XAT 2026 Question Paper

Three concentric circles C1, C2 and C3 with the radius OA, OB and OC are drawn. 

OA, OB and OC are in AP (given). 

OA = 70m, OB = (70 + d)m, OC = (70 + 2d)m , where, d is the common difference. 

OC = 70+2d = 140 (given) 

d = 35m 

OB = 70 + 35 = 105m  

The soldiers are standing on the circumference of these three circles at a distance of 1m. Hence, to find the total number of soldiers, we have the find the length of the circumference of all three circles. 

Total circumference = $$2\pi\ \left(r1+r2+r3\right)$$

= 2 $$\times\ $$ $$\ \frac{\ 22}{7}\times\ \left(70+105+140\right)$$  = 1980

Hence, the total number of soldiers are 1980.

$$\therefore\ $$ The required answer is D.

In the above figure, let the number of students specializing in : 

Only marketing = a, Only finance = b, Only operations = c 

Both marketing and finance but not operations = d, Both marketing and operations but not finance = e, Both finance and operations but not marketing = f

All three subjects = g, None of the subjects = h

Now it is given that only students having an specialization in marketing or finance gets a consulting shortlist. So, we can say that students doing specialization only in operations and students not doing specialization in any of the 3 subjects will not get a shortlist. 

Hence, c + h = 45 (given) $$\longrightarrow\ i$$

Number of students doing specialization in marketing = a + d + e + g = 60 (given) $$\longrightarrow\ ii$$

Number of students doing specialization in finance = b + d + g + f = 50 (given) $$\longrightarrow\ iii$$

Number of students doing specialization in operations = c + e + g + f = 30 (given) $$\longrightarrow\ iv$$

Number of students who received the consulting shortlist = a + b + d + e + f + g =  75  $$\longrightarrow\ v$$

By using equation iv and v, we get, 

a + b + d + 30 - c = 75

a + b + d = 45 + c $$\longrightarrow\ vi$$

Add equation ii and iii, 

a + b + d + (d + g) + e + f + g = 110 $$\longrightarrow\ vii$$

Now, using equation iv, vi and vii, we get, 

45 + c + (d + g) + 30 - c = 110 

d + g = 35 

Hence, the number of students specializing in marketing and finance = 35

$$\therefore\ $$ The required answer is A. 

Let the tree be PC and the archer be RA. 

Given : Height of the tree = 56ft, height of the archer up to the eye level = 6ft, angle of elevation at point A = 45$$^{\circ\ }$$, angle of elevation at point B = 30$$^{\circ\ }$$  

To find : Length of AB

In $$\triangle\ $$PQR, $$\tan\ 45^{\circ\ }=\ \frac{\ PQ}{QR}=\ \frac{\ 50}{QR}$$

QR = 50ft (as $$\tan\ 45^{\circ\ }=\ 1$$)

Now, in $$\triangle\ PQS$$, 

$$\tan\ 30^{\circ\ }=\ \frac{\ PQ}{QS}=\ \frac{\ PQ}{QR+RS}=\ \frac{\ 50}{50+RS}$$

$$\ \frac{\ 1}{\sqrt{3\ }}=\frac{\ 50}{50+RS}$$

RS = $$50\left(\sqrt{3\ }-1\right)$$ ft

Since RS = AB, AB = $$50\left(\sqrt{3\ }-1\right)$$ ft

Hence, the length of AB is $$50\left(\sqrt{3\ }-1\right)$$ feet

$$\therefore\ $$ The required answer is C.

Let the maximum allowed speed from Jamshedpur to Kolkata be s1 kmph and the maximum allowed speed from Kolkata to Jamshedpur be s2 kmph. Since the bus is moving at the maximum allowed speed then we can say that the speed of the bus moving from Jamshedpur to Kolkata (Bus 1) is s1 kmph and the speed of the bus moving from Kolkata to Jamshedpur (Bus 2) is s2 kmph.

Time taken by Bus 1 to travel from Jamshedpur to Kolkata = 4 hrs

Distance travelled by Bus 1 = 4 $$\times\ $$s1

Time taken by Bus 2 to travel from Kolkata to Jamshedpur = 3 hrs

Distance travelled by Bus 1 = 3 $$\times\ $$s2

Since both the bus is travelling on the same road, the distance travelled by both the buses will be same. 

4 $$\times\ $$s1 = 3 $$\times\ $$s2

$$\ \frac{\ s1}{s2}=\ \frac{\ 3}{4}$$

The ratio of speed of Bus 1 to the speed of Bus 2 is 3:4.

Hence, let the speed of Bus 1 be 3x kmph and the speed of Bus 2 be 4x kmph.

Total distance travelled by the buses = $$4\times\ 3x\ =3\times\ 4x=12x$$

Now, both the buses started at the same time and travelled at the maximum allowed speed for 1 hr. 

Distance travelled by Bus 1= JA = $$3x\times\ 1=3x$$

Distance travelled by Bus 2= KB = $$4x\times\ 1=4x$$

Distance left to be travelled= AB = $$12x-\left(3x+4x\right)=5x$$

Now, the speed of Bus 1 is reduced to half due to congestion. 

New speed of Bus 1 = $$\ \frac{\ 3x}{2}$$

After the reduction of speed, let the two buses meet at point C and the time taken by both the buses to reach C is the same. 

Let the distance travelled by Bus 1 from A to C be y km. 

BC = 5x-y km

Hence, $$\ \frac{\ y}{\ \frac{\ 3x}{2}}=\ \frac{\ 5x-y}{4x}$$

y = $$\ \frac{\ 15x}{11}$$

Time required = $$\ \frac{\ \ \frac{\ 15x}{11}}{\ \frac{\ 3x}{2}}=\ \frac{\ 10}{11}$$ hrs

Total time required for both the buses to meet = $$\frac{\ 10}{11}+1=\ \frac{\ 21}{11}$$ hrs

Hence, both the buses will meet after $$\frac{\ 21}{11}$$ hrs from starting. 

$$\therefore\ $$ The required answer is D.

For Chhuttan,

Perimeter of his land = 2 (l + b) = 250m 

l + b = 125m $$\longrightarrow\ i$$ 

$$\ \frac{\ l}{b}=\ \frac{\ 4}{1}$$ (Given) $$\longrightarrow\ ii$$

From i and ii, we get, 

4b + b = 125

b = 25m  

l = 100m 

Area of Chhuttan's land = 100 $$\times\ $$25 = 2500 $$m^2$$

Loan given to Chhuttan by Brijbhushan = 2500 $$\times10$$ = Rs 25000

Interest rate of the loan = 10%

Interest owed by Chhuttan at the end of one year = 10% $$\times\ $$Rs 25000 = Rs 2500

$$\therefore\ $$ The required answer is E.

Let the name of farmers be A,B,C,D,G for simplicity. 

Let the area of G's plot be x $$m^2$$.

Area of A's plot = 3x $$m^2$$

Let area of D's plot be y $$m^2$$. 

The area of A's plot is the average of the area of D's and G's plot. 

3x = $$\ \frac{\ x+y}{2}$$

y = 5x $$m^2$$ 

The width of the plot of A,B and D is the same and the lengths are different. Let the length of the plot of A,B and D be l1,l2 and l3 respectively and the width be y. 

We got the following table. 

From A's plot, $$l1\times\ y=3x$$

$$l1=\ \frac{\ 3x}{y}$$

From D's plot, $$l3\times\ y=5x$$

$$l3=\ \frac{\ 5x}{y}$$

The length of B's plot is the sum of the length of A's plot and D's plot.

l2 = l1 + l3 = $$\frac{\ 8x}{y}$$

Hence, the area of B's plot = $$l2\times\ y=8x$$

The required final table is : 

 Total area of all plots = 2500 + 17x

Total loan given by Brijbhushan = $$Rs\ \left(2500+17x\right)\times\ 10$$

Since, we have to maximize the loan amount, we have to maximize the value of x. 

