**Ans . **

(a) Couple

**Explanation :**All others are synonyms meaning 'to tear or cut'.

**Ans . **

(b) Ruffle

**Explanation :**All others are synonyms of control.

**Ans . **

(a) Cease

**Explanation :**All others mean 'to start'; cease means to stop.

**Ans . **

(b) Hub

**Explanation :**All others mean 'on the edge'.

**Ans . **

(c) Ignominy

**Explanation :**All others refer to something said in praise.

**Ans . **

(c) Ardour

**Explanation :**All others refer to a feeling of hatred.

**Ans . **

(d) Awkward

**Explanation :**All others are adjectives meaning 'skillful'.

**Ans . **

(c) Clamorous

**Explanation :**All others are adjectives for persons who do not speak

much.

**Ans . **

(b) Frequent

**Explanation :**All others are synonyms.

**Ans . **

(d) Rational

**Explanation :**All others refer to persons who are madly enthusiastic about something.

**Ans . **

(c) is responsible for the student's conduct

**Explanation :**'The student's' should be replaced with 'his'.

**Ans . **

(d) of their choice.

**Explanation :**We are talking about 'every man or woman', therefore the pronoun used should be singular 'his/her', instead of 'their'.

**Ans . **

(c) you should choose that option

**Explanation :**The pronoun should remain consistent throughout ther

sentence, hence 'you' should be replaced with 'one'.

**Ans . **

(d) assure a successful cure.

**Explanation :**'Assure' is an intransitive verb and should be followed by an object. The correct usage here would be 'be sure of'.

**Ans . **

(c) who they believe to be

**Explanation :**The man being referred here is the object to the verb, hence 'who' should be replaced with 'whom'.

**Ans . **

(c) Bright : Gloomy

**Explanation :**Both are pairs of antonyms.

**Ans . **

(d) Question : Interrogate

**Explanation :**'Alleviate' is an extended form of 'ease' and 'interrogate' is an extended form of 'question'.

**Ans . **

(b) Covert : Stealthy

**Explanation :**Both are pairs of synonyms. All four words mean 'secret’.

**Ans . **

(b) Game : Spectators

**Explanation :**Audiences watch a drama and spectators watch a game.

**Ans . **

(a) Book : Chapter

**Explanation :**Just as a building can have many stories, a book can have many chapters.

**Ans . **

(d) Excited : Serene

**Explanation :**All others are pairs of synonyms.

**Ans . **

(b) Radar : Satellite

**Explanation :**In all other pairs, the first word is a part of the second

word.

**Ans . **

(c) Connubial : Youth

**Explanation :**In all other pairs, the first word is an adjective referring

to the second word.

**Ans . **

(b) Aquiline : Parrot

**Explanation :**In all other pairs, the first word is an adjective derived

from the second pair.

**Ans . **

(a) Claustrophobia : Height

**Explanation :**In all other pairs, the first word refers to a fear of the

second word.

**Ans . **

(b) DBCA

**Explanation :**D tells us that the passage is about continuation of previous night's discussion. B states what the discussion was about. C adds a point to it by using 'also'. A answers the question raised in C about the reason of conflicts.

**Ans . **

(a) BACD

**Explanation :**B states that the document tells us about history, A states

which part of history it relates to, D elaborates further on

the first generation poets by referring to Wordsworth

and Coleridge. Hence, option (a) is correct.

**Ans . **

(d) CADB

**Explanation :**C introduces the poet's large plans, A shows how they

were replaced by new plans, D states how even these

plans remained unfulfilled and B tells us the ultimate

outcome of the plans. Hence, option (d) is correct.

**Ans . **

(b) BCDA

**Explanation :**B states our attitude towards value of time as we

advance in life; C refers to the same by using the phrase

'we become miser in this sense'; and D shows how we

become misers. A presents the concluding statement.

**Ans . **

(d) CBDA

**Explanation :**C relates knowledge to ignorance; B relates our thinking

to our knowledge and states that our knowledge is

always limited, a fact which leads to D that states that as

knowledge is limited, our thinking is also limited. A

concludes the passage.

**Ans . **

(d) CABD

**Explanation :**C states India's position on exchange rate; A. carries the

idea forward by explaining why India's position is not

surprising; B. continues with the idea; D. gives examples

of exceptions to B.

**Ans . **

(d) DACB

**Explanation :**D talks about the 'power' introduced in 1. A states that if

'it is an anchor in difficulties, it should be remembered in

good times too'. C states the work done by some

organizations and B adds to it.

**Ans . **

(b) BACD

**Explanation :**B states what happens in the absence of punishment; A talks about the effect of such a situation; C adds to it by using 'also' and D states what can be done instead.

**Ans . **

(c) CADB

**Explanation :**C continues with the fact that the vessel was moving

away; A states that he looked around; D states that it

was of no use; B explains why there was no use of

looking around.

**Ans . **

(d) ACDB

**Explanation :**A continues with the idea introduced in 1. C states that

the leader should be personally seen; D states what

else should be insisted upon. B talks of allocating work

to members in clear terms, and this should precede 6,

which states how this has to be done.

**Ans . **

(d) ACBD

**Explanation :**A states that true friends are very rare; C states that as

they are rare, they should be respected; B states some

factors which should not be considered while making

friends; and D states that in business realities, all the

acquaintances are motivated by self interest and thus

cannot be treated as genuine friends.

**Ans . **

(a) DCAB

**Explanation :**1 states what managers should guard against; D states

how one can do so; C continues by using 'also'. A states

that external appearances can be deceptive; B

elaborates on the fact and leads to 6.

**Ans . **

(b) ACBD

**Explanation :**A states how demands for resources are made; C states what is done to offset adverse effects of cuts imposed by seniors; B states the importance of availability of adequate resources; and D re-emphasizes the point made in B.

