CAT 1999 Question Paper

y = $$\frac{4x-1}{17}$$

The integral values of x for which y is an integer are 13, 30, 47,......

The values are in the form 17n + 13, where $$ n \geq 0$$

17n + 13 < 1000

=> 17n < 987

=> n < 58.05

=> n can take values from 0 to 58 => Number of values = 59

$$(ab)^2$$ = ccb

ccb > 300

The last digit of the number ab must be same as that of the square of ab.

So, b can be 0, 1, 5 or 6.

$$20^2$$=400 and $$30^2$$=900 are three digit numbers and greater than 300. But the first 2 digits are not same. Hence, b is not 0.

If b is 5, then the ten's digit of ab's square will be 2 => c = 2. But if c is 2, then ccb is not greater than 300. Hence, b is not 5.

If b is 6, then $$26^2$$ = 576 is the only three digit number that is greater than 300. But, it is not in the form of ccb => b is not 6.

If b is 1, then $$21^2$$=441 satisfies all the given conditions => b is 1.

$$7^3$$ = 343

$$7^{84}$$ = $$(7^3)^{28}$$ = $$343^{28}$$

$$343^{28}$$ mod 342 = $$1^{28}$$ mod 342 = 1

For a triangle to be formed, we need three points.

Case 1: Select 2 points on the line that has 10 points and 1 point on the line that ha 11 points.

This can be done in $$^{10}C_2$$*$$^{11}C_1$$ ways = 495 ways.

Case 2: Select 2 points on the line that has 11 points and 1 point on the line that ha 10 points.

This can be done in $$^{11}C_2$$*$$^{10}C_1$$ ways = 550 ways.

495 + 550 = 1045 ways.

At least one candidate and at most n candidates among 2n+1 candidates => 

^{2n+1}C_1Total number of ways alteast one candidate can be selected = Total number of ways of selecting a candidate - total number of ways of selecting no candidates

$$\Rightarrow ^{2n+1}C_1+^{2n+1}C_2+^{2n+2}C_3+....+^{2n+1}C_{n-1}+^{2n+1}C_n = 63 $$

We know that $$^{2n+1} C_0$$ and $$^{2n+1} C_{2n+1}$$ are equal to 1.

By Binomial Expansion 

$$ ^{2n+1}C_0+^{2n+1}C_1$$+... + $$^{2n+1}C_{2n}+^{2n+1}C_{2n+1} = (1+1)^{2n+1} $$ ---- Eq 1

Also $$^{2n+1}C_1$$ = $$^{2n+1}C_{2n}$$ by symmetry

and $$^{2n+1}C_2$$ = $$^{2n+1}C_{2n-1}$$ and so on

So $$\Rightarrow ^{2n+1}C_{n+1}+^{2n+1}C_{n+2}+....+^{2n+1}C_{2n-1}+^{2n+1}C_{2n} = 63 $$

Therefore, on substituting these values in Eq 1 we get

1 + 63 + 63 +1 = $$2^{2n+1}$$

$$2^{2n+1}$$ = 128

2n+1 = 7

Therefore, n=3

As at most n students can be selected, the correct answer is 3.

The function of the speed of the train = 42 - k$$\sqrt{n}$$ where n is the number of compartments and k is a constant.

42 - k$$\sqrt{9}$$ = 24

=> 3k = 18 => k = 6

=> Function of speed = 42 - 6$$\sqrt{n}$$

Speed is 0 when 42 - 6$$\sqrt{n}$$ = 0

=> 42 = 6$$\sqrt{n}$$

=> n = 49

=> So, with a positive speed, the train can carry 48 compartments.

Let the fixed income be x and the number of boarders be y.

x + 25y = 17500

x + 50y = 30000

=> y = 500 and x = 5000

x + 100y = 5000 + 50000 = 55000

Average expense = $$\frac{55000}{100}$$ = Rs.550.

Let the number of employees be 100.

=> 40 men and 60 women.

Number of men getting more than 25000 = 30

Number of people getting more than 25000 = 45

Number of women getting more than 25000 = 45 - 30 = 15

Fraction of women getting less than 25000 = $$\frac{45}{60}$$ = $$\frac{3}{4}$$

| r-6 | = 11 => r = -5 or 17

| 2q - 12 | = 8 => q = 10 or 2

So, the minimum possible value of q/r = 10/(-5) = -2

Let the four consecutive positive integers be $$a,a+1,a+2$$ and $$a+3$$.
Therefore, $$n=1+a(a+1)(a+2)(a+3)$$
Or, $$n = 1+(a^2+3a)*(a^2+3a+2)$$
Or, $$n = (a^2+3a)^2 + 2*(a^2+3a)+1 = (a^2+3a+1)^2$$
Hence, n is a perfect square and therefore not a prime.

The product of four consecutive positive integers is always even. Hence, n is always odd.
Therefore, from the given statements, only A and C are true.

Let the distribution of votes for each of the proposal be as given below.
From the information given, we know that 

a+b+c+d+e+f+g = 78 --- (1)
a+b+e+f = 50  ---- (2)
b+c+f+g = 30 ----  (3)
e+f+g+d = 20 ---- (4) and 
f = 5 --- (5)

We need to find b+e+g+f = ?
In the above equations, (2)+(3)+(4) - (1) implies

(a+b+e+f)+(b+c+f+g)+(e+f+g+d) - (a+b+c+d+e+f+g) = 50+30+20-78 = 22
Or, b+e+g+2f=22.
As, f = 5, it implies that b+e+g+f=17

Let p and q be any two elements of the set A.
For the computation of the GCF of elements of the set A, we can replace both p and q by just the GCF(p,q) and the result is unchanged.

So, for every application of the function h, we are reducing the number of elements of the set A by 1. (In this case two numbers p and q are replaced by one number GCF(p,q)).
Expanding this concept further, the minimum number of times the function h should be called is n-1

By symmetry, it is safe to assume that the polygon ABCD is a square. So, AB = PO. The perimeter of the inner square = 4 AB. The perimeter of the outer circle = $$ 2 \pi \times AB$$

So, ratio = $$ \frac{2 \pi \times AB}{4AB}$$ = $$ \frac{\pi}{2}$$

All of them can be mislabeled in 2 ways: 

Red box  - white label

White box - Red and white label

Red and white box - Red label

Red box - red and white label

White box - Red label

Red and white box - White label

So, we would try the box with the red and white label and if it has a white ball, labelling to the boxes is done as per case 1. If it has a red ball labelling is done as per case 2. 

Note: It's not a good idea to try the white label as if we get a red ball, we can't make out if we are picking from red box or red and white box. Similarly if we try from the box with red label and we get a white ball, again we can't make out if it is coming from the white box or the red and white box. 

Observe the pattern given below.
$$11^2 = 121$$
$$111^2 = 12321$$
$$1111^2 = 1234321$$ and so on.