The largest area of a land = $$10000\ m^2$$ (Given)

Among the farmers, B will have the land with the largest area. 

8x = 10000 $$m^2$$

x = 1250 $$m^2$$

Hence, maximum loan given by Brijbhushan = $$Rs\ \left(\left(1250\times\ 17\right)+2500\right)\times\ 10$$ = Rs 237500

$$\therefore\ $$ The required answer is C. 

Let the name of farmers be A,B,C,D,G for simplicity.

Let the area of G's plot be x $$m^2$$.

Area of A's plot = 3x $$m^2$$

Let area of D's plot be y $$m^2$$.

The area of A's plot is the average of the area of D's and G's plot.

3x = $$\ \frac{\ x+y}{2}$$

y = 5x $$m^2$$

The width of the plot of A,B and D is the same and the lengths are different. Let the length of the plot of A,B and D be l1,l2 and l3 respectively and the width be y.

We got the following table.

From A's plot, $$l1\times\ y=3x$$

$$l1=\ \frac{\ 3x}{y}$$

From D's plot, $$l3\times\ y=5x$$

$$l3=\ \frac{\ 5x}{y}$$

The length of B's plot is the sum of the length of A's plot and D's plot.

l2 = l1 + l3 = $$\frac{\ 8x}{y}$$

Hence, the area of B's plot = $$l2\times\ y=8x$$

The required final table is :

The width of A's plot = 25m 

y = 25m 

For B's plot, $$l2\times\ 25=8x$$

To minimize the value of l2, we have to minimize the value of x.  

Minimum possible area of land among the farmers = 1000 $$m^2$$

Smallest area of land = G's land = x $$m^2$$

x = 1000

Hence, minimum value of l2 = $$\ \frac{\ 8\times\ 1000}{25}=320\ m$$

$$\therefore\ $$ The required answer is B.

A seven-digit number 735x6y4 is divisible by 44. It means that the number is also divisible by 4 and 11. 

Divisibility rule of 4 = Last two digits of the number is divisible by 4. 

Divisibility rule of 11 = Sum of odd digits starting from left - Sum of even digits starting from left

For the given number to be divisible by 4, y4 should be divisible by 4. 

So, the possible values of y = 0,2,4,6,8

For the number to be divisible by 11, (7+5+6+4)-(3+x+y) = 19-(x+y) should be divisible by 11. 

Case 1 : Both x and y are even numbers. 

If y = 0, x = 8 

If y = 2, x = 6

If y = 4, x = 4

If y = 6, x = 2

If y = 8, x = 0

In this case, we got 5 different combinations of values. 

Case 2 : Both x and y are equal. 

If y = 4, x = 4

In this case, we got a unique solution. 

Hence, we only need condition 2 to uniquely determine the values of x and y. 

$$\therefore\ $$ The required answer is C. 

Let us denote Ayub and Rana as A and R respectively for simplicity. 

Let the speed of A and B in still water be Sa and Sr respectively and the speed of river be r. 

r = 3 kmph = 50 $$\ \frac{\ m}{\min}$$ (clockwise)

Sr = 3 kmph = 50 $$\ \frac{\ m}{\min}$$ (clockwise)

Since A is swimming in counter clockwise direction and R is swimming in clockwise direction, let C be the point where they meet for the first time. 

Distance travelled by A = AC = 60m 

Speed of A = (Sa-50) $$\ \frac{\ m}{\min}$$ (as he is travelling in counter clockwise direction which is upstream)

Time taken by A to reach C = $$\ \frac{\ 60}{Sa-50}\min$$

Speed of R = (Sr+50) $$\ \frac{\ m}{\min}$$ (as he is travelling in clockwise direction which is downstream)

= 100 $$\ \frac{\ m}{\min}$$

Since, the time taken by R to reach C is the same as the time taken by A to reach C (as they started swimming at the same time), distance travelled by R = RC = $$\ \frac{\ 100\times\ 60}{Sa-50}m$$

Total distance travelled by both A and R = AC + RC = $$\ \frac{\ 6000}{Sa-50}+60\ m$$

As A and R travelled in opposite directions from exactly diametrical ends, the distance A to R will be half of the circumference of the circle. 

$$\pi\ r$$ = $$\ \frac{\ 6000}{Sa-50}+60\ m$$ $$\longrightarrow\ i$$

Now, let's assume that they meet again at D after R travelled for 180m, 

Time taken for them to meet again = $$\ \frac{\ 180}{100}\min$$

Distance travelled by A = CD (in counter clockwise direction) = $$\ \frac{\ \left(Sa-50\right)\times\ 180}{100}m$$

Distance travelled by R = CD (in clockwise direction) = 180m 

Total distance travelled = $$\ \frac{\ \left(Sa-50\right)\times\ 180}{100}m$$ + 180 m

This distance will be equal to the circumference of the circle. 

Hence, $$2\pi\ r$$ = $$\ \frac{\ \left(Sa-50\right)\times\ 180}{100}m$$ + 180 m $$\longrightarrow\ ii$$

Take the value of $$\pi\ r$$ from equation i and substitute it in equation ii. 

$$\ \frac{\ 12000}{Sa-50}+120=\ \frac{\ 180\left(Sa-50\right)}{100}+180$$

Let the value of Sa-50 be t.

 $$\ \frac{\ 12000}{t}+120=\ \frac{\ 180\left(t\right)}{100}+180$$

$$\ 3t^2+100t-20000=0$$

t = $$\ \frac{\ 200}{3}$$, -100 (Not possible as the speed can't be negative)

Sa-50 = $$\ \frac{\ 200}{3}$$

Sa = $$\ \frac{\ 350}{3}\ \frac{\ m}{\min}$$

Use this value in equation ii to get, $$2\pi\ r$$ = 300m

Speed of A when he is swimming in clockwise direction = $$\ \frac{\ 350}{3}+50$$

= $$\ \frac{\ 500}{3}\ \frac{\ m}{\min}$$

Time taken by A to complete one round of the circular strip = $$\ \frac{300}{\ \frac{\ 500}{3}\ }\min$$

= $$\ \frac{\ 9}{5}\min$$ = 1 min 48 sec

Hence, the time taken by A to complete one round of the circular strip is 1 min 48 sec. 

$$\therefore\ $$ The answer is D.

125 = $$5^3$$

10 = $$2\times\ 5$$

15 = $$3\times\ 5$$

In each step, we are multiplying 125 by either 10 or 15. So, the power of 5 and the power of either 2 or 3 will only increase by one in every step. So at any point of time, the difference between the power of 5 and the power of 2 and 3 combined will remain constant (which is 3).

Option A : Power of 5 = 691

Power of 2 = 235

Power of 3 = 453

Difference of powers = 691 - (235+453) = 3 

Option B : Power of 5 = 1080

Power of 2 = 253

Power of 3 = 824

Difference of powers = 1080 - (235+824) = 3

Option C : Power of 5 = 1604

Power of 2 = 689

Power of 3 = 912

Difference of powers = 1604 - (689+912) = 3

Option D : Power of 5 = 1034

Power of 2 = 476

Power of 3 = 455

Difference of powers = 1034 - (476+455) = 103

Option E : Power of 5 = 1145

Power of 2 = 689

Power of 3 = 453

Difference of powers = 1145 - (689+453) = 3

Only in option D the difference of power is different than 3. 

$$\therefore\ $$ The answer is D. 