**Ans . **

(d) BADC

**Explanation :**B continues with the idea introduced in 1. A relates the

idea to managers in an organization, who have to take

ruthless decisions; D states how these decisions can

be made easier to accept. C talks about delegation of

power, an idea that is continued in 6.

**Ans . **

(b) CDAB

**Explanation :**C states how the first two categories mentioned in 1

should be dealt with, D talks about the last category; A

continues by referring to 'the persons in this category'. B

states how the wicked must be dealt with and leads to 6.

**Ans . **

(d) 246

**Explanation :**Some dubbles are not bubbles but all dubbles are rubbles,

so it follows that some of the rubbles are not bubbles.

**Ans . **

(b) 236

**Explanation :**If all men are sad and all bad things are men, it follows

that some sad things are bad.

**Ans . **

(c) 126

**Explanation :**All Toms are bright, but no bright Tom is a Dick. Therefore,

no Dick is a Tom.

**Ans . **

(b) 341

**Explanation :**If all witches are devils and all devils are nasty, it implies

that all witches are also nasty.

**Ans . **

(a) 123

**Explanation :**No tingo is a bingo but all jingoes are bingoes. Hence, no

jingo is a tingo.

**Ans . **

(d) I should spend time to understand my own people and literature first, only then can I appreciate other languages and cultures.

**Explanation :**One cannot devote one's whole life to understanding

another culture, if to appreciate other cultures first one

has to spend time understanding one's own culture and

people.

**Ans . **

(a) Only out of fresh experience can the writer get germs for new writing.

**Explanation :**Fresh experience enriches the writers soul, thus

renewing him, in turn leading to the writer being fertile.

**Ans . **

(a) All the people of the society should progress at an equitable rate and there should be no disparity and private property does bring about a tremendous disparity.

**Explanation :**An idea that brings in a tremendous disparity would not

be able to work for general convenience and advantage, as stated in the argument.

**Ans . **

(d) Both (a) and (b)

**Ans . **

(c) no matter how closely you know somebody there still exists an unknown facet of his personality.

**Explanation :**The passage states that even those whom we intimately

know, can surprise us at times with some unknown facet of their personality.

**Ans . **

(b) 8(1+ √2)

**Explanation :**Since base of each triangle will be counted once,

Sum of perimeters of the triangles = Perimeter of the

square + 2 × (Sum of its diagonals).

But each of the other two sides of the triangles is common

to two triangles, so it will be counted twice.

Area of the square = 4, therefore length of its side = 2

and perimeter = 8.

Also its diagonal = 2√2.

So the required perimeter = (8 + 2 × 4√2) = 8(1 + √2).

**Ans . **

(b) 31

**Explanation :**5^6 – 1 = (5^3)^2 – 1 = (125)^2 – (1)^2 = (125 + 1) (125 – 1)

= 124 × 126 = 31 × 4 × 126.

So among the given answer choices, it is divisible by 31.

**Ans . **

(a) Ram paid Rs.275 to Prem

**Explanation :**After 2 years, the price of the flat will be (1)(1.10)^2

= Rs.1.21 lakh.

Correspondingly the price of the land will be

(1.1)(1.05)^2 = Rs.1.21275 lakh.

Hence, the price of the plot = Rs.(1.21275 – 1.21) lakh

= Rs.275 more than that of the flat.

Hence, if they exchange, Ram will have to pay this

amount to Prem .

**Ans . **

(c) Rs.66

**Explanation :**For questions 54 to 57:

Please note that the best way to solve this question is by working

backwards.

E.g. after the 4th round, each one of them had Rs.32. Since it is

Vibha who lost in this round, all the remaining three must have

doubled their share.

In other words, they would have had Rs.16 each after the 3rd

round.

Since the increase is of Rs.16 in each one’s share, i.e., Rs.48

overall which comes from Vibha's share, her share before the

4th round was (32 + 48) = Rs.80, after the 3rd round.

Working backwards in this manner, we can get the following

table.

Suvarna started with Rs.66.

**Ans . **

(d) Vibha

**Explanation :**d It was Vibha who started with the lowest amount, viz.

Rs.10.

**Ans . **

(a) Suvarna

**Explanation :**It was Suvarna who started with the highest amount,

viz. Rs.66.

**Ans . **

(b) 72

**Explanation :**At the end of the second round, Uma had Rs.72.

**Ans . **

(c) Rs.5.51

**Explanation :**Hint: The best way to solve this question is to multiply

the alternatives by 72 and find which one gives you

the middle three digits as 96.7.

To save time, you can multiply 72 by integer values

only.

E.g. 72 × 3 = 216, 72 × 5 = 360 and 72 × 7 = 504.

It is to be noted that when the decimal part of the

answer will be multiplied by 72, the actual answer will

increase.

Let us now roughly multiply the decimal values of the

options also by 72. E.g. 72 x 0.2 = 14.4, 72 × 0.1 = 7.2

and 72 × 0.5 = 36.

So option (a) will yield (216 + 14) = 230

(approximately), (b) will yield (360 + 7) = 367

(approximately), (c) will yield (360 + 36) = 396

(approximately) and (d) will yield (504 + 14) = 528

(approximately).

Of these, only option (c) satisfies our requirement ofv 2nd and 3rd digits being 96.

**Ans . **

(d) 20

**Explanation :**Let us assume that the person has Rs.100.

With this, he can buy 50 oranges or 40 mangoes.

In other words, the price of an orange is Rs.2 and that of

a mango is Rs.2.50.

If he decides to keep 10% of his money for taxi fare, he

would be left with Rs.90.