So, $$11111111^2 = 123456787654321$$

Mrs. Abraham can't be sitting next to him as per the seating arrangement. Wives sit three places away from their husbands.

Mrs. Charlie is sitting to the left of Mr. Abraham. So, she can't be sitting to his right.

Mrs. Elenor is sitting two places to the right of Mrs. Border (and not Mrs. Charlie). So, she can't be sitting right next to Mr. Abraham.

Mrs. Border and Mrs. Dennis are the remaining two wives and each is equally likely to to be sitting to the right of Mr. Abraham.

The distance between Ahmedabad and Baroda is 100 Km
Navjivan express starts at 6:30 am at 50 Km/hr and Howrah expresses starts at 7:00 am at 40 Km/hr.
Distance covered by Navjivan express in 30 minutes (by 7 am) is 25 Km/hr.

So, at 7 am, the distance between the two trains is 75 Kms and they are travelling towards each other a relative speed of 50+40=90 Km/hr.

So, time taken them to meet is 75/90*60 = 50 minutes.

As, Mr. Shah realizes the problem after thirty minutes, time left to avoid collision is 50-30 = 20 minutes

The perimeter of the circle is equal to 2$$\pi $$.

The perimeter of the polygon inscribing the circle is always greater than the perimeter of the circle => L1(13) > 2$$\pi $$

The perimeter of the polygon inscribed in the circle is always less than the perimeter of the circle => L2(13) < 2$$\pi $$

=> $$\frac{L1(13)+2\pi }{L2(17)}$$ > 2

Let EF be the fence.

As the field is in the shape of a square, the straight line face that is put up will cordon a field of the form right angled triangle.

The area of a right angled triangle is maximum when the sides that contain the right angle are equal.

Let the side be a.

$$a^2 + a^2$$ = $$100^2$$ => $$a = 50\sqrt{2}$$

Area = $$\frac{1}{2}*50\sqrt{2}*50\sqrt{2}$$ = 2500 sq m.

From the given passage, it is given that Q>P, R>S.

According to the information Q = 2 when P = 1 or Q = 4 when P = 2.

In first case R = 4 and S = 3 and in the second case R = 3 and S = 1.

In both the instances S is odd.

From the given passage, it is given that Q>P, R>S. Now it is given that R is greater than or equal to S+2. Option B will still remain true because it is given that Q>P.

From the given passage, it is given that Q>P, R>S.

When R = 4 and S = 3, then Q = 2 and P = 1.

P+Q = 2+1 = 3 which contradicts statement 1.

Number of flowers after the first dipping = 60

Number of flowers after the second dipping = 2(60-y) = 120-2y

Number of flowers after the third dipping = 2(120-2y-y) = 240-6y

Number of flowers after the fourth dipping = 2(240-6y-y) = 480-14y

y = 480 - 14y

15y = 480

y = 32

Number of flowers after the first dipping = 2x

Number of flowers after the second dipping = 2(2x-y) = 4x-2y

Number of flowers after the third dipping = 2(4x-2y-y) = 8x-6y

Number of flowers after the fourth dipping = 2(8x-6y-y) = 16x-14y

16x-14y = y

y = 16x/15

Minimum value of y = 16 when x = 15

Number of flowers after the first dipping = 2x

Number of flowers after the second dipping = 2(2x-y) = 4x-2y

Number of flowers after the third dipping = 2(4x-2y-y) = 8x-6y

Number of flowers after the fourth dipping = 2(8x-6y-y) = 16x-14y

16x-14y = y

y = 16x/15

Minimum value of y = 16 when x = 15

For the mixture to be 100 times as sweet as glucose, its sweetness relative to the mixture should be at least 74.

1 gm of saccharin = 675

Let the number of grams of sucrose to be added be N. Thus, the total weight of the mixture = N + 1.

So, (675 + N) / (N+1) = 74

=> 675 + N = 74N + 74

=> 601 = 73N => N = 8.23

When N=9, sweetness will be S = (675+9)/10 = 684/10 = 68.4

When N=8, sweetness will be S = (675+8)/9 = 683/9 = 75.8

So, option b) is the correct answer.

The relative sweetness of the mixture is (1*0.74 + 2*1 + 3*1.7) / (1+2+3) = 7.84/6 = 1.30

Option a) is the correct answer.

We are given that there are two housewives, one lecturer, one architect, one lawyer and one accountant among A, B, C, D, E and F.

The other information given is that only two married couples are in the group.

We are given that the lawyer is married to D, and D is a housewife.

We are also given that no woman in the group is either an architect or an accountant.

C is an accountant, has to be male, and is married to F, who is a lecturer, who has to be female.

Putting this information in the table, we get,

We are also given that A is married to D, so this has to be the second couple, and A has to be the lawyer.

This leaves us with B and E, as well as housewife and architect professions. Given that E is not a housewife, E has to be the Architect and B has to be the housewife. Since the Architect cannot be a woman, E has to be a man, and B has to be a woman.

Putting all the information in the table, we get,

From the table, we can see that E is an Architect.

Hence, the correct answer is option B.

We are given that there are two housewives, one lecturer, one architect, one lawyer and one accountant among A, B, C, D, E and F.

The other information given is that only two married couples are in the group.

We are given that the lawyer is married to D, and D is a housewife.

We are also given that no woman in the group is either an architect or an accountant.

C is an accountant, has to be male, and is married to F, who is a lecturer, who has to be female.

Putting this information in the table, we get,

We are also given that A is married to D, so this has to be the second couple, and A has to be the lawyer.

This leaves us with B and E, as well as housewife and architect professions. Given that E is not a housewife, E has to be the Architect and B has to be the housewife. Since the Architect cannot be a woman, E has to be a man, and B has to be a woman.

Putting all the information in the table, we get,

From the table, we can see 3 males in the group.

Hence, the correct answer is option B.

_ _ _ B _ _ _

A and G will sit in 6th and 7th position from left in any order.

C and D must be as far apart as possible. Hence, they'll sit in 1st and 5th positions from left in any order.

Hence, only A, C, D and G can sit in the corners.

Among, the given options F cannot sit in the extreme end.

The arrangement of people is as follows: C/D F/E E/F B D/C A/G G/A

So, E and A can never sit together.

The sides of the rectangle PRSU are PR = 15 cm and
RS = 10 cm. The maximum possible distance i.e. diagonal will be $$\sqrt{325}=5\times\sqrt(13)$$ cm. 
The maximum possible distance among C, D and E is $$5\times\sqrt(5)$$.
The maximum possible distance among A, B and F is $$5\times\sqrt(8)$$.  
The minimum distance between points formed by taking one from A, B, F and C,D, E is $$10\times\sqrt(3)=5\times\sqrt(12)$$cm.
wkt, among all 6 points, the closest pair among them has to be less than $$5\times\sqrt(5)$$
Hence, this pair cannot be the closest among the 6 pair of points. So, the statement in option a) should be true.

The length of the diagonal of rectangle QRST is $$\sqrt{125}$$ cm = 11 cm approximately.