Let us assume that the total number of candidates who appeared for the admission test$$=100k$$

So, as per the data, the number of diligent candidates$$=10k$$

The number of lazy candidates$$=30k$$

and, the number of lazy candidates$$=60k$$

Now, let us assume that the probability of a lazy candidate to clear the test $$=p$$

$$\therefore$$ The probability of a lazy candidate to clear the test $$=10p$$

Let us also assume that the probability of a confused candidate to pass the exam $$=q$$

Now, we know that 

Probability of a deligent candidate passing the test,$$10p=\dfrac{\text{No of deligent candidates who passed}}{\text{total deligent candidates who appeared}}$$

or, $$p=\dfrac{\text{No of deligent candidates who passed}}{10k}$$

or, number of the diligent candidates who passed the test $$=10k*10p=100kp$$

Similarly, the number of lazy candidates who passed the test $$=30k*p=30kp$$

and, the number of confused candidates who passed the test $$=60k*q=60kq$$

Now, we are told that 40% of the candidates who clear the admission test are confused.

$$\therefore \dfrac{60kq}{100kp+30kp+60kq}=\dfrac{40}{100}$$

On simplifying this equation, we get:

$$q=\dfrac{13p}{9}$$

Now, in order to maximise $$q$$, we need to maximise $$p$$.

Now we know that the probability of a diligent candidate passing the test, $$10p\leq1$$

or, $$p\leq\dfrac{1}{10}$$

So the maximum value of $$p=\dfrac{1}{10}$$

Now, calculating the maximum value of $$q$$.

Hence, the MAXIMUM possible value of the probability of a confused candidate clearing the test, $$q=\dfrac{13}{90}$$

Hence, option B is correct.

Let the number of correct and wrong questions be x and y respectively. 

Number of unattempted questions = 20 - (x+y) $$\longrightarrow\ i$$

4 marks are awarded for every correct questions and 2 and 1 marks are deducted for every wrong and unattempted questions respectively. 

Total original marks scored = 4x-2y-((20-(x+y)) = 5x-y-20 $$\longrightarrow\ ii$$

But the teacher deducted 1 and 2 marks for every wrong and unattempted questions respectively by mistake. 

Total marks = 4x-y-2(20-x-y) = 6x+y-40

Total marks = 46 (given)

6x+y-40 = 46

6x+y = 86 

The possible pairs of (x,y) are (14,2), (13,8), (12,14), ........ , (1,80), (0,86). 

x+y = 16, 21, 26, ........ , 81,86

Only one case will be possible as (x+y) $$\le\ $$ 20 (as equation i $$\ge\ 0$$)

Hence, Number of correct questions = x = 14

Number of wrong questions = y = 2 

Number of unattempted questions = 20 - (14+2) = 4

Hence, final marks = $$\left(5\times\ 14\right)-2-20$$ = 48 (from equation ii) 

$$\therefore\ $$ The required answer is C.

Given : f(0,y) = y+1 and f(x+1,y) = f(x,f(x,y)) + x

To find : f(2,2)

f(x+1,y) = f(x,f(x,y)) + x

Let x=0

f(1,y) = f(0,f(0,y))

f(1,y) = f(0,y+1)  (as f(0,y) = y+1 (given))

f(1,y) = (y+1)+1 = y+2

Hence, f(1,y) = y+2 $$\longrightarrow\ i$$

Now, 

f(x+1,y) = f(x,f(x,y)) + x

Let x=1

f(2,y) = f(1,f(1,y)) + 1

f(2,y) = f(1,y+2) + 1 (from equation i)

f(2,y) = (y+2) + 2 + 1 = y+5

Put y=2

f(2,2) = 2+5 =7

$$\therefore\ $$ The required answer is B.

List of all prime numbers less than 25 = 2,3,5,7,11,13,17,19,23 = 9 numbers

$$a_1$$ = 2, $$a_2$$ = 3, $$a_3$$ = 5, $$a_4$$ = 7, $$a_5$$ = 11, $$a_6$$ = 13, $$a_7$$ = 17, $$a_8$$ = 19, $$a_9$$ = 23

Sum of all the above prime numbers ($$a_1$$ + $$a_2$$ + ...... + $$a_9$$) = 100

$$X_i=\ \frac{\ b_i}{a_i}$$ ,where, $$b_i$$ = Sum of all prime numbers $$a_1\ to\ a_{n\ }$$ except $$a_i$$

Example : $$b_3$$ is the sum of all the prime numbers $$a_1$$ to $$a_9$$ except $$a_3$$. 

$$X_1$$ = $$\ \frac{\ b_1}{a_1}$$ = $$\ \frac{\ 100-a_1}{a_1}$$ = $$\ \frac{\ 100-2}{2}$$ = 49

$$X_2$$ = $$\ \frac{\ b_2}{a_2}$$ = $$\ \frac{\ 100-a_2}{a_2}$$ = $$\ \frac{\ 100-3}{3}$$ = $$\ \frac{\ 97}{3}$$

$$X_3$$ = $$\ \frac{\ b_3}{a_3}$$ = $$\ \frac{\ 100-a_3}{a_3}$$ = $$\ \frac{\ 100-5}{5}$$ = 19

$$X_4$$ = $$\ \frac{\ b_4}{a_4}$$ = $$\ \frac{\ 100-a_4}{a_4}$$ = $$\ \frac{\ 100-7}{7}$$ = $$\ \frac{\ 93}{7}$$

$$X_5$$ = $$\ \frac{\ b_5}{a_5}$$ = $$\ \frac{\ 100-a_5}{a_5}$$ = $$\ \frac{\ 100-11}{11}$$ = $$\ \frac{\ 89}{11}$$

$$X_6$$ = $$\ \frac{\ b_6}{a_6}$$ = $$\ \frac{\ 100-a_6}{a_6}$$ = $$\ \frac{\ 100-13}{13}$$ = $$\ \frac{\ 87}{13}$$

$$X_7$$ = $$\ \frac{\ b_7}{a_7}$$ = $$\ \frac{\ 100-a_7}{a_7}$$ = $$\ \frac{\ 100-17}{17}$$ = $$\ \frac{\ 83}{17}$$

$$X_8$$ = $$\ \frac{\ b_8}{a_8}$$ = $$\ \frac{\ 100-a_8}{a_8}$$ = $$\ \frac{\ 100-19}{19}$$ = $$\ \frac{\ 81}{19}$$

$$X_9$$ = $$\ \frac{\ b_9}{a_9}$$ = $$\ \frac{\ 100-a_9}{a_9}$$ = $$\ \frac{\ 100-23}{23}$$ = $$\ \frac{\ 77}{23}$$

B is the set of all integer-valued $$X_i$$ = {$$X_1$$, $$X_3$$} = {49, 19}

The smallest element of B = 19

$$\therefore\ $$ The required answer is B.

The image will be drawn as:

We will assume the side of the square to be 2a. XY will be half of CD i.e. 2a/2 = a. This means that OX = radius - XY ==> 5 - a.
Similarly, CX = radius - AC ==> 5 - 2a and OC = radius.
Now, we can use pythagoras theorem in triangle OCX:
$$\left(5-a\right)^2+\left(5-2a\right)^2=5^2$$ ==> $$25\ +\ a^2-10a\ +\ 25\ +\ 4a^2\ -20a=25$$
==> $$5a^2-30a+25\ =\ 0$$ ==> $$a^2\ -\ 6a\ +\ 5\ =\ 0\ $$.
This gives a = 5 or 1. 
a can not be 5 as that will make CX i.e. 5 - 2a to be of negative length.
This means that side of the square is 2*1 = 2 cm and Area of the square is 2*2 = 4 sq. cm.

Let the price of blueberries, kiwis and peaches be Rs b, k and p respectively. 