Now if he buys 20 mangoes, he would spend Rs.50 and

will be left with Rs.40.

Thus, he can buy 20 oranges.

**Ans . **

(a) 100

**Explanation :**The given expression is of the form \( \frac{x^3 + y^3}{x^2 - xy + y^2 } \)

We know, x^3 + y^3 = (x + y)( x^2 – xy + y^2).

Thus, required value = (x + y) = (55 + 45) = 100.

**Ans . **

(c) 1 : 3 : 6s

**Explanation :**The largest angle in a right-angled triangle is 90º, which

corresponds to the highest part of the ratio.

Let us evaluate each option.

In (a), the remaining two angles would be 30º and 60º,

which is possible.

In (b), the remaining two angles would be 45º each,

which is again possible.

In (c), the remaining two angles would be 15º and 45º,

which is not possible as the sum of the angles is not

s 180º.

**Ans . **

(d) Never divisible by 237

**Explanation :**Since n(n + 1) are two consecutive integers, one of

them will be even and thus their product will always be

even.

Also, sum of the squares of first ‘n’ natural numbers is

given by \( \frac{n(n + 1) (2n + 1)}{6} \)

Hence, our product will always be divisible by this.

Also you will find that the product is always divisible by

3 (you can use any value of n to verify this).

However, we can find that option (d) is not necessarily

true. E.g. If n = 118, (2n + 1) = 237 or if n = 236, then

(n + 1) = 237 or if n itself is 237, etc.

**Ans . **

(b) 1 or 5

**Explanation :**The best way to solve this question is by the method of

simulation. Choose any prime number greater than 6 and

verify the result.

When 7 is divided by 6, it gives a remainder 1. So our

answer could be (a) or (b). When 11 is divided by 6, it

gives a remainder 5. Hence, our answer is (b).

**Ans . **

*

**Explanation :**There cannot be four or more blue balls.

Case 1: If there are three blue balls, then they can be

only in box 1, 3 and 5.

Case 2: If there are two blue balls, then total number of

cases = 5C2 = 10

But in 4 cases the blue ball will be in adjacent boxes.

These cases are when blue balls in boxes 1 and 2 or 2

and 3 or 3 and 4 or 4 and 5.

Therefore, total number of cases when there are two

blue balls = 10 – 4 = 6

Case 3: If there is one blue ball, then total number of

cases = 5C1 = 5

Case 4: If there is no blue ball, then total number of

cases = 5C5 = 1

Hence, total number of cases = 1 + 6 + 5 + 1 = 13.

* The correct answer is not available in the given

options.

**Ans . **

(b) 60°

**Explanation :**

In ΔABC, ∠ACB = 180° – 90° – 30° = 60°.

∴ ∠DCE = 30°, since ∠CDE = 90°.

In ΔCED, ∠CED = 180° – 90° – 30° = 60°.

**Ans . **

(c) Rs.1,500

**Explanation :**Using alligation, the ratio of the amounts invested at both

the rates = 2 : 1.

Since he has invested Rs.3,000 at 5%, he should further

invest Rs.1,500 at 8% to earn a total interest of 6% per

annum.

Alternative method:

Let the amount invested at 8% be Rs.x.

Then,

= 3000 × \( \frac{105}{100} \)+ x × \( \frac{108}{100} \)=(3000 + x)\( \frac{106}{100} \

⇒ 0.02x = 30 ⇒ x = 1,500

∴ He should further invest Rs.1,500 at 5% to earn a total

interest of 6% per annum.

**Ans . **

(a) 100

**Explanation :**Let there be 100 voters in all.

Initially, 40 of these promised to vote for P, while 60 of

them promised to vote for Q.

On the last day, (15% of 40) = 6 voters went back of

their promise and voted for Q.

Also, 25% of 60 = 15 voters shifted their interest from Q

to P.

So finally, P end up getting (40 – 6 + 15) = 49 votes and

Q end up getting (60 – 15 + 6) = 51 votes.

Hence, margin of victory for Q = (51 – 49) = 2, which is

true. Hence, there were 100 voters in all.

**Ans . **

\( \frac{π}{3} \)

**Explanation :**In the given figure, the area of the circle = πr^s2.

To find out the area of the square, we need to find the

length of the side of the square.

We know, OR = OT + TR = OT + OS = 2r.

In right-angled triangle ORS, OR = 2r and OS = r.

So SR^2 = OR^2 – OS^2.

∴SR^2 = Area of the square = 4r^2 – r^2 = 3r^2.

Hence, the required ratio = \( \frac{π}{3} \)

**Ans . **

(a) 11.11 m

**Explanation :**In the same time as A runs 200 m in the race, S runs 180

m and N runs 160 m.

In other words, in the same time as S runs 180 m, N runs

160 m.

So in the same time as S runs 100 m, N will run

100 × \( \frac{160}{180= 88.89 m.

Hence, in a 100 m race, S will beat N by (100 – 88.89)

= 11.11 m.} \)

**Ans . **

(b) 14

**Explanation :**If the numbers are (x – 2), x and (x + 2), then

3(x – 2) – 2 = 2(x + 2) ⇒ x = 12

∴ x + 2 = 14.

**Ans . **

(a) 165

**Explanation :**If x men were there on day one, there would be (x – 110)

men on the 12th day.

Hence, on an average, there were (x – 55) men.

The job takes \( \frac{3}{2} \)times the normal time.

Hence, the average number of people = \( \frac{2}{3} \)

⇒ x – 55 = \( \frac{2}{3} \)x

Hence, x = 165

**Ans . **

(a) \( \frac{1}{12} \)

**Explanation :**Total number of four-digit numbers that can be

formed = 4!. If the number is divisible by 25, then the last two digits are 25. So the first two digits can be arranged in 2! ways. Hence, required probability = \( \frac{2!}{4!} \)= \( \frac{1}{12} \)

**Ans . **

(c) 10 hr and 8 hr

**Explanation :**Let the first typist takes X hours and the second takes

Y hours to do the whole job.