BF = $$6\sqrt5$$ cm > 12 cm

So, CE is definitely shorter than BF.

Option d) is the correct answer.

The correct relation between the two is: F(x) = | F1(x) |

So, all the three options a), b) and c) can be ruled out. Option d) is the correct answer.

The value of F(x) for x < 0 is the same as the value of F1(x) for x > 0.

So, F1(x) = F(-x)

Option b) is the correct answer.

The value of F(x) for x > 0 is the same as the value of F1(x) for x < 0.

So, F1(x) = F(-x)

Option b) is the correct answer.

F(0) = 1 ; F1(0) = -1

F(1) = 0 ; F1(-1) = 0

F(2) = -1 ; F1(-2) = 1

=> F1(x) = -F(-x).

$$v_1 > 0.5$$

$$v_m < 1$$

As we cannot empty a blue vessel into a white vessel unless there is enough space to hold all the volume in blue vessel in the white vessel, we have to use m white vessels. This is because we cannot empty more than 1 blue vessel into 1 white vessel.

The minimum volume that can be left in each white vessel is $$1-v_m$$.

=> The minimum volume that can be left in m white vessels is $$m(1-v_m)$$, which is the least upper bound.

To find the limiting value, let us consider that all the blue vessels are of 1 litre capacity.

If all the blue vessels have 1 litre capacity, then the number of white vessels required is smallest integer greater than or equal to (m/2).

But, blue vessels are all not of the same capacity => the above value of n1 is the upper bound.

We will give an example to disprove each of the three options A, B and C and hence, the correct answer will be option D.

Initially, if the least integer in S1 is -20 and the greatest integer in S2 is 50, then after the doing the operations mentioned in the question, the greatest integer in S1 is not greater than 50. Hence option A is false.

G is in S2 as per the given information => Option B is false.

If S1 contains numbers from 1 to 24 and S2 contains numbers from 25 to 50. Then G = 50 and L = 1. If all the numbers of S1 change in sign, G will remain 50 and will be in S2 while L will be -24 and will be in S1.

Hence, none of the statements is true always.

We know that $$a_{24}$$ is less than $$a_{25}$$.

So, even if $$a_{25}$$ replaces $$a_{24}$$, the ascending order still exists in S1.

But, $$a_{25}$$ is less than $$a_{26}$$. Hence, the descending order does not exist in S2 anymore.

For the least element L in $$S1$$ to be greater than the greatest element or equal to G in $$S2$$, the number that is added to L cannot be less than G - L.

f(x,y) = |x+y|

F(f(x,y)) = -f(x,y) = -|x+y|

G(f(x,y)) = -F(f(x,y)) = |x+y|

Option A: F(f(x, y)) . G(f(x, y)) = -F(f(x, y)) . G(f(x, y))  =>LHS = -|x+y|$$^2$$, RHS = |x+y|$$^2$$  Hence false.

Option B: F(f(x, y)) . G(f(x, y)) > -F(f(x, y)) . G(f(x, y)), Since, LHS is smaller than RHS. False

Option C: F(f(x, y)) . G(f(x, y)) $$\neq $$ G(f(x, y)) . F(f(.x, y)), Here LHS=RHS. Hence false.

Option D:

=> G(f(x,y)) + F(f(x,y)) = 0

f(x,y) = f(-x,-y)

=> G(f(x,y)) + F(f(x,y)) + f(x,y) = f(-x.-y)

F(f(x,y)) = -f(x,y)

G(f(x,y)) = -F(f(x,y)) = f(x,y)

G(f(1,0)) = 1

F(f(1,2)) = -3

G(f(1,2)) = 3

f(F(f(1,2)),G(f(1,2))) = 0

f(G(f(1, 0)), f(F(f(1, 2)), G(f(1, 2)))) = 1 + 0 = 1

F(f(x,-x)) = 0 and G(f(x,-x)) = 0

F(f(x,x)) = -2x and G(f(x,x)) = 2x

F(f(x,x)).G(f(x,x)) = -$$4x^2$$

$$\log_216$$ = 4

=> $$\frac{-F(f(x,x)).G(f(x,x))}{\log_216}$$ = $$x^2$$

Before, the third instruction, the point on which the robot is present is (6,2).

Before, the second instruction, the point on which the robot is present is (4,2).

Hence, the values of x and y are 4 and 2 respectively.

WALKX(-x) and WALKY(y) are the commands to be used for the robot to reach origin in any order.

Hence, the answer is 2.

Y takes the direct route AC and travels at 45 km per hour on segment AD. Y's speed on segment DC is 55 km per hour.

AD=DC =a(D is the midpoint on the road connecting A and C.)

The time taken by Y to reach D= a/45

Further, the time taken by Y to reach C= a/55

Y has travelled equal distances are constant speed.

=> Average speed = $$\frac{2a}{\frac{a}{45}+\frac{a}{55}}$$=$$\frac{2*45*55}{100}$$ = 49.5 kmph

$$BC^2$$ + 10000 = $$AC^2$$.

$$\frac{BC+100}{61.875}$$ = $$\frac{AC}{49.5}$$ => $$\frac{BC+100}{AC}$$ = 1.25 = > BC = 1.25AC - 100

On solving these equations, we get AC as 105 and BC a 31.

=> Y traveled 105 km.

$$BC^2$$ + 10000 = $$AC^2$$.

$$\frac{BC+100}{61.875}$$ = $$\frac{AC}{49.5}$$ => $$\frac{BC+100}{AC}$$ = 1.25 = > BC = 1.25AC - 100

On solving these equations, we get AC as 105 and BC a 31.

Let the point B be (0,0) => A = (0, -100) and C = (31,0)

D = Mid point of AC = (15.5, -50)

BD = $$\sqrt{15.5^2+50^2}$$ = 52.5 (approximately).

Total distance = 35*2 + 45*2 = 160 km

Distance traveled by Aditi at each constant speed value = $$\frac{160}{3}$$

Total petrol consumed by Aditi = $$\frac{160/3}{16}$$ + $$\frac{160/3}{24}$$ + $$\frac{160/3}{16}$$ = $$\frac{10}{3}$$ + $$\frac{20}{9}$$ + $$\frac{10}{3}$$ = 6.67 + 2.22 = 8.9 litres

To minimize the petrol consumption, he must travel at 40kmph constantly through out the 160 km.

Total petrol consumed = $$\frac{160}{24}$$ = 6.67 litres.

After the first game, Ghosh Babu picked 8 of clubs => He gets Rs 8. Then the dealer picked Queen of clubs => Ghosh Babu pays Rs 16 => Ghosh Babu is at a loss of Rs 8 after 1st game.

After the second game, Ghosh Babu picked 10 of hearts => He gets Rs 10. Then the dealer picked 2 of spades => Ghosh Babu gets another Rs 10 => Ghosh Babu is now at a profit of Rs 12.