Money spent on blueberries = Rs 9b

Money spent on kiwis = Rs 22k

Money spent on peaches = Rs 50p

Since, money spent everyday is the same, 

9b = 22k = 50p = M , where, M is the total money spent everyday. 

b = $$\ \frac{\ M}{9}$$

k = $$\ \frac{\ M}{22}$$

p = $$\ \frac{\ M}{50}$$

Since, b, k and p are integers, M should be the LCM of (9,22,50).

M = LCM (9,22,50) = LCM (22,450) = Rs 4950

Total money spent on the 4th day = Rs 4950 - Rs 15 = Rs 4935

Weight of mangoes bought on the 4th day = $$\ \frac{\ Rs\ 4935}{Rs\ \frac{35}{kg}}$$ = 141 kg

Cost Price of mangoes = Rs 35/kg

Sell Price of mangoes = Rs 50/kg

Profit on 4th day = $$\ \frac{\ Rs\ \left(50-35\right)}{kg}$$ $$\times\ $$141 kg = Rs 2115

Hence, the minimum possible profit on the 4th day is Rs 2115. 

$$\therefore\ $$ The required answer is B.

$$x+y^2+z^3=50$$

Let z = 1, $$x+y^2=49$$ 

Pairs of (x,y) = (48,1),(45,2),(40,3),(33,4),(24,5),(13,6) = 6 solutions

Let z = 2, $$x+y^2=42$$

Pairs of (x,y) = (41,1),(38,2),(33,3),(26,4),(17,5),(6,6) = 6 solutions 

Let z = 3,$$x+y^2=23$$

Pairs of (x,y) = (22,1),(19,2),(14,3),(7,4) = 4 solutions 

Total possible solutions = 16 

$$\therefore\ $$ The required answer is C.

The figure of one of the structure is given above. 

Since, ABCD is a square, AB = CD = 0.5 m

Now, CE=EF=DF= (Given) = CD/3 = $$\ \ \ \frac{\ 0.5}{3}=\ \frac{\ 1}{6}m$$

Let PE = x m and EB = y m respectively. 

In $$\triangle\ $$PFE and $$\triangle\ $$PAB, 

$$\angle\ P=\angle\ P$$ (common angle)

$$\angle\ PFE=\angle\ PAB$$ (since FE is parallel to AB)

Hence, $$\triangle\ $$PFE and $$\triangle\ $$PAB are similar. 

$$\ \frac{\ PE}{PB}=\ \frac{\ FE}{AB}$$

$$\ \frac{\ PE}{PE+EB}=\ \frac{\ FE}{AB}$$

$$\ \ \ \frac{\ x}{x+y}=\ \frac{\ \ \frac{\ 1}{6}}{0.5}$$

y = 2x i.e. EB = 2 $$\times\ $$PE

Now, in $$\triangle\ $$ECB, 

$$EB^2=EC^2+CB^2$$

$$\left(2x\right)^2=\ \left(\frac{1\ }{6}\right)^2+\ \left(\frac{1\ }{2}\right)^2$$

$$x=\ \frac{\ \sqrt{10\ }}{12}m$$

PB = PE + EB = x + 2x = 3x = $$\ \frac{\ \sqrt{10}}{4}\ $$m

Length of the structure = PA + PB + AB + BC + CD + DA

= $$\ \frac{\ \sqrt{10}}{4}\ $$ + $$\ \frac{\ \sqrt{10}}{4}\ $$ + $$\ \frac{\ 1}{2}$$ + $$\ \frac{\ 1}{2}$$ + $$\ \frac{\ 1}{2}$$ + $$\ \frac{\ 1}{2}$$

= $$\left(2+\ \frac{\ \sqrt{10\ }}{2}\right)$$m

Length of 20 such structures =$$\left(2+\ \frac{\ \sqrt{10\ }}{2}\right)\times\ 20$$

= $$10\left(4+\sqrt{10\ }\right)m$$

$$\therefore\ $$ The required answer is C. 

The figure of the path is given below. Gate 1 and Gate 2 is situated at A and B respectively. 

We have drawn ED which is perpendicular to AB in order to get a right angled triangle AED where AE = 60m and ED = 80m. 

From pythagoras theorem, $$AD^2=AE^2+ED^2$$

$$AD^2=60^2+80^2$$

AD = 100m

Length of the semi circular path AD = $$\pi\ r=\pi\ \left(\frac{AD\ }{2}\right)\ $$ = $$50\pi\ \ $$ = 157 m

Length of path ABCD = 80+80+20 = 180 m

A person entered through gate 1 and travelled along path 1 and path 2 and exited from gate 1. 

Total distance covered = 180+157 = 337m

Speed of the person = 5 kmph = $$\ \frac{\ 5\times\ 1000}{60}=\ \frac{\ 250}{3}\ \frac{\ m}{\min}$$

Total time taken = $$\ \frac{\ 337}{\ \frac{\ 250}{3}}\min$$ = 4 min (approx)

So the total time taken for the person to travel across the park is 4 min. 

$$\therefore\ $$ The required answer is A.

The 5 digits which are used in the combination lock are 9,8,7,5 and 4.

The sum of first 3 digits and the last 3 digits are divisible by 3. Hence, we can say that the third digit is common in both the combinations.

The possible groups of 3 digits whose sum is divisible by 3 are (9,8,7),(9,8,4),(9,7,5),(9,5,4). 

Out of these 4 possible groups, we have to select two groups which can be used as the first and last 3 digits. 

The selection should be done in such a way that both the groups should only have one digit in common. 

Example : If we select (9,8,7) and (9,8,4) and let the middle digit be 9, then we will have 8 in both the first 3 digits and the last 3 digits which is only possible for the 3rd digit which is occupied by 9 in this case. Hence, this case is not possible. 

So the only possible combinations for the first and last 3 digits are :

Case 1: (9,8,7) and (9,5,4) where the 3rd digit will be 9. 

Case 2: (9,8,4) and (9,7,5) where the 3rd digit will be 9.

Now, it is given that the sum of the last 4 digits is divisible by 4. 

The possible cases of the above scenario are :

Case 3: (9,8,7,4) where the first digit will be 5. 

Case 4: (8,7,5,4)where the first digit will be 9 which is not possible as 9 is fixed as the 3rd digit from Case 1 and 2.

Since, the first digit is 5 and the third digit is 9, the second digit will either be 4 or 7 and the last two digits will be either (8,7) or (8,4)

So, the possible combinations of the lock are 54987, 54978, 57984 and 57948.  

Hence, the option which is definitely false is E as no possible combinations has 8 as its 2nd digit. 

$$\therefore\ $$ The required answer is E. 

The length, width and height of Tank 1 is m meters each. 

Volume of Tank 1 = $$m^{3\ }$$ cubic meters

The length, width and height of Tank 2 is n meters each. 

Volume of Tank 2 = $$n^{3\ }$$ cubic meters

The length, width and height of Tank 3 is m, n and 1 m respectively. 

Volume of Tank 3 = mn cubic meters 

Since, Tank 1 is filled first and after Tank 1 is full, water is flowing into Tank 2 and Tank 3, 

Volume of water left in Tank 1 after Tank 2 and Tank 3 are filled = $$\left(m^{3\ }-n^3-mn\right)$$ cubic meters

Volume of water left in Tank 1 = 85000 L (given) = 85$$m^3$$

Hence, $$\left(m^{3\ }-n^3-mn\right)$$ = 85 , where, m and n are integers. 

$$n^3+mn=m^3-85$$

From option B, we get $$n^3+7n=258$$ $$\longrightarrow\ $$ n=6

From option C, we get $$n^3+5n=40$$ $$\longrightarrow\ $$ No integer solution

From option D, we get $$n^3+6n=131$$ $$\longrightarrow\ $$ No integer solution 

From option E, we get $$n^3+10n=915$$ $$\longrightarrow\ $$ No integer solution 

Hence, we got m = 7 and n = 6. 

$$\therefore\ $$ The required answer is B.

