SRCC GBO 2012 Question Paper

An issue can mean the following:

Legal term for children- He died without an issue- died without children. Hence, D is the correct usage.

The issue also means publication in print, the August issue of the magazine. Hence, option A is the correct usage.

Issue can also mean formal release of something. The government issued a stamp is also correct.

The problem came to a successful issue. This is indicating resolution and issue in none of its contexts means resolution, so this is the incorrect usage.

Option A: "He is saving his strength for the heavy work he will have to do this afternoon" is a correct and common usage of the verb "save". It means to reserve or conserve energy for later use.

Option B: Malati saved the little boy from drowning. This is the correct use of 'save,' referring to protection. 

Option C: This is correct, formal usage of "save" meaning "except" or "but". It indicates that the only piece of information known about Vijay is the exception clause that follows.

Option D: "I have saved myself of the truth of the report" is not correct standard English usage. The verb "save" requires a different preposition (usually "from" or "for") to describe being spared from something, such as "I saved myself from the truth".

Option A: "She could not master the courage to tell her friend" about her loss. It refers to the fact that she could not gather enough courage, so muster is the correct word to be used here, not master.

Mastered means to have gained expertise in something, so all other uses are correct. 

The thief over witted the police and got away with the loot. This is incorrect usage of over. 

The correct usage is "out-witted" which means to defeat or bypass. Over-witted is incorrect usage.

Expect refers to regarding something as likely to happen

Except means to exclude something 

In this sentence, the intent is to convey that the managing committee arranged for everything but excluded/ omitted  the weekly meetings.

So here, except is the valid choice, and expect does not fit, as there is no likelihood or expectation for the meetings.

The corrected sentence is: "He lay for an hour in an unconscious state until a policeman picked him up." This correction is needed because "lay" is the past tense of the intransitive verb "to lie" (rest/recline), whereas "laid" is the past tense of the transitive verb "to lay" (put down).

The word lay and its form are incorrect usage here because it refers to placing something or putting something down. Hence, an inanimate object or direct obejct is laid down, since lay is a transitive verb.

Example- Raman laid the book down. 

To figure out a similar pair, we first need to understand the pair already present.

Stare: Glance- stare refers to intensely looking at someone or something, and glance refers to a quick, short look. 

So the relationship is one of a high-intensity word and a low-intensity word describing the same action.

Gulp and sip are the best pair, as gulp refers to taking in a substantial amount of liquid in one go, and sip refers to taking in short amounts of liquid at once.

To figure out a similar pair, we first need to understand the pair already present.

A storey is a single unit or floor of the building; multiple storeys stacked on top of each other would make a building. So, the relationship is that of a part to a whole.

Similarly, a rung is the horizontal slab/ support that, when stacked on top of another, forms a ladder. So, rung: ladder is a similar pair.

Option A: A plot is the general sequence of events that make up a story, and an outline is the structured roadmap detailing the story's key moments. Plot or outline is not the unit of either, and hence is not a similar pair.

Option C: A cable is a mode of transportation connecting two ends of a mountainous region with a rope; an elevator is a mode of transportation moving up and down. 

Option D: Every skyscraper will have a foundation, but there will only be a single foundation. Foundations will not be in multiples stacked or arranged to form a skyscraper. Hence, it is not a similar pair.  

To figure out a similar pair, we first need to understand the pair already present.

Scales are a symbol of justice. Reference: measuring scales in law and court symbols. 

Similarly, a torch symbolises the concept of liberty. Reference: Statue of Liberty holding a torch. Hence, torch is a similar pair. 

Other options do not represent symbols of a concept. 

To figure out a similar pair, we first need to understand the pair already present.

A bolt of fabric is a long, continuous length of cloth wound around a flat, tube-like, or rectangular cardboard/plastic core for storage, shipping, and display. Therefore, a bolt is an object that is made up of a fabric completely and is a representative of one particular fabric. 

Similarly, a roll is an object that is completely made up of one particular film. Hence, this is a similar relation.

Lock key and needle thread are different objects that are used as complements. 

The book and paper are not correct because paper is an individual unit that makes up a book and does not represent the entire book on its own. 

To figure out a similar pair, we first need to understand the pair already present.

Moisten: Drench refers to the action of wetting with varying intensity, moisten is very low intensity, and drenching is very high intensity. 

So the relationship is one of a high-intensity word and a low-intensity word describing the same action. A prick is a light, shallow or small puncture, whereas a stab is a deep, forceful and violent thrust. 

Prick and stab are the best pair; both refer to piercing a surface with a sharp object. 