After the third game, Ghosh Babu picked six of diamonds => He gets Rs 6. Then the dealer picked ace of hearts => Ghosh Babu pays Rs 6 to dealer => Ghosh Babu is still at a profit of Rs 12.

In the fourth game, Ghosh Babu picks 8 of spades => He gets Rs 8. The the dealer picks jack of spades => Ghosh Babu pays Rs 16 to dealer => Ghosh Babu is at a profit of Rs 4.

Hence, the maximum profit earned is Rs 12.

After the first game, Ghosh Babu picked 8 of clubs => He gets Rs 8. Then the dealer picked Queen of clubs => Ghosh Babu pays Rs 16 => Ghosh Babu is at a loss of Rs 8 after 1st game.

After the second game, Ghosh Babu picked 10 of hearts => He gets Rs 10. Then the dealer picked 2 of spades => Ghosh Babu gets another Rs 10 => Ghosh Babu is now at a profit of Rs 12.

After the third game, Ghosh Babu picked six of diamonds => He gets Rs 6. Then the dealer picked ace of hearts => Ghosh Babu pays Rs 6 to dealer => Ghosh Babu is still at a profit of Rs 12.

In the fourth game, Ghosh Babu picks 8 of spades => He gets Rs 8. The the dealer picks jack of spades => Ghosh Babu pays Rs 16 to dealer => Ghosh Babu is at a profit of Rs 4.

Hence, the maximum profit earned is Rs 12.

The maximum loss that Ghosh Babu had was Rs 8.

He must have had at least Rs 8 so that he did not have to borrow any amount from others.

After the first game, Ghosh Babu picked 8 of clubs => He gets Rs 8. Then the dealer picked Queen of clubs => Ghosh Babu pays Rs 16 => Ghosh Babu is at a loss of Rs 8 after 1st game.

After the second game, Ghosh Babu picked 10 of hearts => He gets Rs 10. Then the dealer picked 2 of spades => Ghosh Babu gets another Rs 10 => Ghosh Babu is now at a profit of Rs 12.

After the third game, Ghosh Babu picked six of diamonds => He gets Rs 6. Then the dealer picked ace of hearts => Ghosh Babu pays Rs 6 to dealer => Ghosh Babu is still at a profit of Rs 12.

In the fourth game, Ghosh Babu picks 8 of spades => He gets Rs 8. The the dealer picks jack of spades => Ghosh Babu pays Rs 16 to dealer => Ghosh Babu is at a profit of Rs 4.

As Ghosh Babu earned a profit of Rs 4 and now he has Rs 100, he initially would have had 100 - 4 = Rs 96.

A raises the main topic of the paragraph that is move towards political mode of organisational theory. D follows the suit where political mode is explained. B will follow D as it talks about power. C is the concluding statement of the paragraph. So the correct sequence is ADBC.

Option B starts with the information of checks and balances in nature. Option D follows B which talks about human interventions in nature. option C and Option A follows the suit where it is mentioned that institutions need to have a proper system of checks and balances.

In the sentences A, B and D, pronouns are used whereas the noun "Bennis" is used in only sentence C. Hence, C is the first sentence.

B follows D because of the cause and effect relationship. The cause is mentioned in D and B is the result.

But C and D are not related directly. Hence, A follows C and D follows A.

=> CADB is the answer.

A, B and C cannot be the first sentence of the paragraph because of the pronouns and the situational phrases(of the situations that are not described yet) used=> D is the opening sentence of the paragraph.

As a result of the author asking for a shampoo mixture, the pharmcist wrapped a six-ounce bottle. The idea is continued in sentence C => C follows D.

As a result of the author asking for something for acute gastric cramp, the pharmacist shuffled away into the back regions. => B follows C.

Hence, DCBA is the answer.

A, B and D do not fit to be the first sentence of the paragraph because of the usage of the words "since then", "in other words" and "such tests" respectively. They need at least one sentence to appear before them.

Between C and E, E fits to be the best starting sentence.

Next comes D as the author talks about what was the first development that was done in "intelligence tests".

D is followed by A as the idea created in D is continued in A.

C and B are a pair and B follows C because the content in B is a rephrase of the content in C.

Hence, EDACB is the answer.

The stated conclusion is that volume of air travel will increase if the airfare drops. The underlying assumption is that the travellers decide whether or not to fly based on the cost of the ticket. Option C bolsters the assumption and hence supports the conclusion.

Option D weakens the argument as if travellers are not paying for their ticket, they will not be price-sensitive. The extension of the scheme to other routes or airline profitability does not necessarily reflect on how the scheme is doing over the given route.

The paragraph states that a memorized passage could be duplicated multiple times. Thus, we can infer that a Vedic priests memory was as reliable as an audio tape. Thus, option B can be inferred from the paragraph.

The main conclusion of the paragraph is that the working population should save for its future given that the Indian state is not in a position to provide social security for its citizens. The underlying assumption is that the Indian state would not be in a position to provide social security even in the future. If option C is true, then this assumption is attacked and the conclusion is weakened.

The stated conclusion is that richness in biodiversity goes hand in hand with educational backwardness. The underlying assumption is that in areas with low biodiversity, the educational performance is better. As option D bolsters this assumption, it strengthens the conclusion.

The stated conclusion is that the tax base will increase if the taxes levied on cigarettes is reduced. The underlying assumption is that tobacco users who are not smoking cigarettes will shift to cigarettes if the taxes on them decrease. Option B supports this assumption and hence gives credence to the conclusion.

Options A, B and D offer explanations on how human population can survive. Hence, they undermine the stated conclusion.

The stated conclusion is that human population cannot last long on this planet. The underlying assumption is that what has been observed till now will continue in the future. Hence, option C bolsters this assumption and add credence to the main conclusion.

The main conclusion of the paragraph is that the company can continue to improve its coffee yield as it has done in the past. The underlying assumption is that the techniques used by them to improve the yield in the past would continue working in the future. Option A refutes this assumption and hence does most to weaken the argument.

From the options given, we can eliminate options C and D as they are unsupported by the facts given in the paragraph. Option A is not an inference that can be built from the information given in the paragraph.

The paragraph states that animals, from elephants and beavers down to the bee, lose their spirit and intelligence when they are separated from the communities and their environments are invaded by humans. Hence, option B directly follows from this premise.

In this paragraph, the author states that the unreasonable man tends to do things with other people which they don't want to do. For eg, the person who has lost the money won't pay the bill or the person who has just come from a long ride won't go for a ride again

Option D correctly states the tendency of the unreasonable man as the person who has heard a particular story won't hear it again.

In this paragraph, the author states that the unreasonable man tends to do things with other people which they don't want to do or is irrational. For eg, the person who has lost the money won't pay the bill or the person who has just come from a long ride won't go for a ride again.

Option A correctly highlights this as it would be irrational if a person brings a higher bidder to the salesman who has just closed the deal.