It is given to us that Light Chemicals has a total of 210 junior employees.
This means that: 25 + w + 30 + v + u + 15 + 18 + z + 16 + y + x + 10 = 210 ==> u + v + w + x + y + z = 96.

Then, Light Chemicals has a total of 146 employees in the IT department.
This means that: 22 + 15 + 25 + w + 14 + 8 + 16 + y + 12 + 10 = 146 ==> w+y = 24.

Then, Light Chemicals has a total of 77 employees in the Hyderabad office.
This means that: 13 + 11 + 9 + 7 + x + 10 + 9 + 6 = 77 ==> x = 12.
From these 3 equations, we get u + v + z = 60.

Then, In the Mumbai office, the number of junior female employees is 55.
This means that: w + v + u = 55.
Subtracting this from the 1st equation, we get x + y + z = 41 and subtracting value of x from this, we get y+z = 29.

We are given that: At every level, the number of employees at any location/department/rank/gender are proportional to the corresponding area of the region represented in the chart.
it implies that v > u > w.
This means that the possible option is either B or D. But in option D, v is 4 time u which is not proportionately correct in the chart.
Thus, the possible values are 20, 25, 10 i.e. Option B.

It is given to us that Light Chemicals has a total of 210 junior employees.
This means that: 25 + w + 30 + v + u + 15 + 18 + z + 16 + y + x + 10 = 210 ==> u + v + w + x + y + z = 96.

Then, Light Chemicals has a total of 146 employees in the IT department.
This means that: 22 + 15 + 25 + w + 14 + 8 + 16 + y + 12 + 10 = 146 ==> w+y = 24.

Then, Light Chemicals has a total of 77 employees in the Hyderabad office.
This means that: 13 + 11 + 9 + 7 + x + 10 + 9 + 6 = 77 ==> x = 12.
From these 3 equations, we get u + v + z = 60.

Then, In the Mumbai office, the number of junior female employees is 55.
This means that: w + v + u = 55.
Subtracting this from the 1st equation, we get x + y + z = 41 and subtracting value of x from this, we get y+z = 29.

Now, the values of:
A. IT department, all offices together is 146(b).
B. Bengaluru office : 22+20+18+z+16+y+12+10+8+6 = 102 + y+z = 102+29 = 131.
C. Sales Department of Mumbai Office: 30+v+12+10 = 52 + v. As w+v+u = 55, v is definitely smaller than 55 and thus 52+v is smaller than 107.
E. Mid-level, all offices together: 22+15+18+12+20+22+13+11 = 133.

The maximum value is of Option A.

It is given to us that Light Chemicals has a total of 210 junior employees.
This means that: 25 + w + 30 + v + u + 15 + 18 + z + 16 + y + x + 10 = 210 ==> u + v + w + x + y + z = 96.

Then, Light Chemicals has a total of 146 employees in the IT department.
This means that: 22 + 15 + 25 + w + 14 + 8 + 16 + y + 12 + 10 = 146 ==> w+y = 24.

Then, Light Chemicals has a total of 77 employees in the Hyderabad office.
This means that: 13 + 11 + 9 + 7 + x + 10 + 9 + 6 = 77 ==> x = 12.
From these 3 equations, we get u + v + z = 60.

Then, In the Mumbai office, the number of junior female employees is 55.
This means that: w + v + u = 55.
Subtracting this from the 1st equation, we get x + y + z = 41 and subtracting value of x from this, we get y+z = 29.

Number of female junior employees in Finance department of Bengaluru = z and number of female junior employees in IT department in Bengaluru = y.
$$y\ne\ z$$ because y+z = 29 and thus they have to be distinct otherwise they won't be having a natural number value.
thus, the answer is Option D.

As Ratan was terminated after 4 months, he did not register a loss of more than 20000 at the end of 3 months but registered a loss of more than 20000 in 2nd, 3rd and 4th month. This implies: x - 30 >= -20 and x - 35 < -20 ==> 15 > x >= 10. As x is an integer and x/2 must also be an integer x could be 10, 12 or 14.

For Shri, as he was terminated after 7 months, his loss for the first 6 months did not exceed 10000. It implies that x + 1.5y - 65 >= -10 ==> x+1.5y >= 55.
Also, for the first 6 months, his loss did not exceed 20000 for any group of 3 consecutive months. It implies that: x+y-25 >= -20 ==> x+y >= 5
y - 45 >= -20 ==> y >= 25 and 0.5y - 45 >= -20 ==> y >= 50.
Now, he could be terminated for 2 reasons i.e. 1. his loss for May, June, July exceeded 20000 OR 2. his loss for last 6 months exceeded 10000.
Case 1: 0.5y - 50 < -20 ==> y < 60.
Case 2: 1.5y - 95 < -10 ==> y < 56.667.
As y is also even, possible values for y are 50, 52, 54, 56 and 58.

As Tamal was terminated after 10 months, in ay consecutive period of 3 months for the first 9 months, his loss did not exceed 20000 and for any consecutive period of 6 months, his loss did not exceed 10000.
This implies: 0.5x + y + x >= -20 ==> 1.5x + y >= -20.
There are 2 cases for Tamal also.
Case 1: 5 + 10 - z < -20 ==> z > 35
Case 2: x - 20 + 20 -z < -10 ==> z -10 > x.

Similarly, for Upanshu, the equations will be that the total profits should exceed 0 : 5z - x + y - 81 >= 0
z -48 >= -20 ==> z >= 28 and y - x - 58 >= -10 ==> y -x >= 48. This is only possible when x = 10 and y = 58.

So, value for x is 10 i.e. Option E.

As Ratan was terminated after 4 months, he did not register a loss of more than 20000 at the end of 3 months but registered a loss of more than 20000 in 2nd, 3rd and 4th month. This implies: x - 30 >= -20 and x - 35 < -20 ==> 15 > x >= 10. As x is an integer and x/2 must also be an integer x could be 10, 12 or 14.

For Shri, as he was terminated after 7 months, his loss for the first 6 months did not exceed 10000. It implies that x + 1.5y - 65 >= -10 ==> x+1.5y >= 55.
Also, for the first 6 months, his loss did not exceed 20000 for any group of 3 consecutive months. It implies that: x+y-25 >= -20 ==> x+y >= 5
y - 45 >= -20 ==> y >= 25 and 0.5y - 45 >= -20 ==> y >= 50.
Now, he could be terminated for 2 reasons i.e. 1. his loss for May, June, July exceeded 20000 OR 2. his loss for last 6 months exceeded 10000.
Case 1: 0.5y - 50 < -20 ==> y < 60.
Case 2: 1.5y - 95 < -10 ==> y < 56.667.
As y is also even, possible values for y are 50, 52, 54, 56 and 58.

As Tamal was terminated after 10 months, in ay consecutive period of 3 months for the first 9 months, his loss did not exceed 20000 and for any consecutive period of 6 months, his loss did not exceed 10000.
This implies: 0.5x + y + x >= -20 ==> 1.5x + y >= -20.
There are 2 cases for Tamal also.
Case 1: 5 + 10 - z < -20 ==> z > 35
Case 2: x - 20 + 20 -z < -10 ==> z -10 > x.

Similarly, for Upanshu, the equations will be that the total profits should exceed 0 : 5z - x + y - 81 >= 0
z -48 >= -20 ==> z >= 28 and y - x - 58 >= -10 ==> y -x >= 48. This is only possible when x = 10 and y = 58.