When the first was busy typing for 3 hr, the second

was busy only for 2 hr.

Both of them did \( \frac{11}{20} \)of the whole work.

∴ \( \frac{3}{X} \) + \( \frac{2}{Y} \) = \( \frac{11}{20} \)

When the assignment was completed, it was revealed

that each typist had done half the work.

∴The first one spent \( \frac{X}{2} \)hr, and the second,\( \frac{Y}{2} \)hr.

And since the first had begun one hour before the

second, we have \( \frac{X}{2} \) - \( \frac{Y}{2} \)=1

**Ans . **

(d) 15

**Explanation :**Since I live X floors above the ground floor and it takes

me 30 s per floor to walk down and 2 s per floor to ride

the lift, it takes 30X s to walk down and 2X s to ride the

lift after waiting 420 s.

⇒ 30X = 2X + 420 ⇒ X = 15.

Alternative method:

X > 14 as time taken to walk has to be greater than

7 min.

**Ans . **

(d) None of these

**Explanation :**Since 5-12-13 forms a Pythagorean triplet, the triangle

under consideration is a right-angled triangle with height

12 and base 5.

So area of the triangle =\( \frac{1}{2} \)(12)(5)= 30 sq. units.

If area of the rectangle with length 10 units is 30 sq. unit

its breadth = 3 units.

Hence, its perimeter = 2(10 + 3) = 26 units.

**Ans . **

(c) 60

**Explanation :**Since AD = BC (Opposite sides of a rectangle are equal.)

AB + AC = 5BC and AC – BC = 8 or AC = BC + 8

∴AB = 4(BC – 2)

By Pythagoras’ Theorem, AB^2 + BC^2 = AC^2

Expressing AB and AC in terms of BC we get, BC = 5.

∴ AB = 12 and AC = 13

So area of the rectangle = 5 × 12 = 60.

**Ans . **

(d) –2

**Explanation :**If the roots are a and a2, the product of roots = a^3 = –8.

∴ a = –2.

Hence, sum of the roots = k = –(a + a^2) = –(–2 + 4) = – 2.

**Ans . **

(a) 40°

**Explanation :**

If we draw the imaginary lines AC and BD, we find that

∠CAD and ∠CBD are subtended by the same chord DC.

∴∠CAD = ∠CBD = 30°.

Thus, ∠DBA = (70° – 30°) = 40°.

Also, ∠DBA and ∠ACD are subtended by the same chord DA.

Hence, ∠ACD = ∠DBA = 40°.

**Ans . **

(b) 15 m

**Explanation :**

The figure can be drawn as shown above.

Height of the wall = AD = AC = (AB + 3) or AB = (AC – 3).

In right-angled triangle ABC, AB^2 + BC^2 = AC^2.

Thus, (AC – 3)2 + 81 = AC^2.

∴ AC = 15 m.

Hence, height of the wall = 15 m.

Hint: Please note that the same multiple of all the triplets

should also be triplets. E.g. if 3-4-5 is a triplet,

then 3(3-4-5) should also be triplet or 9-12-15 is also a triplet.

Note that the base of the triangle is 9, so other two sides

should be 12 and 15.

**Ans . **

(b) II

**Explanation :**Profit percentage in each case is (i) 10%

(ii) \( \frac{100 × 100}{90} \) = \( \frac{100}{9} \)%

(iii)\( \frac{100 × 1.1-100}{100} \)× 100 = 10%

(iv) \( \frac{10 × 100}{95} \)= \( \frac{200}{19} \)%

**Ans . **

(b) II

**Explanation :**Let the length of the escalator be 90 ft.

(There is no loss of generality in making this assumption.)

Let the speed of the escalator be y ft per second and the

man’s walking speed be x ft per second.

According to the question, we get

\( \frac{90}{30} \)= x + y

\( \frac{90}{90} \)= x - y

Adding the above equations, we get 2x = 4, i.e., x = 2. ∴ Time taken by the man to walk up the escalator when it is not moving = \( \frac{90}{2} \)= x + y or 45 s.

**Ans . **

(a) 3

**Explanation :**Let one of the numbers be x. So the other number would

be(x + 4).

According to the question, we have \( \frac{1}{x} \) + \( \frac{1}{x+4} \)= 21 or x = 3.

Hint: Please note that the sum of reciprocals is basically

\( \frac{(Sum of the int egers)}{(Product of the int egers)} \)So we have to find two

integers whose sum is 10 and whose product is 21.

So x + (x + 4) = 10 or x = 3.

**Ans . **

(b) 4 hr and 48 min

**Explanation :**The bells will chime together after a time that is equal to

the LCM of 18, 24 and 32 = 288 min = 4 hr and 48 min.

**Ans . **

(c) 2 < m < 5

**Explanation :**3m^2 – 21m + 30 < 0

∴ m^2 – 7m + 10 < 0 ⇒ (m – 5)(m – 2) < 0.

So either (m – 5) < 0 and (m – 2) > 0 or (m – 2) < 0 and

(m – 5) > 0 (which is not feasible).

Hence, either m < 5 and m > 2, i.e., 2 < m < 5.

**Ans . **

(d) 726

**Explanation :**Required cost = 6[1+\( \frac{1000}{100} \)]^2 = 6(11)^2 = 121 × 6 = 726.

**Ans . **

c) 3

**Explanation :**If x = 1, we have min(3, 3) = 3.

If x = 2, we have min(6, 0) = 0.

If x = 3, we have min(11, –3) = –3.