In this sentence, "he" is the object while "us" is the subject. While using the third-person pronoun as a subject, we need to use "we" instead of "us". In this case, the second half of the sentence should have simple past tense. Hence, option D.

To pass on means to die or expire. Hence, it would be incorrect in the given context. Hence, we need to use the verb "passed". Thus, we can eliminate option B and D.

"In her opinion" and "she thought" mean the same thing. Hence, we can eliminate option C as it contains repetition.

Thus, option A is the grammatically correct option.

The two attributes of Mr. Pillai should have parallel structure. Thus, we need to use simple present tense for the underlined part with no additional conjunctions like 'since' and 'in addition'.

Hence, option C is the correct answer.

The context indicates that the action has taken place over a period of time from some time in the past to the present. Thus, we need to use present perfect tense.

The appropriate form of the verb would be "has taken". Thus, option B.

For parallelism to exist, the correct word is "severing" and not "severed". Hence, options B and C can be eliminated.

A comma is not needed after lessons. Therefore, option D can be eliminated.

=> Option A is the answer.

This sentence is correctly phrased and there is no error in either punctuation or grammar.

The word proclaim should be followed by "that" and not "to". Hence, we can eliminate options A and C. The correct phrase to use in this context is "nothing less than ...". Hence, option D.

The context indicates that the action would be completed at some point in the future i.e. the patient will have passed away at some point in the future. Hence, the correct tense to use in this case is the future perfect tense i.e. 'would be delayed'. The sentence gives two reasons for administering quick death and hence these two reasons should be separated by the conjunction 'and'. From the context, we can infer that there will be a delay of a few days if quick death is not administered by the doctor. Hence, a negative conjunction like otherwise is needed for the sentence to make sense. Hence, option C.

(b) is the correct answer choice: This answer emerges from para 2, second sentence: “... WTO was a product of a series of trade-offs between principal actors and groups.” The important players were essentially the United States; Europeans; countries like Canada and other middle and smaller trading partners; and the developing countries, which continued negotiations as part of the Uruguay Round till the 1990s. The Tokyo Round of the 1970s was an attempt at a ‘constitutional reform’ of the GATT, while what the important players eventually settled for in the WTO was the evolution of a rules-based system through multiple negotiations which obviously required time.

The passage states many countries individual reasons for accepting WTO. However, it highlights that "Finally, and perhaps most important, many countries at the Uruguay Round came to put a higher priority on the export gains than on the import losses that the negotiation would produce, and they came to associate the WTO and a rules-based system with those gains. This reasoning - replicated in many countries - was contained in U.S. Ambassador Kantor's defence of the WTO, and it amounted to a recognition that international trade and its benefits cannot be enjoyed unless trading nations accept the discipline of a negotiated rules-based environment." Hence, option B correctly captures why many countries accepted WTO.

Refer to the lines "Legal development can be defined as promotion of the technical legal values of consistency, clarity (or, certainty) and effectiveness; these are values that those responsible for administering any legal system will seek to maximise. As it played out in the WTO, consistency meant integrating under one roof the whole lot of separate agreements signed under GATT auspices; clarity meant removing ambiguities about the powers of contracting parties to make certain decisions or to undertake waivers; and effectiveness meant eliminating exceptions arising out of grandfather-rights and resolving defects in dispute settlement procedures and institutional provisions." Hence, we can eliminate options C and D as the passage states that these are contrary to technical legal values. From the passage, we can infer that technical legal values were promoted by integrating under one roof the different agreements signed under GATT. Hence, option A.

The passage states that:

One means the Court used to expand integration was the 'teleological method of interpretation', whereby the actions of member states were evaluated against 'the accomplishment of the most elementary community goals set forth in the Preamble to the [Rome] treaty'.

Hence, option D is the correct answer.

Let's look at the passage:

"Finally, and perhaps most important, many countries at the Uruguay Round came to put a higher priority on the export gains than on the import losses that the negotiation would produce, and they came to associate the WTO and a rules-based system with those gains. This reasoning - replicated in many countries - was contained in U.S. Ambassador Kantor's defence of the WTO, and it amounted to a recognition that international trade and its benefits cannot be enjoyed unless trading nations."

Here, "it" refers to the subject of the sentence which is "This reasoning" as contained in the defence of Ambassador Kantor of the WTO. Hence, option A.

The passage states that:

Over the past two decades the European Court of Justice (ECJ) has consistently rendered decisions that have expanded incrementally the EU's internal market, in which the doctrine of 'mutual recognition' handed down in the case Cassis de Dijon in 1979 was a key turning point.

Hence, the doctrine of "mutual recognition" was a key turning point. Hence, option D.

All of the options have been stated in the passage by the author as reasons given by critics of modern abstract art. Hence, option D.

The passage states that

"People feel more comfortable with something they can relate to and understand immediately without too much thought. "

Thus, option C correctly states why people are more comfortable with representational art.

The passage states that:

Guernica was meant as a protest against the bombing of that city by the Germans. To express the terror and suffering of the victims more vividly, he distorted the figures and presented them in a black and white journalistic manner. If he had used representational images and colour, much of the emotional content would have been lost and the piece would not have caused the demand for justice that it did.

Thus, the reason Guernica caused the demand for justice was because it vividly conveyed the terror and suffering of the victims. As the emotional content of the suffering was conveyed through the art, it produced the desired impact. Hence, option B correctly captures this point and is the answer.

The passage states that:

For example, through his work, Mondrian was trying to present a system of simplicity, logic, and rational order. As a result, his pieces did end up looking like a scrabble board.

Hence, option C is the right answer.

The passage states that:

Finally, abstract artists and representational artists maintain different ideas about 'reality'. To the representational artist, reality is what he sees with his eyes. This is the reality he reproduces on canvas. To the abstract artist, reality is what he feels about what his eyes see. This is the reality he interprets on canvas.

Hence, the two types of artists have completely different ideas about reality and how they represent it on canvas also differs. Thus, option A.

The passage states that "Each of our perceptions is accompanied by the consciousness that human reality is a 'revealer', that is, it is through human reality that 'there is' being, or, to put it differently, that man is the means by which things are manifested. It is our presence in the world which multiplies relations."
Hence, option C is stated in the paragraph.

We can eliminate options C and D as they are contrary to what is stated in the passage. The passage states that all facets of nature, and not artistic creations, are revealed by human consciousness. The passage states that:

"The latter seeks essentiality in the creation and obtains it, but then it is the object which becomes the inessential."

Hence, we can infer option B.

Perception and Creation are explained in terms of essentiality and non-essentiality in the third and fourth paras of the passage.
Hence the answer is Option D.

The passage states that :

The dialectic is nowhere more apparent than in the art of writing, for the literary object is a peculiar top which exists only in movement. To make it come into view a concrete act called reading is necessary, and it lasts only as long as this act can last.

Hence, option A directly follows from the passage.

The passage states that:

One of the chief motives of artistic creation is certainly the need of feeling that we are essential in relationship to the world.