So, value of y is 58 i.e. Option A.

As Ratan was terminated after 4 months, he did not register a loss of more than 20000 at the end of 3 months but registered a loss of more than 20000 in 2nd, 3rd and 4th month. This implies: x - 30 >= -20 and x - 35 < -20 ==> 15 > x >= 10. As x is an integer and x/2 must also be an integer x could be 10, 12 or 14.

For Shri, as he was terminated after 7 months, his loss for the first 6 months did not exceed 10000. It implies that x + 1.5y - 65 >= -10 ==> x+1.5y >= 55.
Also, for the first 6 months, his loss did not exceed 20000 for any group of 3 consecutive months. It implies that: x+y-25 >= -20 ==> x+y >= 5
y - 45 >= -20 ==> y >= 25 and 0.5y - 45 >= -20 ==> y >= 50. 
Now, he could be terminated for 2 reasons i.e. 1. his loss for May, June, July exceeded 20000 OR 2. his loss for last 6 months exceeded 10000.
Case 1: 0.5y - 50 < -20 ==> y < 60.
Case 2: 1.5y - 95 < -10 ==> y < 56.667.
As y is also even, possible values for y are 50, 52, 54, 56 and 58.

As Tamal was terminated after 10 months, in ay consecutive period of 3 months for the first 9 months, his loss did not exceed 20000 and for any consecutive period of 6 months, his loss did not exceed 10000.
This implies: 0.5x + y + x >= -20 ==> 1.5x + y >= -20. 
There are 2 cases for Tamal also.
Case 1: 5 + 10 - z < -20 ==> z > 35 
Case 2: x - 20 + 20 -z < -10 ==> z -10 > x.

Similarly, for Upanshu, the equations will be that the total profits should exceed 0 : 5z - x + y - 81 >= 0
z -48 >= -20 ==> z >= 28 and y - x - 58 >= -10 ==> y -x  >= 48. This is only possible when x = 10 and y = 58.

Profits generated by Upanshu at the end of his probation period are 5z + y-x - 81. Now, z >= 28 and y-x = 48 which gives 5z +y-x >= 188 and 5z +y-x -81 >= 107.
Thus, the correct answer is Option A i.e. atleast 107000.

On the initial glance itself the cartoon seems to be depicting the sheep as being appreciative of the fact that the predator on the poster is coming out clean and clear about his intentions- of eating the sheep, even though the intent is harmful to the sheep.

Option A: Incorrect. Though it seems like a legitimate option but in this case truth being called more powerful than manipulation is highlighting a positive aspect of truth, hinting that it might help the sheep. But here the truth is not helping out the sheep. It is just serving as a blunt statement.

Option B: Incorrect. The image in no way conveys the ease of believing selfish assurances (negative) over altruistic promises (positive). There is no comparison being drawn between the two.

Option C: Correct. This is exactly what the cartoon implies. The sheep prioritizes clarity and certainty despite being in probable danger.

Option D: Incorrect. There is no submission to authority being indicated, only appreciation for clarity.

Option E: Incorrect. There is no learning to be taken away about leaders, neither there is a mention of a leader. It’s just a direct interpretation of a cartoon.

The passage describes how people instinctively reject career options the moment a pay cut is involved, treating it as a "mark of personal failure." This reveals the underlying psychology: employees equate their salary with their personal value. 

If a lower salary = failure, then logically, people see their current salary as a benchmark of their self-worth, which is exactly what C concludes. Option A is too absolute ("cannot" is too strong — the passage says they baulk, not that it's impossible). 

Option B is a general advice statement about risk-taking that the passage never prescribes. 

Option D makes an unsupported leap connecting pay cut acceptance to entrepreneurial personality. 

Option E introduces a hiring scenario involving failure that the passage never discusses. 

C is the best conclusion because it captures the root cause of why pay cuts feel taboo — it's not just about money, it's about identity and perceived self-worth.

The author starts the discussion by writing about World Wars I and II, saying that although the weaknesses of liberal democracies surfaced after the First World War and then faded after the Second, primarily because of the highly successful domestic and international institutions, they never really went away. The author continues the discussion by discussing the various deficiencies of liberal democracies. In this discussion, the author points out that, since liberal democracies restrain majorities, the quick and decisive execution of policies is often hindered. From this, the author concludes that "liberal democracy requires more patience than many possess." Option C captures this best and is the correct answer.

Option A talks about the fact that liberal democracies are conservative, which has not been discussed in the paragraph, and also contradicts the very name of 'liberal' that the author attaches to the noun. Option B is partially true, but exaggerates the ideas by writing that 'all views must be considered.' Option D presents a wrong binary; a liberal democracy is only said to be restraining majorities, not necessarily preferring the views of the minorities. Option E is incorrect, environmental impact as a consideration that hinders all progress and forces liberal democracies to be more 'patient' is a limited way of looking at why the author discussed the point. Option C remains the correct answer.

The author discusses the second problem of liberal democracies by writing that liberal democracy "requires tolerance for minority views and ways of life to which many citizens are deeply opposed." This leads to a few groups of people holding divergent values and ideologies that, as a state, the liberal democracy does not share. Due to this, individuals belonging to those groups often find themselves carrying a 'civic identity' (one that aligns with the values of the liberal democracy as a state), and a 'personal or group identity' (one that an individual holds dear and aligns with the values of the group that he or she belongs to). Therefore, option D, "by tolerating the views we disagree with, we suffer from multiple identities," follows directly from the information presented in the passage.

Option A does not capture the third problem: the identity crisis arising from the misalignment between individual and civic values. Because it addresses only what this issue would appear to be on the surface, it is incorrect. Option B presents a comparative lever, that the intensity of our permissibility of how much we accept a particular point of view is a function of how much liberal democracy forces us to accept that view, which is not discussed in the passage. Option C hints at the fact that, as individuals, we often tolerate unpopular views as we understand that the person holding the views has the right to have those views; this does not capture that, inherently, individuals often tolerate unpopular views only on the surface, and might have multiple identities ('civic' and 'group' identity). Option E is partly true; it hinges on the distinction between 'having' a civic identity versus 'demonstrating' a civic identity, the former of which is discussed in the passage, but the latter is not. Option D remains the correct answer.

The author discusses the 'necessity of compromise' by mentioning the fourth inherent difficulty of a liberal democracy. An individual would not believe in something that he or she considers to be bad and false, i.e, they would always believe that what they hold as an ideology is 'good and true', thus, it can be said that liberal democracy forces people to compromise by having them accept views that they do not consider to be aligning with their definitive ideas of good and true. The author says that the alternative to this compromise is either inaction (do nothing about the situation at hand) or oppression (force minorities to give up their perception of truth), which, more or less, are both damaging.

Option A is incorrect, as the compromise is discussed as a forced proposition among citizens in a liberal democracy, not as a threat to its ideals in and of itself. Option B is incorrect. Although it is true that we want our ideas reflected in the public sphere, it is also true that people often tolerate opposing views, and it is tolerance of opposing views that determines whether a liberal democracy is compromising. Option D is incorrect for the same reason as option C. Option E captures the nuances mentioned in the last paragraph by discussing liberty, compromise, incompatibility, and rights, and how they do not fit well with the compromise defined above. Option E is the correct answer.

The passage emphasises the importance of metaphors in communication among individuals who might not share the same language, writing that "Metaphorical imagination is a crucial skill in creating rapport and in communicating the nature of unshared experience." Based on this, let us analyse each option provided.

