option c) is the correct answer.

Refer to the first few lines of the paragraph:"If Western civilization is in a state of permanent crisis, it is not far-fetched to suggest that there may be something wrong with its education. No civilization, I am sure, has ever devoted more energy and resources to organised education, and if we believe in nothing else, we certainly believe that education is, or should be, the key to everything. In fact, the belief in education is so strong that we treat it as the residual legatee of all our problems." Here the author criticises our view when we consider the solutin of some problem as more education.

Consider the following sentences: "We often notice the existence of more or less fixed ideas in other people's minds - ideas with which they think without being aware of doing so. We then call them prejudices". So, a prejudice is a fixed idea with which people think without being aware of doing so. Option b) is the correct answer.

The author quotes Lord Snow in the passage: "and finally to train politicians, administrators, and entire community...". Option a) is the correct answer.

From the passage, we can infer that the author feels that the neutrality of science would be under threat in the future. Hence, he does not question whether it is currently neutral or not. Similarly, we cannot infer that scientists question the neutrality of science. Hence, we can eliminate options A and B. 

The author does question the scientists stand that their labours are neutral and the fruits depend on the actions of others. The author particularly worries about this given the fact that most people don't even understand the work of the scientists. Hence, the author questions the scientists stand on the neutrality of their labours. Hence, option C is the right answer.

Refer to the following sentence: "The essence of education, i suggested, is the transmission of values...". So, according to the author, the main responsibility of education is to transmit ideas of value. Option a) is the correct answer.

Refer to the following sentences: "These ideas on education, which are by no means unrepresentative of our times, ...Second Law of Thermodynamics". From these sentences, we can understand that the author is not of the opinion that the gulf between science and literature needs to be bridged. Also, there is nothing in the passage to suggest that the author believes that ideas should be maintained for a holistic view of society and its problems or that words are not ideas.

Option d) is the correct answer.

Refer to the following sentences: "The essence of education, I suggested, ... more than mere formulae or dogmatic assertions..". From these sentences, we understand that according to the author, values are not merely dogmatic assertions". Option b) is the correct answer.

Refer to the following sentence: "I say, therefore, that we think with or through ideas and that what we call thinking is generally the application of pre-existing ideas to a given situation or set of facts". So, thinking is an application of pre-existing ideas to a situation. Option c) is the correct answer.

Refer to the following sentence: "Quite apart from the dollar sign on it,...word trade". From this, we can understand that a large part of the American population indulges in word trade. Option b) is the correct answer.

Throughout the passage, the author brings out various examples which show that the primary hallmark of a gag writer is that he/she has fun with words. Refer to the words 'hilarious', 'joke' etc. strewn throughout the passage. This is clearly brought out in option b).

This fact is highlighted when the author talks about the gag writers in two aspects of the language. Refer to the following lines:"Gag writers' tricks with words point up the fact that we have two distinct levels of language: familiar, ordinary words that everybody knows; and more elaborate words that don't turn up so often, but many of which we need to know if we are to feel at home in listening and reading today." These line confirm option a as an answer.

Refer to the following lines:"Gag writers' tricks with words point up the fact that we have two distinct levels of language: familiar, ordinary words that everybody knows; and more elaborate words that don't turn up so often, but many of which we need to know if we are to feel at home in listening and reading today. To be sure gagmen play hob with the big words, making not sense but fun of them. They keep on confusing bigotry with bigamy, illiterate with illegitimate, monotony with monogamy, osculation with oscillation." In this passage the author states that the gag writers make the use of double meaning language in order to make everyone feeling cozy.