If x = 0.5, we have min(2.25, 4.5) = 2.25.

If x = 0.3, we have min(2.09, 5.1) = 2.09.

Thus, we find that as x increases above 1 and when it

decreases below 1, the value of the function decreases.

It is maximum at x = 1 and the corresponding value = 3.

**Ans . **

(d) 24

**Explanation :**Let us choose a town, say A.

If I were to consider this as the base town and construct

two roads such that I connect any pair of towns, I get

the following combinations:

1. AB – BC, 2. AB – BD, 3. AC – CB, 4. AC – CD,

5. AD – DB and 6. AD – DC.

From any of these combinations, if I were to construct a

road such that it again comes back to A, then it would

form a triangle.

To avoid a triangle, the third road that I construct should

not be connected to A but to the third town.

Hence, the combination would be:

1. AB – BC – CD, 2. AB – BD – DC, 3. AC – CB – BD,

4. AC – CD – DB, 5. AD – DB – BC and 6. AD – DC – CB.

Thus, from each town, we can construct 6 such

combinations.

Hence, total number of combinations that we can have

from four towns = (6 × 4) = 24.

**Ans . **

(a) 1

**Explanation :**If a = –2 and b = –3, then our expression will be

me(–2 + mo(le(–2, –3)), mo(–2 + me(mo(–2), mo(–3)))

= me(–2 + mo(–3), mo(–2 + me(2, 3)))

= me(–2 + 3, mo(–2 + 3))

= me(1, mo(1)) = me(1, 1) = 1.

**Ans . **

(d) mo(le(a,b)) = le(mo(a), mo(b))

**Explanation :**the method of simulation, i.e., select any arbitrary values

in the range given and verify whether the option holds

good. E.g. a = 2, b = 3.

In this case, option (a) LHS = mo(le(2, 3)) = mo(2) = 2.

RHS = (me(mo(2), mo(3)) = (me(2, 3)) = 3. Hence, LHS <

RHS.

(b) LHS = mo(le(2, 3)) = mo(2) = 2. RHS = (me(mo(2),

mo(3)) = (me(2, 3)) = 3. Hence, LHS < RHS.

(c) LHS = mo(le(2, 3)) = mo(2) = 2. RHS = (le(mo(2),

mo(3)) = le(2, 3) = 2. Hence, LHS = RHS.

(d) LHS = mo(le(2, 3)) = mo(2) = 2. RHS = (le(mo(2),

mo(3)) = le(2, 3) = 2. Hence, LHS = RHS.

**Ans . **

(b) 0 < a

**Explanation :**specified.

(a) a > 3. Let a = 4.

So me(a2 – 3a, a – 3) = me(4, 1) = 4 > 0.

(b) 0 < a < 3. Let a = 2.

So me(a2 – 3a, a – 3) = me(–2, –1) = –1 < 0.

(c) a < 0. Let a = –1.

So me(a2 – 3a, a – 3) = me(4, –4) = 4 > 0.

(d) a = 3, me(a2 – 3a, a – 3) = me(0, 0) = 0.

**Ans . **

(d) Both b and c

**Explanation :**We can work this on the above lines. E.g.

(a) a > 3. Let a = 4. So le(a^2 – 3a, a – 3) = le(4, 1)

= 1 > 0.

(b) 0 < a < 3. Let a = 2. So le(a^2 – 3a, a – 3) = le(–2, –1)

= –2 < 0.

(c) a < 0. Let a = –1. So le(a^2 – 3a, a – 3) = le(4, –4)

= –4 < 0.

**Ans . **

(a)

**Explanation :**Statement I suggests that xyz is odd. This is only possible

if all three of them are odd.

Hence, z – x is even.

So only statement I is required to answer the question.

**Ans . **

(d)

**Explanation :**Statement I is useless as it only tells that if x and y are

consecutive positive even integers, then (x – y)^2 has to

be equal to 4.

Statement II suggests the possibility that the numbers

could be 2 and 4. But it does not suggest which is x and

which is y.

Hence, we cannot find the value of x using either

statements.

**Ans . **

(a)

**Explanation :**It is clear that only statement I is required to answer the question, if CP = 0.8 SP, then SP = \( \frac{1}{0.8} \) CP. ∴SP = 1.25 CP

Thus, profit percentage is 25.

**Ans . **

(c)

**Explanation :**Both statements are required to answer the question.

Statement I tells us that the triangle is an isosceles triangle.

In an isosceles triangle, the altitude is also the median.

Hence, if we know the altitude and the length of the

congruent sides in an isosceles triangle, we can find its

base and area.

**Ans . **

(b)

**Explanation :**Statement II in itself suggests the price of a banana.

Since we can buy 48 bananas in Rs.12, price of a banana

= Re.0.25. And since this price is after 50% reduction,

the actual price of a banana = Re.0.5.

**Ans . **

(a)

**Explanation :**Since 116 is less than 112, it can be figured out that both

the first two terms of the AP should be less than 10.

There is only one pair of positive integers whose squares

add up to 116 and they are 10 and 4.

Thus, these two should be the first two terms of the AP.

Hence, the first term is 4, and can be obtained only from

statement I.

Statement II merely suggests that the fifth term is of the

form 7k. Nothing correct can be concluded from this.

**Ans . **

(c)

**Explanation :**This can be solved using both the statements together.

From statement I, we know that L × B = 48 or B = \( \frac{L}{48} \)

From statement II, we know L^2 + B^2 = 100

Combining statements I and II,

L^2 + (\( \frac{L}{48} \))^2 = 100.

L is the only unknown in this equation and can be found

out.

**Ans . **

(c)

**Explanation :**We know that product of two numbers = LCM × HCF

= 36 × 2 = 72.