Option A is incorrect. The passage states only that metaphors are crucial for creating rapport and for communicating the nature of 'unshared experience', not merely for 'lived experience' that causes a gap in communication. An experience that is not a 'lived experience', such as an abstract thought or a fragment of an individual's imagination, can still be communicated through metaphors.

Option B is incorrect. The passage does not suggest that science can communicate complex ideas in 'simple ways' necessarily. Although the aspect of 'relatability' is somewhat implied.

Option C is incorrect; the fact that metaphors play a crucial role in communication does not follow from their capacity to build empathy and social understanding, but rather from their translational purpose of "creating rapport and in communicating the nature of unshared experience."

Option D is incorrect; the alignment of one's cultural knowledge or expertise with others as an argument about the importance of metaphors is limited in scope, based on the information provided in the passage.

Option E best follows from the arguments presented in the passage, as it captures the nuances of differences in lived experiences among individuals and how metaphors communicate those experiences to (and from) everyone.

The most appropriate way to answer the question on the perceived premise of the passage would be to analyse the ideas presented in each of the options one by one and then select the one that best captures the discussion. 

Option A writes, "Large-scale communication systems, built on the CONDUIT metaphor, fuel misunderstanding and fracture social order." This cannot be the premise of the passage, as it is merely a limited account of the examples of the CONDUIT metaphor discussed in the last paragraph and of the discussions surrounding the CONDUIT metaphor.

Option B, assuming that the overview refers to the perspective a person has of effective communication, is not implied in the passage. The passage only addresses the communicative aspect, not whether the information conveyed through metaphors is subjective or objective. Another way to understand the meaning of 'overview' in this context is to say that it focuses primarily on conveying summaries rather than entire ideas, a point not hinted at in the passage.

Option C is a sound notion, based on the discussion in the passage. The very idea that we need metaphors to communicate unshared experiences, and that CONDUIT metaphors can turn from pathetic to evil "when they are applied indiscriminately on a large scale", because in CONDUIT metaphors, one person transmits a fixed, clear proposition to another by means of expressions in a common language, which not everyone shares. All these ideas support the conclusion that, for a genuine understanding of human interactions, we should acknowledge the limits of our own worldview.

Option D somewhat exaggerates the differences between people with shared and unshared language by claiming that it is rare for humans to achieve effortless understanding ('rare convenience'), which is not implied in the passage. All that the passage talks about is that "with enough flexibility in bending your world view and with luck and skill and charity, you may achieve some mutual understanding." 

Option E, although a good statement, fails to capture why metaphors are discussed in the passage (especially why CONDUIT metaphors are discussed in the passage) and is incorrect.

The correct answer is option D.

The primary limitation of CONDUIT metaphors pointed out by the author lies in the fact that through the CONDUIT metaphor, "when it really counts, meaning is almost never communicated, that is, one person transmits a fixed, clear proposition to another by means of expressions in a common language, where both parties have all the relevant common knowledge, assumptions, values, etc." Thus, when it truly matters to communicate (meaning), in situations where people do not speak the same language, the CONDUIT metaphor is of no use.

Option A does not capture the limitations of unshared language discussed above. Whether the idea to be communicated is abstract or concrete, the CONDUIT metaphors fail to communicate it in scenarios in which the languages differ. Option B is incorrect because the very idea of communication is not necessarily to 'co-create understanding' but always to communicate one's interpretation/ knowledge to others.

Option C is incorrect; the limitation of the CONDUIT metaphor has little to do with its tendency to simplify ideas and avoid complexity, but rather with its limited capacity to account for the diverse interpretations people hold and the languages they speak. 

Option D is correct: using a CONDUIT metaphor, "one person transmits a fixed, clear proposition," and therefore the underlying assumption behind a CONDUIT metaphor is that meaning spans all possible interpretations, i.e., that words (or language expressions in general) have inherent 'fixed' meanings.

Option E is incorrect as neither in the CONDUIT metaphor, nor in any other metaphor in general (that the author would discuss positively) is it the case that the efforts needed to interpret the message are taken into consideration/ ignored. What would be true is that, in CONDUIT metaphors, the meaning is never conveyed to someone who does not share the language, not that, even if the meaning is conveyed, the interpretive effort is ignored. Option D remains the correct answer.

Let us evaluate the structure of and the arguments presented in each of the paragraphs of the passage.

The first paragraph introduces the common thread that connects seemingly disparate practices that trolls engage in. Discussing the irony of lulz and the fact that trolls do not believe that anything should be taken seriously. The second paragraph discusses how trolls insist on the celebration of their anonymity and further examines the benefits of anonymity that trolls enjoy, which they would not have had if they had used their real identities. The third paragraph, conversely, discusses how the lack of anonymity for the victim of trolling works to the victim's detriment, primarily because, for a troll, the internet should be an 'attachment-free zone.' 

Since the passage does not imply that the victims of trolling are necessarily 'weak,' option A cannot be inferred and is incorrect. Option C is incorrect because the passage suggests that trolls gravitate toward public forums because they see them as places where they can be anonymous and engage in their pursuit of "lulz." Option D cannot be inferred from the discussions in the passage, as summarised above, and is also incorrect. It cannot be said that trolls use offensive and provocative comments to emotionally upset the targets. Option E also cannot be inferred from the information presented in the passage. According to the passage, trolls consider a person who is willing to disclose real-life attachments, interests, and vulnerabilities an immediate target for trolling. This is the same reason why option B is the correct answer.

In the second paragraph, the author writes that "anonymity allows trolls to engage in behaviors they would never replicate in professional or otherwise public settings, either because the specific behaviors would be considered socially unacceptable, or because the trolls’ online persona would clash with their offline circumstances."

Based on this, option C directly follows and is the correct answer. Option A mentions that trolls aim to create 'caricatured versions of themselves' and is incorrect; trolls do not aim to create caricatured versions of themselves, but rather to spread or practice their ideas. Option B comes close, but also fails to capture the ideas of socially acceptable and unacceptable, and of professional and unprofessional behaviour. Option D talks about anonymity granting trolls the freedom to pursue their 'interests' and fails to capture that trolling, as a behaviour, might not qualify as an 'interest' in the first place. Option E is incorrect because the passage does not mention trolls as people with contradictory pursuits. The passage does talk about the irony of lulz and the trolls (in their own minds) doing their targets a favour, but the author never intends to pose these arguments as moral contradictions of the troll. Option C remains the correct answer.

In the final paragraph, the author writes that trolls frame their trolling explicitly in pedagogical terms (perhaps trying to 'teach' their victim the lesson that the internet is more of an 'attachment-free' zone than a place to disclose real-life attachments, interests, and vulnerabilities). The author says that trolls, in their own minds, understand this as a favour to the victim, causing the victim a sense of understanding that he or she perhaps did not have.

Option E captures this best: "trolls scare away their victims from being themselves ever again online," furthering their ideological stance that the internet is a place for anonymity. Option A is slightly broader than what the discussions in the passage intend to convey. The 'social conditioning' mentioned is not the same as 'internet conditioning' that the passage largely implies. Option B portrays the pursuit trolls engage in as largely positive, which the author would not agree with. Option C says that trolls make their targets resilient to any kind of bullying, which is false, as this is something only the trolls themselves believe. Option D is incorrect for the same reason as option B. Option E remains the correct answer.

Throughout the passage, the author emphasises that the pursuit of science is not towards moral correctness. The author uses the example of nuclear power and the discovery of fission, saying that someday or another, somewhere, we would have discovered nuclear power. These discoveries were going on at the time of Nazi Germany. To say then that physicists would have come together at as barbaric a place as the Nazi footholds to keep the discovery a secret is a stretch. The author is suggesting that the discovery of nuclear power was inevitable, regardless of its later consequences.