Hence, an artist makes us feel essential vis-a-vis nature.

The passage states that:

"In the name of modernisation in the West, of socialism in the Eastern bloc, and of development in the Third World, it was expected to guarantee the happiness of individuals as citizens and of peoples as societies."

Hence, only option A is correct.

Option A can be inferred from the following line:"There are two ways in which the current upsurge in demands for the recognition of identities can be looked at." The author goes on to mention an upside and a downside.

Option B can be concluded from the given lines:"On the downside, however, militant action for recognition tends to make such groups more deeply entrenched in their attitude and to make their cultural compartments even more watertight."

Option C can be concluded from the following lines:"What these groups are doing - proclaiming that they are different, rediscovering the roots of their culture or strengthening group solidarity - may accordingly be seen as legitimate attempts to escape from their state of subjugation and enjoy a certain measure of dignity."

Hence, all three options directly follow from the passage.

The passage states that:

"First, we must bear the arbitrary nature of identity categories in mind, not with a view to eliminating all forms of identification—which would be unrealistic since identity is a cognitive necessity ."

Hence, we can eliminate option C.

It also states that:

"Identity is thus a necessity in a constantly changing world, but it can also be a potent source of' violence and disruption. "

Thus option B can be eliminated.

The passage states that:

"Paradoxically, precisely because identity represents a simplifying fiction, creating uniform groups out of disparate people, that identity performs a cognitive function."

Hence, all options except D are eliminated. Hence, none of the above.

The passage states that:

"However, the state today appears to have broken down in many parts of the world. It has failed to guarantee either security or social justice, and has been unable to prevent either international wars or civil wars. Disturbed by the claims of communities within it, the nation-state tries to repress their demands and to proclaim itself as the only guarantor of security of all. In the name of national unity, territorial integrity, equality of all its citizens and non-partisan secularism, the state can use its powerful resources to reject the demands of the communities; it may even go so far as genocide to ensure that order prevails."

Hence, we can eliminate options A, C and D as they contradict what is given above. The author states that the state will do anything, including genocide, to preserve order. Hence, we can infer option B.

The passage states that:

However, the state today appears to have broken down in many parts of the world. It has failed to guarantee either security or social justice, and has been unable to prevent either international wars or civil wars. Disturbed by the claims of communities within it, the nation-state tries to repress their demands and to proclaim itself as the only guarantor of security of all. In the name of national unity, territorial integrity, equality of all its citizens and non-partisan secularism, the state can use its powerful resources to reject the demands of the communities; it may even go so far as genocide to ensure that order prevails.

Hence, options A, B and D are directly given in the passage. However, option C is not mentioned in the passage and is inconsistent with what is stated in the passage.

In the passage, the author talks about how America was not able to adapt its way of fighting according to the terrain and culture it found itself in. America was used to fighting open field battles and struggled to fight in the jungles against guerilla war tactics. Hence, option D best captures this point.

Option B is given as an example of the Western way of war while options A, C and D are characteristics of the Asian way of war. Hence, option B.

Option A is contrary to what is stated in the passage.

In Sun-tzu and other Chinese writings, the highest achievement of arms is to defeat an adversary without fighting. He wrote: "To win one hundred victories in one hundred battles is not the acme of skill. To subdue the enemy without fighting is the supreme excellence."

Sun-tzu believed that war should not be the first resort. Hence, option A is definitely not one of his ideas.

The passage states that:

The West's great strategic writer, Clausewitz, linked war to politics, as did Sun-tzu. Both were opponents of militarism, of turning war over to the generals. But there all similarity ends.

Hence, we can eliminate options A and B.

The contrast between the two strategic writers view has been described by the following lines. Clausewitz's view was:

In this view, war proceeds along a fixed course and occupies a finite extent of time, like a play in three acts with a beginning, a middle, and an end. The end, the final scene, decides the issue for good.

Hence, the two writers had different conceptions of how the structure, time and sequence of war.

The passage states that:

To the American strategic mind, the Viet Cong guerrilla did not fight fairly. He should have come out into the open and fought like a man, instead of hiding in the jungle and sneaking around like a cat in the night.

Hence, option A.

Refer to the following lines:"Pearl Harbor, the Chinese intervention in Korea, and the Tet offensive in Vietnam all came out of a tradition of surprise and stealth. U.S. technical intelligence - the location of enemy units and their movements was greatly improved after each surprise, but with no noticeable improvement in the American ability to foresee or prepare what would happen next". 

Here the author suggests that even though the techanical intelligence of USA increased, they couldn't counter stealth based attack.

The first sentence is B as it continues the tone of the opening sentence. OptionA follows next where one of the situation is mentioned where the advertisements can fall flat. D follows B where the author mentions the consequences of amusement to reap the sales benefit. C follows D as it mentions the instances where the ads amuses the audience. Sentence 6 is the conclusion presented.

The correct order is BADC.

(1) talks about a “mud hump” which is further talked about in D which describes “the hump is alive ...”. Hence, D follows 1. Similarly, BA is also a pair as B talks about ‘the proportion of soldiers to workers’ i.e. some kind of ratio and A talks about unsettling this balance. This should be followed by C which talks about ‘restoring of fortunes’ by the ‘queen termite laying eggs on a as required basis’ which in turn should be followed by 6 which comments on this ‘mysterious ability’ of the queen termite. Thus, the correct sequence is- DBAC.

From the first sentence, we know that high-powered outboard motors are not major threats anymore because of the usage of the word "were".

The author starts explaining this statement by giving information about the past in sentence D.

A follows D bacause the athor explains in A how the motors are used.

Now, the author talks about the present in C, whose idea is continued in B.

Hence, DACB is the answer.

B is the first sentence in the sequence. "Misconstructions" is the key word here. In (1), there is a mention of "misconstructions" which is referred to again in B. Since, only option A mentions B first in the list, option A is the right answer.

A says that all software companies employ knowledge workers.

C says that Tara tech is a software company.

So, we can say that Tara Tech employs knowledge workers.

Hence, ACB is the answer.

Option A: Traffic congestion and increase in carbon monoxide are hazardous to health. But, we cannot infer that one is a result of other. Hence, option A is wrong.

Option B: Option B is wrong because the traffic congestion that does not cause increased carbon monoxide might cause some thing else that is hazardous to health.

Option C: C and D are not related. So, we cannot infer E.

Option D: Increase in Carbon monoxide is hazardous to health and traffic congestion increases Carbon monoxide. So, we can say that traffic congestion is hazardous to health.

Option A: All sweets are tasty and no apple is tasty

=> Apples and sweets are disjoint sets.

=> A can be inferred.

Hence, CEA is the correct order.

Option A: We do not know if town Meghana is in India. So, we cannot infer the statement E. Hence, option A is wrong.

Option B: All polluted towns must be destroyed and some towns in India are polluted => Some towns in India must be destroyed. Option B is correct.