So x = \( \frac{72}{18} \)= 4.

Hence, both the statements are required to answer the

question.

**Ans . **

(c)

**Explanation :**This can be answered using both the statements.

Statement II suggests that both t and z are odd.

Statement I suggests that (x + y + t) is even.

Since the difference between an even and an odd

number is always odd, (x + y + t) – z will be odd.

**Ans . **

(d) Welfare state dismantling

**Explanation :**The dismantling of the welfare state helped Gingrich lead

to the Republican revolution of 1994. Refer second

paragraph line 2.

**Ans . **

(b) Money

**Explanation :**Money has not been mentioned as what a party needs to

win elections. Refer first paragraph, line 1.

**Ans . **

(d) None of these

**Explanation :**All of the mentioned names belong to the Republicans.

**Ans . **

(a) of the shutdown of the government.

**Explanation :**They were tactically defeated by the Democrats because

of the government shutdown. Refer fourth paragraph line 2.

**Ans . **

(b) Follies and Foibles of the Republican Party

**Explanation :**The passage is basically about the mistakes committed

by the Republicans and their odd ways of thinking.

**Ans . **

(a) antiquated

**Explanation :**'Obsolete' has been used to imply old/antiquated.

**Ans . **

(c) The fact that it is axioms, and not just policies that are under fire.

**Explanation :**The real danger to the Republicans is the fact that its axioms, and not its policies, are under fire. Refer ninth paragraph line 1.

**Ans . **

(a) Big government

**Explanation :**The idea of small governments is being ground to dust by

Buchman. Refer seventh paragraph line 1.

**Ans . **

(c) Threes

**Explanation :**A car, a jeep and a snowplough have been mentioned

here.

**Ans . **

(c) a ritual ceremony

**Explanation :**The weather bulletin has been compared to a ritual

ceremony. Refer fifth paragraph line 2.

**Ans . **

(b) It made the Mississippi flow northward

**Explanation :**An earthquake had caused the Mississippi to flow

northward.

**Ans . **

(b) it organises people into a shared moment.

**Explanation :**The author says that weather organizes people into a shared moment, hence inspite of being destructive, it can be said to be stimulating.

**Ans . **

(a) fascinated

**Explanation :**The use of the language to describe the snow storm

reflects the author's fascination with it.

**Ans . **

(b) it is apolitical

**Explanation :**The greatest attractions of weather, for the author, is

that it is apolitical.

**Ans . **

(a) In his house

**Explanation :**The author is watching the weather channel, thus he is

in his house.

**Ans . **

(b) It is pleasantly manipulables

**Explanation :**The weather is not manipulable.

**Ans . **

(d) curved

**Explanation :**'Undulously' means curved.

**Ans . **

(d) All are socialists

**Explanation :**All are socialists, though Robespierre has been mentioned

as an example of a person who till now was thought to

be a typical instance of attributes needed for being a

revolutionary socialist, does come up to them.

**Ans . **

(a) The second form of socialism has more difficulties than the first.

**Explanation :**The second form of socialism involves all the difficulties

of the first one and much more.

**Ans . **

(c) the first believe in gradual change while the others believe in revolutionary change.

**Explanation :**The difference is in their attitude towards change.

**Ans . **

(c) Both (a) and (b)

**Explanation :**Both have been mentioned as the characteristics of the

two persons.

**Ans . **

(c) Corruption in high places

**Explanation :**Corruption in high places has not been mentioned in the

passage.

**Ans . **

(b) the government takes over all productive resources of the country at one stroke.

**Explanation :**The aim of the revolutionary socialism is to substitute the

new rule for the old one at one stroke.

**Ans . **

(a) proclaim

**Explanation :**'Avow' means to proclaim.

**Ans . **

(a) neither side.

**Explanation :**The author does not symapthize with either of the two

sides.

**Ans . **

(c) A Defence of Philosophy

**Explanation :**The author has tried to defend philosophy in the passage.

**Ans . **

(c) Both (a) and (b)

**Explanation :**The passage states that philosophy is politely respected

but secretly despised.

**Ans . **

(d) That it is immoral

**Explanation :**Philosophy has not been said to be immoral.

**Ans . **

(d) It makes the world a better place to live in.

**Explanation :**Philosophy has not been mentioned as being responsible

for making the world a better place to live in.

**Ans . **

(a) Masses would be easier to manipulate as they would not think for themselves.

**Explanation :**If philosophy did not exist, masses would not think for

themselves, and would thus be easier to manipulate for

the politicians.

**Ans . **

(b) departments.

**Explanation :**'Chairs at the universities' refers to the departments at

the universities.

**Ans . **

(b) the defence measures it provokes.

**Explanation :**The existence of philosophy is proved by the defence

measures it provokes.

**Ans . **

(a) Jaws

**Explanation :**Jaws has not been mentioned as Spielberg's movie.

**Ans . **

(b) The book had a more convincing villain.

**Explanation :**The author says that at least the book had a convincing

villain.

**Ans . **

(c) a film review.

**Explanation :**The passage is obviously talking about a film review.

**Ans . **

(a) Crichton

**Explanation :**The book was written by Crichton.

**Ans . **

(c) The film is technically slick but does not have a good storyline.

**Explanation :**The author praises the film for its technical effects and

sophistication at the technological level, but is

disappointed with its story line.

**Ans . **

(d) not very favourable.

**Explanation :**The writer says, “one leaves it vaguely disappointed.”

**Ans . **

(a) Because they fill the halls, and thus people will finance more films.