Option A is incorrect because the author repeatedly emphasises that science does not address moral questions, or that the moral quandary is not a consideration of science as it moves towards human discoveries; thus, science is neither benevolent nor not benevolent. Option B is incorrect. Although science lacks consideration of moral questions as it moves towards discovery, this is not because it is inconsiderate, but because it is a function of the pursuit of truth and not of morality. Option C is correct for the same reason; 'amoral' refers to something which is unconcerned with whether something is right or wrong.

Option D is incorrect; the author emphasises the pursuit of truth that science embodies, but also quotes Bohr by saying that science is a 'gradual removal of prejudices'. Since it cannot be said that science, at any point in time, has pursued the whole of the truth, option D cannot be inferred. Option E is incorrect for the same reason as option A, and also for the same reason why option C is correct; science is neither moral nor immoral, therefore, it is 'amoral'.

Option A can be inferred from the last paragraph. The author quotes Niels Bohr and writes that "the modest but relentless goal of science is the gradual removal of prejudices." Therefore, it can be said that science gradually removes false beliefs about the world. Option B claims that science is not driven by the pursuit of truth, which is contradicted when the author quotes Robert Oppenheimer by writing that "the deep things in science are not found because they are useful; they are found because it was possible to find them." Thus, it is not utility, but the pursuit of truth that drives science.

Option C can be inferred from the passage, the author writes, "Knowledge is itself the basis for civilisation, you cannot have the one without the other". Option D is also true as per the information provided ("the scientific method doesn’t filter for benevolence"). Option E, lastly, can also be inferred from the information provided in the passage: "to stop it (a discovery), you would have had to stop physics."

Out of the options provided, only option B is false based on the information presented in the passage, and is the correct answer.

Based on the information provided in the passage about science and scientists in particular, let us analyse each option:

Option A is mostly true; the author keeps emphasising that science is amoral, that it indulges in the gradual removal of prejudices, and that the pursuit of knowledge is itself the basis of civilization. Option B conflates scientists only looking at the idea of truth as an inspiration to work towards making discoveries with scientists 'not caring' about the consequences of their work, and is incorrect.

Option C is incorrect, although science is amoral, and that it is unconcerned with moral priorities when it comes to the pursuit of truth, it cannot be said that science is not useful when it comes to answering moral questions. Science may provide insight into how we answer moral questions. Option D is incorrect; the author suggests throughout the passage that science can have both positive ('removal of prejudices') and negative ('weapons of mass destruction') effects in the real world. Option E is incorrect; although it is true that scientists (in general, according to the information provided in the passage) are driven by the urge to explore and not by the urge to produce consequences, there might indeed be exceptions.

Among the options provided, only option A can be inferred from the information presented in the passage, and is the correct answer.

Based on the information provided in the passage regarding social and temporal comparisons, let us analyse each option.

Option A mentions that temporal comparison relies on threat responses, whereas social comparison eliminates threat circuitry. The paragraph defines threat as 'a narrative sense of inferiority' or 'self-sabotage'. The author suggests that social comparison drives this loop of vulnerability, in which people with low self-esteem continually engage in upward comparison, which reinforces negative feedback. The author suggests that temporal comparison would sometimes be preferable to social comparison because it allows individuals to judge themselves against their past selves. The author also suggests that social comparison can still be a good measure if "we interpret comparison as information rather than a verdict".

Option A is incorrect based on the information provided; for the same reason, option B is correct.

Option C is incorrect as the passage does not suggest that temporal comparison relies on threat circuits. Option D is incorrect because social comparison tends to place individuals in a hierarchy, not temporal comparison. Option E is out of the scope of the passage's discussion because objectivity and emotional interpretations are not addressed in the passage's elaboration of social and temporal comparison. Option B remains the correct answer.

Based on the information provided in the passage regarding the effects of high/low self-esteem on an individual engaged in social and temporal comparisons, let us analyse each option.

Option A directly follows from "Those with a secure sense of self are more likely to use comparison as a learning tool" and is therefore correct. Option B misphrases the aspects discussed in the passage; although a high self-esteem contributes to the positive overall effect of upward comparison, it cannot be said that it 'ensures' that upward comparison 'must' yield positive results. 

Also, based on the discussion in the passage, it can indeed be said that upward comparison is complemented by high self-esteem to produce positive results, but it cannot be said that high self-esteem affects upward comparison. High self-esteem affects the effects of upward comparison on individuals, but not upward comparison itself. Option C is incorrect.

Option D is incorrect because the passage only talks about a negative reinforcing loop that upward comparison creates in the context of low self-esteem, and does not say anything about how high self-esteem can be affected by a similar reinforcing loop. Option E is also incorrect because upward comparison is discussed as helpful ("Those with a secure sense of self are more likely to use comparison as a learning tool") when it contributes to the individual's growth positively.

Based on the information provided in the passage about comparison in general, let us analyse each option:

Option A follows from the discussion in the second paragraph: " The same external stimulus—a colleague’s achievement, a peer’s attractiveness, a friend’s popularity—can have radically different effects depending on internal stability." The passage also discusses how we can alter our approach to and view of comparison: "The most skilful approach to comparison may lie not in eliminating it, but in reframing it as feedback." 

Option B also follows from the passage, as discussed above. Option C follows from the discussion in the third paragraph of the passage: "Someone who feels unworthy may unconsciously seek out targets that reinforce that sense, perpetuating a narrative of inferiority." Option D is not implied in the passage. Although the author is clear about the positive effects of social comparison on individuals with high self-esteem, he does not indicate whether individuals with high self-esteem require temporal comparison. Option E, similar to option C, can also be inferred from the third paragraph.

As option D does not follow from the information about comparison laid out in the passage, it is the correct answer.

The author begins by discussing newspapers as hosting 'snakes' between them, but proceeds to write the following:

"That white corner has spread its hood.
A forked tongue
shoots out of its mouth."

The author compares the white corner of the newspaper to a snake spreading its hood. Although the author initially refers only to newspapers that shelter snakes, he subsequently compares the newspapers themselves to snakes. The most suitable choice, therefore, would be option E: "Old newspapers symbolize the repressed stories that may confront the present." Where repressed stories are alluded to as the author hints at ignorance in the face of information repeatedly through the stanzas.

Option A is incorrect because the author suggests that newspapers can be discarded in the morning (and thus disturbed), which may imply that ignored newspapers are more of a 'threat' as we continue to perceive them as such. Option B is incorrect because the paragraph does not indicate whether the newspapers' hostility is in any way related to societal voices. Option C is a good alternative to E, but calling the decay of knowledge 'turning into toxic remnants' does not capture the symbolism that is meant to be represented by newspapers themselves. Option D is incorrect for the same reason as option A, 'newspapers can be discarded in the morning' implies that they are more of a confrontation than a tangible future threat.

The author writes 

"Keep your eyes closed.
Get rid of the whole goddamn pile if you
want to
in the morning."

There are multiple ways to interpret the stanza, such as:

1. Since newspapers are hinted to be symbolising repressed knowledge, perhaps saying that we should get rid of the whole goddamn pile in the morning, 'if we want to', would actually help us avoid confrontation. Or perhaps it also alludes to the fact that it is individual choice that determines how we react when we are confronted with ignorance.
2. The author might not be alluding to either ignorance or confrontation; maybe the author merely wants to point out that it is up to the individual how he/she approaches the knowledge, especially when it might be a threat.

Regardless of our interpretation of the stanza, there's an easier way to approach the question. Out of the five options provided, four of them, more or less, say the same thing. Options B, C, D, and E all talk about ignorance (escaping/ being delusional/ confrontation is not the best way/ better to avoid the past), whereas option A discusses 'acting on an unsettling past'. For this reason, option A is the correct answer.