Option A: No patriot is a criminal and Bundledas is a Patriot => Bundledas is not a Criminal.

Option A is correct as we can infer B from A and C.

Option A: DCA

A cannot be inferred from D and C.

Option B: ADC

Ant eaters like ants and Balaram likes ants. From this, we cannot say that Balaram is an anteater.

But, from A and C, we can infer D.

Hence, ACD is the answer => Option D.

Option a) is incorrect. Ram need not necessarily be a popular actor.

Option b) is also incorrect. The first two statements talk about actors whereas the third statement talks about people. So, it cannot be deduced.

Option c) is also incorrect. The first two statements talk about Ram whereas the third statement talks about all actors. So, it cannot be deduced.

Option d) is the correct answer. The third statement can be deduced from the first two statements.

The statements can be understood by the Venn Diagram below.

Modern industry is technology driven ( Modern industry is a subset of technology driven)

BTI is a modern industry ( BTI is a subset of modern industry)

Hence, BTI is technology driven (BTI is a subset of technology driven.)

Since this holds, the statements are implied.

The relationship between Golmal Islanders, Blue colored people and some smart people is as shown in the diagram below.

Since some smart people and golmal islanders are non-intersecting sets,option B holds true.

The sentence Ram and Sita are in great demand is a conclusion that can be drawn from Ram and Sita are MBAs and MBAs are in great demand.

The sentence can be written as follows:

Orangutan is angry => He frowns upon the world.

Orangutan doesn't frown upon the world => He is not angry.

So, CB and DA follow.

Ravana is not a hero implies he is a demon

Ravana is not a demon implies he is a hero.

And both these statements are implied from the original sentence.

So the answer is both DB and CA.

Of the given four options, only A is correct.

Note: If Rajiv dreamt about spiders, it doesn't necessarily mean that he used the internet. But if he didn't dream about spiders, he didn't use the internet.

If A => B, then ~B => ~A

Using this logic, we can say that:

I talked to the professors => I did not need to take a pill for headache

I needed to take a pill for headache => I did not talk to the professors.

So, AB and CD are correct.

Consider A: Some sphinxes laugh. No cowboy laughs => Some sphinxes are definitely not cowboys.

So, it will be either option a) or c).

Consider D: All crazy people are whistlers. Some crazy people are pianists. So, the crazy people who are pianists are also whistlers => Some whistlers are pianists.

So, option c) is the correct answer.

Options C and D are the correct ones as shown in the Venn Diagrams below.

Only B is the correct option. That can be explained from the Venn Diagram below:

In A, there need not be an intersection between earthquakes and landslides.

In B, the curios that are glass things are transparent. So, some curios are transparent. So, B is correct.

In C, since all clay objects are brittle and XY are clay objects, some XY are brittle.

Option c) is the correct answer.

The relationship between men, cops and brave people is shown in the Venn Diagram below. Hence, B is the correct option.

A)

All IIMs are in India. For IIMs to be BIMs, at least some BIMs must be in India. But they are not according to the second part of the sentence. Hence, No IIMs are BIMS => Third part can be inferred => A is true

B)

All IIMs are in India. For BIMs to be IIMs, at least some BIMs must be in India. But they are not according to the second part of the sentence. Hence, No BIMs are IIMs.

C and D cannot be inferred as there is a possibility that no IIMs are BIMs.

Mammals are not oviparous. Some creatures are oviparous. Those creatures are not mammals. Hence, C is the correct answer.

Only B is the correct option and that can be explained from the Venn Diagram below:

A) The few farmers who are rocket scientists need not be the rocket scientists that catch snakes. Hence, A is wrong.

B) Poonam need not be one of those Kangaroos that are made of teak. Hence, B is wrong.

C) No bull eats grass and all matadors eat grass. We can infer that bulls and matadors are distinct sets. Hence, C is correct.

D) Bears that are Cadillacs will also be polar bears. Hence, some polar bears are Cadillacs is true. So, D is correct.

Percentage growth in sales in the year 1995-96 is 250/100 - 1 = 150%
Percentage growth in sales in the year 1996-97 is 300/250 - 1 = 20%
Percentage growth in sales in the year 1997-98 is 290/300 - 1 = -3.33%
Percentage growth in sales in the year 1998-99 is 680/290 - 1 = 134%
Hence, the percentage growth in sales is maximum in the year 1995-96

Percentage growth in net profit in the year 1995-96 is 4.5/2.5 - 1 = 80%
Percentage growth in net profit in the year 1996-97 is 6/4.5 - 1 = 33.33%
Percentage growth in net profit in the year 1997-98 is 8.5/6 - 1 = 41.67%
Percentage growth in net profit in the year 1998-99 is 12/8.5 - 1 = 41.17%

Hence, the percentage growth in net profit is maximum in the year 1995-96

Profitability in the year 1994-95 is 2.5/100 = 2.5%
Profitability in the year 1995-96 is 4.5/250 = 1.8%
Profitability in the year 1996-97 is 6/300 = 2%
Profitability in the year 1997-98 is 8.5/290 = 2.93%
Profitability in the year 1998-99 is 12/680 = 1.76%

Hence, the profitability is maximum in the year 1997-98

Profitability in the year 1994-95 is 2.5/100 = 2.5%
Profitability in the year 1995-96 is 4.5/250 = 1.8%
Profitability in the year 1996-97 is 6/300 = 2%
Profitability in the year 1997-98 is 8.5/290 = 2.93%
Profitability in the year 1998-99 is 12/680 = 1.76%

Profitability increased/decreased in some years, hence the first three options are wrong.

So, the correct answer is option (d)

The four major trading partners with India in 1997-98 are A, G, H and I.
From the numbers, we can ignore the others for this questions.

Total trade with A in the year 1997-98 is 9%*40779 + 19%*33979 = 10,126
Total trade with G in the year 1997-98 is 19%*40779 + 10%*33979 = 11,146
Total trade with H in the year 1997-98 is 23%*40779 + 10%*33979 = 12,777
Total trade with I in the year 1997-98 is 14%*40779 + 20%*33979 = 12,505
Hence, the correct option is block H which is OPEC

In both imports and exports, India did the least amount of trade in 1997-98 with K (both equal to 1%).

Hence, India had the lowest total trade with K in the year 1997-98.

The amount of Indian exports equals 1%*33979 = 340 millions

In order to find the trading partner with the highest trade deficit, we have to look for countries from whom India imported a lot but exported little.

The two countries which are important here are G and H. However, the exports to both are the same. But the imports from H are more than the imports from G.

So, the trading partner with whom India has the highest trade deficit is H.

The amount of trade deficit equals 23%*40779 - 10%*33979 = 5981 mio ~ 6 bn

In order to find the country which  has the least trade deficit with India, we have to look for countries whom India exported a lot and imported less.

The only two countries which fit the bill are countries A and I.