**Explanation :**He is thankful for such films because they fill the cinemas,

**Ans . **

(d) Neither (a) nor (b)

**Explanation :**The author finds it neither frightening nor amusing.

**Ans . **

(b) interfere with

**Explanation :**'Muck about with nature' implies 'interfere with nature'.

**Ans . **

(c) an expert

**Explanation :**'Pundit' in the passage means an expert.

**Ans . **

(c) The foreign exchange market problem.

**Explanation :**The problem the new cabinet faced was of the foreign

exchange market. Refer first line paragraph fourth.

**Ans . **

(a) Neil Kinnock

**Explanation :**Neil Kinnock has been mentioned as being the leader of

the Labour Party. Refer first line paragraph third.

**Ans . **

(b) Rise in interest rates

**Explanation :**The only way out was to raise the interest rates by at

least 2 per cent. Refer fifth paragraph line 6.

**Ans . **

(d) the Bank of England could put enormous pressure on the government to formulate policy.

**Explanation :**We can infer that the Bank of England could exert

enormous pressure on the government in its policy

formulation.

**Ans . **

(d) Neither (a) nor (b)

**Explanation :**He wanted to complete his cabinet appointments and to

consult his own advisors.

**Ans . **

(a) Because other countries may not follow the British lead in devaluation.

**Explanation :**It was not clear if the other countries would follow the

lead, hence realignment was not a viable option.

**Ans . **

(c) Mr Maastricht

**Explanation :**Maastricht has not been mentioned as part of the Labour

cabinet.

**Ans . **

(b) Wrong policies

**Explanation :**The wrong policies have not been mentioned as a reason for the defeat of the Conservative Party.

**Ans . **

(d) 1994

**Explanation :**We know, Dividends + Retained earnings = Profit before

tax – Tax.

Tax = Profit before tax – (Dividends + Retained earnings).

Hence, tax per rupee of ‘Profit before Tax’ was the lowest

in 1994.

**Ans . **

(d) Neither (a) nor (b)

**Explanation :**">

Hence, sales per rupee of share capital was the highest

in 1991.

**Ans . **

(d) 1994

**Explanation :**

Hence, profit before tax per rupee of sales was the

highest in 1994.

**Ans . **

(a) 1991

**Explanation :**

Hence, the highest percentage addition to reserves was

in 1991.

**Ans . **

(a) Rs.935 lakh

**Explanation :**From the above table, it is clear that the amount of

reserves at the end of 1994 = (535 + 400) = Rs.935 lakh.

**Ans . **

(b) 50%

**Explanation :**It can be seen that the market share of CO in Kolkata has

halved in 1994. None of the other products show such a

drastic decrease in any city. Hence, percentage

decrease in market share = 50%.

**Ans . **

(b) Delhi

**Explanation :**Mumbai and Kolkata have two products whose market

shares were increased. Chennai has 1 while Delhi has none.

**Ans . **

(d) None of these

**Explanation :**We can see that among the given options, the market

share of HD decreased in Mumbai, Kolkata and Delhi.

The market share of CO decreased in Kolkata, Delhi and

Chennai and the market share of BN decreased in Mumbai.

**Ans . **

(a) 0

**Explanation :**None of the products had 100% market share.

**Ans . **

(b) 1

**Explanation :**Only MT doubled its market share in Kolkata in 1993-94.

**Ans . **

(a) 23%

**Explanation :**Percentage increase = (160 – 130) \( \frac{100}{130} \)= \( \frac{300}{13} \)(a) 23% = 23%.

**Ans . **

(b) Rs.25 lakh

**Explanation :**Interest in 1990-91 = 30% of 130 = Rs.39 lakh

Interest in 1991-92 = 40% of 160 = Rs.64 lakh

Hence, required difference = (64 – 39) = Rs.25 lakh

**Ans . **

(d) Rs.515 lakh

**Explanation :**Total interest = (30% of 130) + (40% of 160) = (39 + 64)

= Rs.103 lakh.

If this total interest is charged on borrowed funds, then

(20% of borrowed funds) = 103. Hence, borrowed funds

= (5 × 103) = Rs.515 lakh.

**Ans . **

(d) lower by 1.5%

**Explanation :**Retained profit in 1990-91 = (25% of 130) = Rs.32.5 lakh

Retained profit in 1991-92 = (20% of 160) = Rs.32 lakh

Hence, percentage change in retained profit

= \( \frac{32.5 − 32}{32.5} \) = 1.5% lower.

**Ans . **

(c) Rs.12.8 lakh

**Explanation :**Total dividend earned by shareholders in 1991-92

= (8% of 160) = Rs.12.8 lakh.

**Ans . **

(b) 1988-89

**Explanation :**Trade deficit = Imports – Exports, was the highest for the

year 1988-89, viz. 7 billion dollars.

**Ans . **

(d) 4

**Explanation :**Trade deficit is less than that in the succeeding year in

1987-88, 1989-90, 1991-92 and 1993-94.

**Ans . **

(c) 90%

**Explanation :**Required percentage = \( \frac{18}{20} \) × 100 = 90%

**Ans . **

(d) 88%

**Explanation :**In the last three years, Imports = (22 + 23 + 27) = 72 and

Exports = (18 + 21 + 24) = 63. Hence, the required

percentage = \( \frac{63}{72} \) × 100 = 87.5% = 88% (approximately).

**Ans . **

(a) I only

**Explanation :**The first statement is obviously true as the trade deficit

in each year is less than the export earning. The export

earning has remained constant for three years between

1990 and 1993. Hence, statement II is not true. Even

statement III is not true as the exports in 1994-95 is more

than the imports in 1993-94.

**Ans . **

(c) 1991

**Explanation :**For questions 171 to 175: The graph given in the question can

be depicted in the following table:

The highest change in the revenue obtained from journals

is (47 – 45) = 2 in 1991.