Behest (noun) means an authoritative order, command, or urgent request, often used in the phrase "at the behest of". It implies doing something because someone in authority instructed or requested it.

Hence, command is the appropriate synonym. 

A colossus is an exceptionally large statue, or figuratively, a person or entity of immense size, power, or importance.

Colossus is used to represent something of immense size.  

It derives from the Greek kolossos (large statue) and is commonly used for figures such as the Colossus of Rhodes or influential historical figures.

Hence, huge is the appropriate synonym. 

Defer means to delay or postpone something to a later time. 

Hence, postpone is the correct synonym. 

Exasperation means the feeling of anger or irritation caused by someone or something.

Hence, irritation is the correct synonym. 

Fragment refers to a part of something.

Hence, portion would be the correct synonym since it also means a part of something. 

The correct phrase is "brings out." The complete sentence is: "This photo clearly brings out the difference between the two brothers." The phrasal verb "bring out" means to highlight, reveal, or make a particular quality or feature noticeable, which fits the context of showing distinctions

Why not others:

• Brings up means to raise a child or mention a topic.
• Brings in means to introduce or earn.
• Brings about means to cause, create, or lead to a specific result, change, or even

We were in the thick of decorating the living room when our guests from Chicago arrived, a week early. 

The phrase "in the thick of" means to be in the middle of an intense or busy activity, and is hence the correct choice. 

Why not others:

• "Piling it on thick" (or "laying it on thick") means exaggerating something, usually flattery, praise, or sympathy, to an excessive degree.
• "Fast and thick" (more commonly "thick and fast") describes things coming rapidly and in large quantities, all at once.
• "Thick on the ground" means something is very common or abundant, and is often used in the negative.

Luscious means richly pleasing to the senses; intensely sweet, flavorful, or sensually appealing. Think of ripe fruit or rich food.

Insipid means lacking flavour, interest, or vitality; bland, dull, and utterly unremarkable.

Hence, they make a good antonym pair.

Why not others:

• Fickle means changeable and unreliable
• Languid means lacking energy or vitality primarily; slow, dreamy, and without enthusiasm or urgency. It can suggest either pleasant laziness or a weary, listless exhaustion. It refers to energy and not other things like flavour, colours, or interests. 
• Deteriorating means gradually getting worse

Merciless refers to the lack or absence of mercy, as apparent by the presence of the 'less' suffix. 

The correct antonym for the same is kind, which means being merciful and of a giving nature. 

Mar means to destroy, damage, disfigure or spoil something.

Example: A scar marred his face.

'make' can be the most appropriate antonym among all the options present, as the antonym of destroy should be to create or make something.

Opaque means something that cannot be seen through; light does not pass through it. Figuratively, it also means difficult to understand, obscure, or unclear.

Transparent means something that can be seen through completely; light passes through it freely. Figuratively, it means open, obvious, and easy to understand, with nothing hidden.

Why not clear: Though clear seems like a close contender, it is not the right choice because clear can mean a broader number of things; it can mean something that can be seen through clearly, but it can also mean something free from cloudiness, darkness or dirt. 

Because, we have a more precise and exact option present we choose transparent. 

Magnanimity means generous nobility of spirit; being big-hearted, forgiving, and generous, especially toward a rival or someone you have power over.

Meanness means petty, small-minded stinginess, not just with money but with spirit, generosity, and kindness.

They are good opposites because they sit at opposite ends of the same scale of human generosity and character.

Why not others:

• disability means the absence of a certain ability
• Hypocrisy refers to being two-faced
• Miserliness refers to the unwillingness to spend money, driven by a desire to hoard it

30% of people watch more than 1 movie in city A which is equal to 57,000 people

=> Total population in city A = $$\frac{57000}{30}\times100=1,90,000$$

Similarly, for other cities :

There are 19500 film watchers in City B who see only one film a week.

=> Ans - (B)

30% of people watch more than 1 movie in city A which is equal to 57,000 people

=> Total population in city A = $$\frac{57000}{30}\times100=1,90,000$$

Similarly, for other cities :

City D has the highest number of film watchers (2,88,000)

=> Ans - (C)

30% of people watch more than 1 movie in city A which is equal to 57,000 people

=> Total population in city A = $$\frac{57000}{30}\times100=1,90,000$$

Similarly, for other cities :

Clearly, city B has the lowest number of film-watchers who see only one film is a week (19,500).