Trade deficit of A with India in 1997-98 is  9%*40779 - 19%*33979    = -2.78 billion
Trade deficit of I with India in 1997-98 is  14%*40779 - 20%*33979   = -1.08 billion

Hence, the country with the least trade deficit is country A or USA

Since the increase in imports and exports is at average, the exports and imports in the next 4months will be half of their respective first eight months.

Exports in the first 8 months of 1998-1999 is $21436 so, in the next 4 months it will be 21436/2 = 10718

Total exports= 21346+10718=32154.

Although total imports have been increased the percentage share for all is decreased expect A and G. This means surely one of A and G has the highest increase. 

Percentage growth in exports of country A is (23%*32154 - 19%*33979)/19%*33979 = 14.5%
Percentage growth in exports of country G is (12%*32154 - 10%*33979)/10%*33979 = 13.5 %
Hence, the region to which Indian exports witnessed the highest percentage growth is region A i.e USA

Since the increase in imports and exports is at average, the exports and imports in the next 4months will be half of their respective first eight months.

Exports in first 8 months of 1998-1999 is $21436 so, in next 4 months it will be 21436/2 = 10718

Total exports= 21346+10718=32154.

Similarly, total imports= 28126+ 28126/2 = 42189

Trade deficit = 42189-32064= 10035

Trade deficit in 1997-98= 40779-33979=6800.

Increase = (10035-6800)/6800 = 47.5%

Price change of arhar = (2105-1700)/1700 = 23.82%
Price change of pepper = (19250-18500)/18500 = 4.05%
Price change of sugar = (1430 - 1440)/1430 = -0.69%
Price change of gold = (3850 - 4250)/3850 = -9.41%

Hence, the price change is maximum for arhar.

Volatility for arhar is (2300-1500)/1900 = 42%
Volatility for pepper is (19500-17500)/18500 = 10.8%
Volatility for sugar is (1500-1410)/1450 = 6.2%
Volatility for gold is (4300-3800)/4050 = 12%

Hence, the volatility is least for sugar.

The profit percentage equals 25%*(2105/1700-1) + 25%*(19250/18500-1) + 25%*(1430/1440-1) + 25%*(3850/4250-1)
This equals 25%*(23.82% + 4.05% -0.69% - 9.41%) = 25%*17.77 = 4.4%

The closest option to this is option (d)

Volatility for arhar is (2300-1500)/1900 = 42%
Volatility for pepper is (19500-17500)/18500 = 10.8%
Volatility for sugar is (1500-1410)/1450 = 6.2%
Volatility for gold is (4300-3800)/4150 = 12%

Hence, the highest volatility is around 40%

Bangladesh has the highest percentage in drinking water facilities. Let us see which countries it dominates. This is possible if it has greater sanitation facilities also as compared to the other country.

Bangladesh has better sanitation facilities than India, China, Pakistan and Nepal. So those Bangladesh dominates those four countries and they are not on the coverage frontier.

Similarly, Philippines has the highest percentage of sanitation facilities. Let us see which countries it dominates. This is possible if it has greater drinking water coverage also.

Philippines has greater drinking water coverage than all countries except Bangladesh. Hence, it dominates all the countries except Bangladesh. So, no other country is on the coverage frontier.

Hence, the only countries on the coverage frontier are Bangladesh and Philippines.

India has lesser sanitation facilities than Pakistan. Hence it is false that India > Pakistan. So statement A is false.

India has greater sanitation facilities as well as drinking water coverage than China. Similar is the case between India and Nepal.
Hence, India > China and India > Nepal. So, statement B is true.

Sri Lanka has lesser drinking water coverage than China. Hence, statement C is false.

China has greater sanitation facilities as well as drinking water coverage than Nepal. Hence, China > Nepal and statement D is true.

So, the only two true statements are B and D.

Let total rural population in India be R and urban population in India be U.

Total population in India = T = U + R

Based on the sanitation facilities table, 

$$\frac{70}{100}$$ U + $$\frac{14}{100}$$ R = $$\frac{29}{100}$$(U + R)

Solving, we get

$$\frac{U}{R}$$ = $$\frac{15}{41}$$

U : R = 15 : 41

Rural population % = $$\frac{41}{15+41}\times\ 100$$ = $$\frac{41}{56}\times\ 100$$ = 73.2%

Let total rural population in China be A and urban population in China be B.

Total population in India = T = A + B

Based on the sanitation facilities table,

$$\frac{74}{100}$$ B + $$\frac{7}{100}$$ A = $$\frac{24}{100}$$(A + B)

Solving, we get

$$\frac{A}{B}$$ = $$\frac{50}{17}$$

A : B = 50 : 17

Rural population % = $$\frac{50}{50+17}\times\ 100$$ = $$\frac{50}{67}\times\ 100$$ = 74.6%

Let total rural population in Indonesia be C and urban population in Indonesia be D.

Total population in India = T = C + D

Based on the sanitation facilities table,

$$\frac{40}{100}$$ C + $$\frac{73}{100}$$ D = $$\frac{51}{100}$$(C + D)

Solving, we get

$$\frac{C}{D}$$ = $$\frac{22}{11}$$

C : D = 2 : 1

Rural population % = $$\frac{2}{2+1}\times\ 100$$ = $$\frac{2}{3}\times\ 100$$ = 66.7%

Let total rural population in Philippines be R and urban population in Philippines be U.

Total population in India = T = R + U

Based on the sanitation facilities table,

$$\frac{88}{100}$$ U + $$\frac{66}{100}$$ R = $$\frac{77}{100}$$(U + R)

Solving, we get

$$\frac{U}{R}$$ = $$\frac{11}{11}$$

U : R = 1 : 1

Rural population % = $$\frac{1}{1 + 1}\times\ 100$$ = $$\frac{1}{2}\times\ 100$$ = 50%

Ascending order: Philippines, Indonesia, China

Therefore, answer is option A.

For a country to be on the coverage frontier, it should not be dominated by any other country. That is no other country should have both (sanitation facilities and drinking water coverage) better than it.
The first three options, though true, are not the reason for India not being on the coverage frontier. That is because they don't mention the other parameter at all.

For example, option A doesn't mention sanitation facilites while options B and C don't mention drinking water coverage. Hence, none of A,B and C are the reason India is not on the coverage frontier.

Option D is factually wrong as Indonesia has lesser drinking water coverage than India and doesn't dominate it.

Hence, none of the options given are correct.

The most disparity in rural sector is in India = 79-14 = 65

The disparity in all other countries is less than 65.

The least disparity => The least difference between the coverage in urban drinking water facilities and the coverage in urban sanitation facilities.

Phillipines has a disparity of 92-88 = 4, which is the least.

Hence, option C is the answer.

Using statement A, we cannot infer the number of students in the class.

Using statement B, we can say that the sum of weights of heaviest and the lighest persons is equal to twice the average weight of the class. But we cannot infer the number of students in the class.

Using both the statements as well, we do not have any information through which we can find the answer.

Hence, option D is the answer.