**Ans . **

(a) 45%

**Explanation :**In 1992, percentage of total revenue that came from

books = \( \frac{79}{173} \) × 100 = 45.6% = 45% (approximately).

**Ans . **

(b) 2

**Explanation :**In 1990, there was an increase in revenue for all the 3

categories. In 1991, it increased for magazines and books.

And in 1992, it increased only for magazines. So the

answer is b, viz. 2 years.

**Ans . **

(d) Rs.177 lakh

**Explanation :**Growth rate in 1992 over 1991 = \( \frac{(173 −169)}{169} \)= 2.36%.

If this rate remained same in 1993 as well, then the

revenue in 1993 would be 173 × \( \frac{(173 −150)}{150} \) = Rs. 177

lakh.

**Ans . **

(c) 15%

**Explanation :**Percentage growth in the total revenue from 1989 to

1992 = \( \frac{(173 −150)}{150} \) = 15.33% = 15% (approximately).

**Ans . **

(b) 160

**Explanation :**Since time taken to manufacture Q by both the machines

is the least, we have to manufacture only Q in order to

maximize the output for the day. In such a case, total

number of units of Q produced by M1 = \( \frac{(8 × 60)}{6} \) = 80

units and that by M2 = \( \frac{(8 × 60)}{6} \) = 80 units. So the maximum

number of units that can be produced in one day

= (80 + 80) = 160 units.

**Ans . **

(d) 119

**Explanation :**If M1 works at half of its normal efficiency, time taken by

M1 to manufacture 1 unit of P = 20 min and Q = 12 min.

For producing maximum number of units, we have to

produce Q on M2 first as it takes only 6 min per piece.

Also since at least one unit of P has to be manufactured

and it is more efficient to do so on M2, we would do that.

So time taken to manufacture 1 unit of P on M2 = 8 min.

Hence, time remaining on M2 = (480 – 8) = 472. In this

remaining time number of units of Q that can be

manufactured on M2 = \( \frac{472}{6} \) = 78 (only completed units

taken). Now since it takes less time to manufacture Q on

M1 as well, we will maximize Q on M1. Since 1 unit of

number of units that can be produced = \( \frac{(8 × 60)}{12} \) = 78 = 40.

Hence, the total number of units manufactured = (1 + 78 + 40) = 119 units.

**Ans . **

(a) 6 hr 30 min

**Explanation :**In order to minimize time required, we will manufacture P

on M2 and Q on M1. Number of machine hours required

to manufacture 30 units of P on M2 = (30 × 8) = 240 min

= 4 hr. Number of machine hours required to manufacture

25 units of Q on M1 = (25 × 6) = 150 min = 2.5 hr. So total

time taken = (4 + 2.5) = 6.5 hr or 6 hr 30 min.

**Ans . **

(a) 0 min

**Explanation :**Since P has to be produced in more number than Q and

since time taken to produce P is least on M2, to maximize

the output utilize the entire time available on M2 for

producing P. Number of units of P produced in this time

= \( \frac{(8 × 60)}{8} \) = 60 units. Now since the number of units of

Q should be one-third that of P, we should manufacture

20 units of Q. To manufacture this on M1, it would take

(20 × 6) = 120 min. So there are still (480 – 120) = 360 min

of M1 to be utilized. Now for every 3 units of P that is

manufactured, we have to manufacture 1 unit of Q. To

run one such cycle on M1, it would take (3 × 10 + 1 × 6)

= 36 min. Hence in 360 min, we have 10 such cycles and

utilize all the idle time of M1. Hence, to maximize the

output under the given condition it is possible to have no

idle time on any of the machines.

**Ans . **

(c) 53 of each with 10 min idle

**Explanation :**The least efficient way is the option that gives least

production with highest idle time. So we can compare

the options in the following two ways. Assume that

production is constant (viz. LCM of 48, 64, 53 and 71) in

all 4 options and compare the corresponding idle time. Or

we can assume the idle time to be constant (viz. LCM of

3, 12, 10 and 9) in all 4 options and compare the

corresponding production. The latter method is more

preferable as finding LCM of idle time is easier. So LCM

of 3, 12, 10, 9 = 180. If we assume that the idle time has

to be 180 min, then as per option (a) we would get

production = (\( \frac{180}{3} \)× 48) = 2,880 units, as per option (b),

we would get production = (\( \frac{180}{12} \)× 64) = 960 units, as

per option (c), production = ( \( \frac{180}{10} \)× 53 ) = 954 units and

as per option (d), production = ( \( \frac{180}{9} \)× 71 )= 1,420 units.

Since option (c) gives the least production, it is the least

efficient way.

**Ans . **

(a) 1,50,000 m

**Explanation :**Total requirement of cloth

= Total number of shirts × Cloth required per shirt

= (20 + 30 + 30 + 10 + 10) × 1000 × 1.5 = 1,50,000 m.

**Ans . **

(b)46,500 m

**Explanation :**Total low quality cloth consumed

= 1.5 (30% of 30000 + 30% of 30000 + 40% of 10000

+ 90% of 10000) = 46,500 m.

**Ans . **

(c) 24,000 m

**Explanation :**Total quantity of high quality cloth consumed by A-type

shirts = (80% of 20000) × 1.5 = 24,000 m.

**Ans . **

(d) Cannot be determined

**Explanation :**We only know the relationship between the type of shirt

and cloth used and type of shirt and dye used. We

cannot find any relationship between type of cloth and

dye used.

**Ans . **

(b) 2 : 1

**Explanation :**Amount of low quality die used for C-type shirts

= (40% of 30000) = 12,000 units.

Amount of low quality die used for D-type shirts

= (60% of 10000) = 6,000 units.

Hence, required ratio = \( \frac{12000}{6000} \)= 2 : 1.