=> Ans - (B)

30% of people watch more than 1 movie in city A which is equal to 57,000 people

=> Total population in city A = $$\frac{57000}{30}\times100=1,90,000$$

Similarly, for other cities :

Average of film watchers in all cities (in '000) = $$\frac{190+50+250+288+181.8}{5}=\frac{959.8}{5}=191.96$$ = $$191960$$

$$\therefore$$ In 2 cities, C and D, the number of film watchers are above the average number of all film watchers in the cities above taken together.

=> Ans - (B)

30% of people watch more than 1 movie in city A which is equal to 57,000 people

=> Total population in city A = $$\frac{57000}{30}\times100=1,90,000$$

Similarly, for other cities :

=> Ratio of the number of film watchers who see only one film a week in cities B and C = $$\frac{19500}{195000}=1:10$$

=> Ans - (A)

Actual production in 2004 = 45

Target production in 2005 = 60

=> Required % = $$\frac{45}{60}\times100=75\%$$

=> Ans - (C)

Total target production over the years = 15+30+30+35+60+40+60 = 270

=> Required average target production = $$\frac{270}{7}\approx38.5$$

$$\therefore$$ In 4 years, i.e. 2004,2005,2006 and 2007 actual production is above the average target production over the years.

=> Ans - (A)

The target production in 2002, 2004 and 2007 together = 30+35+60 = 125

Actual production in 2001 and 2003 = 20+30 = 50

=> Required % = $$\frac{125}{50}\times100=250\%$$

=> Ans - (D)

Total actual production over the years = 20+25+30+45+40+45+45 = 250

Total target production over the years = 15+30+30+35+60+40+60 = 270

=> Required ratio = $$\frac{250}{270}=25:27$$

=> Ans - (B)

Number of years in which target production is less than or equal to the actual production is 4 times, in 2001, 2003, 2004 and 2006

=> Ans - (D)

Expression : $$\left(\sqrt[6]{27} - \sqrt{6\frac{3}{4}}\right)^2 + \frac{2(\sqrt{2} + \sqrt{6})}{3\sqrt{2} + \sqrt{3}}$$

= $$[(3)^{\frac{3}{6}}-(\frac{3\sqrt3}{2})]^2$$ $$+\frac{2(\sqrt{2} + \sqrt{6})}{3\sqrt{2} + \sqrt{3}}$$

= $$(\sqrt3-\frac{3\sqrt3}{2})^2+$$ $$\frac{2(\sqrt{2} + \sqrt{6})}{3\sqrt{2} + \sqrt{3}}$$

= $$(\frac{-\sqrt3}{2})^2+$$ $$\frac{2(\sqrt{2} + \sqrt{6})}{3\sqrt{2} + \sqrt{3}}$$

= $$\frac{3}{4}+$$ $$\frac{2(\sqrt{2} + \sqrt{6})}{3\sqrt{2} + \sqrt{3}}$$

= $$\frac{9\sqrt2+3\sqrt3+8\sqrt2+8\sqrt6}{4(3\sqrt2+\sqrt3)}$$

= $$\frac{3\sqrt3(\sqrt6+1)+8\sqrt2(\sqrt3+1)}{4\sqrt3(\sqrt6+1)}$$

Expression : $$\left(1 - \frac{1}{2^2}\right)\left(1 - \frac{1}{3^2}\right)\left(1 - \frac{1}{4^2}\right).....\left(1 - \frac{1}{11^2}\right)\left(1 - \frac{1}{12^2}\right)$$

= $$\left(1^2 - \frac{1}{2^2}\right)\left(1^2 - \frac{1}{3^2}\right)\left(1^2 - \frac{1}{4^2}\right).....\left(1^2 - \frac{1}{11^2}\right)\left(1^2 - \frac{1}{12^2}\right)$$

= $$\left(1 - \frac{1}{2}\right)(1+\frac{1}{2})\left(1 - \frac{1}{3}\right)(1+\frac{1}{3})\left(1 - \frac{1}{4}\right)(1+\frac{1}{4}).....\left(1 - \frac{1}{11}\right)(1+\frac{1}{11})\left(1 - \frac{1}{12}\right)(1+\frac{1}{12})$$

= $$(\frac{1}{2})(\frac{3}{2})\times(\frac{2}{3})(\frac{4}{3})\times(\frac{3}{4})(\frac{5}{4})\times(\frac{4}{5})(\frac{6}{5})\times.................\times(\frac{10}{11})(\frac{12}{11})\times(\frac{11}{12})(\frac{13}{12})$$

= $$\frac{1}{2}\times\frac{13}{12}=\frac{13}{24}$$

=> Ans - (D)

Option D has to be the smallest, since $$\sqrt{\ 26}$$ is nearly 5.1, which when multiplied with 10 shall get almost totally cancel out the positive number 51. 

Terms : $$2^{\frac{1}{2}}, 3^{\frac{1}{3}}, 8^{\frac{1}{8}}$$ and $$9^{\frac{1}{9}}$$

L.C.M. (2,3,8,9) = 72

Multiplying the exponents by 72, we get :

= $$2^{\frac{72}{2}}, 3^{\frac{72}{3}}, 8^{\frac{72}{8}}$$ and $$9^{\frac{72}{9}}$$

= $$(2)^{36},(3)^{24},(8)^9,(9)^8$$

Now, clearly, $$(2)^{36}>(8)^9$$ and $$(3)^{24}>(9)^8$$

Now, among $$(2)^{36}$$ and $$(3)^{24}$$

these can be written as : $$(8)^{12}$$ $$<$$ $$(9)^{12}$$

Thus, greatest among these are : $$3^{\frac{1}{3}}$$

=> Ans - (B)

Expression : $$3^{1001} \times 7^{1002} \times 13^{1003}$$

= $$3^{4k+1} \times 7^{4k+2} \times 13^{4k+3}$$

Unit's digit will be same as unit digit of $$(3)^1\times(7)^2\times(3)^3$$

Only unit digit considered = $$3\times9\times7=9$$

=> Ans - (D)

Expression : $$\frac{1}{1 - \sqrt{2} + \sqrt{3}} + \frac{1}{1 - \sqrt{2} - \sqrt{3}} - \frac{2}{1 + \sqrt{2} - \sqrt{3}} + \frac{3}{\sqrt{2}}$$

= $$[\frac{1}{1-\sqrt2+\sqrt3}\times\frac{(1-\sqrt2)-\sqrt3}{(1-\sqrt2)-\sqrt3}]+[\frac{1}{1-\sqrt2-\sqrt3}\times\frac{(1-\sqrt2)+\sqrt3}{(1-\sqrt2)+\sqrt3}]-2[\frac{1}{1+\sqrt2-\sqrt3}\times\frac{(1+\sqrt2)+\sqrt3}{(1+\sqrt2)+\sqrt3}]+[\frac{3}{\sqrt2}]$$

= $$[\frac{1-\sqrt2-\sqrt3}{(1-\sqrt2)^2-(\sqrt3)^2}]+[\frac{1-\sqrt2+\sqrt3}{(1-\sqrt2)^2-(\sqrt3)^2}]-2[\frac{1+\sqrt2+\sqrt3}{(1+\sqrt2)^2-(\sqrt3)^2}]+[\frac{3}{\sqrt2}]$$

= $$[\frac{1-\sqrt2-\sqrt3}{1-2\sqrt2+2-3}]+[\frac{1-\sqrt2+\sqrt3}{1-2\sqrt2+2-3}]-2[\frac{1+\sqrt2+\sqrt3}{1+2\sqrt2+2-3}]+[\frac{3}{\sqrt2}]$$

= $$[\frac{1-\sqrt2-\sqrt3}{-2\sqrt2}]+[\frac{1-\sqrt2+\sqrt3}{-2\sqrt2}]-2[\frac{1+\sqrt2+\sqrt3}{2\sqrt2}]+[\frac{6}{2\sqrt2}]$$

= $$[\frac{-1+\sqrt2+\sqrt3}{2\sqrt2}]+[\frac{-1+\sqrt2-\sqrt3}{2\sqrt2}]+[\frac{-2-2\sqrt2-2\sqrt3}{2\sqrt2}]+[\frac{6}{2\sqrt2}]$$

= $$\frac{1}{2\sqrt2}[(-1-1-2+6)+(\sqrt2+\sqrt2-2\sqrt2)+(\sqrt3-\sqrt3-2\sqrt3)]$$

= $$\frac{1}{2\sqrt2}(2-2\sqrt3)$$

= $$\frac{1-\sqrt3}{\sqrt2}$$

= $$\frac{1}{2}(\sqrt2-\sqrt6)$$

=> Ans - (D)

Let $$x=5,z=4,y=3$$

(A) : $$(x-z)^2y =1\times3=3$$ is odd

(B) : $$(x-z)^2y^2=1\times9=9$$ is odd

(C) : $$(x-z)y=1\times3=3$$ is odd

(D) : $$(x-y)^2z=4\times4=16$$ is even

=> Ans - (A)

We are given that p on being divided by d given that quotient q and remainder r, giving us the equation
p = qd + r

From the second relation, we can get the second equation to be q = d'q' + r'

Substituting the value of q from the second equation into the first equation, we get p to be (q'd' + r')d + r
p = q'd'd + r'd + r

Dividing this by dd', the first term will not give any remainder as it is a multiple of dd', and the second and third terms are not multiples of dd', giving the remainder to be r'd +r

Therefore, Option A is the correct answer. 

Expression : $$N = \sqrt{25^{64} \times 64^{25}}$$

= $$\sqrt{(5)^{128}\times(2)^{150}}$$

= $$(5)^{64}\times(2)^{75}$$

= $$(2)^{11}\times(10)^{64}$$

= $$2048\times(10)^{64}$$

Thus, there are 68 digits in the numbers and sum of digits = $$2+0+4+8=14$$

=> Ans - (C)

Let $$p=\frac{1}{q}$$

If $$p$$ increases by 20%, => $$p'=\frac{6p}{5}=\frac{6}{5q}$$

Now, $$p'=\frac{1}{q'}$$

=> $$q'=\frac{1}{p'}$$

=> $$q'=\frac{5q}{6}$$

$$\therefore$$ Percentage decrease in $$q=\frac{1}{6}\times100=16\frac{2}{3}\%$$

=> Ans - (D)

Since, each has the same remainder, we need to find the H.C.F. [(1417-1059),(2312-1417),(2312-1059)]

= H.C.F. (358,895,1253) = 179

Now, when we divide 1059, 1417 and 2312 by 179, we get remainder as 164

$$\therefore$$ $$r+k=164+179=343$$

=> Ans - (C)

Let length of each candle be $$l$$ cm

Time taken to burn each candle is 3 hours and 4 hours respectively.

=> Candle burn in 1 minute = $$\frac{l}{180}$$ cm and $$\frac{l}{240}$$ cm

Let required time be $$t$$ minutes.

Thus, candle burnt in $$t$$ minutes = $$l-\frac{tl}{180}$$ cm and $$l-\frac{tl}{240}$$ cm

According to ques,

=> $$(l-\frac{tl}{180}):(l-\frac{tl}{240})=1:2$$

=> $$2l-\frac{tl}{90}=l-\frac{tl}{240}$$

=> $$l=\frac{tl}{30}(\frac{1}{3}-\frac{1}{8})$$

=> $$\frac{30}{t}=\frac{5}{24}$$

=> $$t=30\times\frac{24}{5}=144$$ minutes

$$\therefore$$ Candles should be lit 144 minutes prior to 5 pm, i.e. at 2:36 pm

=> Ans - (B)

Using, $$\frac{M_1D_1H_1}{W_1}$$ $$=\frac{M_2D_2H_2}{W_2}$$

Let number of articles produced be $$x$$

=> $$\frac{2\times2\times2}{2}=\frac{4\times4\times4}{x}$$

=> $$x=\frac{64}{4}=16$$

=> Ans - (C)

Let speed of A, B and C be $$a,b,c$$ m/s respectively.

Time taken by A to cover $$d$$ metres = Time taken by B to cover $$(d-20)$$ metres

=> $$\frac{s_a}{s_b}=\frac{d}{d-20}$$ ---------------(i)  [Since, speed is directly proportional to distance]

Similarly, Time taken by A to cover $$d$$ metres = Time taken by C to cover $$(d-28)$$ metres

=> $$\frac{s_a}{s_c}=\frac{d}{d-28}$$ --------------(ii)

and Time taken by B to cover $$d$$ metres = Time taken by C to cover $$(d-10)$$ metres

=> $$\frac{s_b}{s_c}=\frac{d}{d-10}$$ -------------(iii)

Equating equations (i) and (ii), => $$\frac{s_b}{s_c}=\frac{d-20}{d-28}$$

Comparing it with equation (iv), => $$\frac{d}{d-10}=\frac{d-20}{d-28}$$

Solving above equation, we get : $$d=100$$ m

=> Ans - (C)

Time taken by the machines working together = $$x$$ hours

According to ques,

=> $$\frac{1}{x+6}+\frac{1}{x+1}+\frac{1}{x+x}=\frac{1}{x}$$

=> $$\frac{(x+6)+(x+1)}{(x+6)(x+1)}=\frac{1}{x}-\frac{1}{2x}$$

=> $$\frac{2x+7}{(x+6)(x+1)}=\frac{1}{2x}$$

=> $$4x^2+14x=x^2+7x+6$$

=> $$3x^2+7x-6=0$$

=> $$3x^2+9x-2x-6=0$$

=> $$(3x-2)(x+3)=0$$

=> $$x=\frac{2}{3},-3$$

$$\because$$ $$x$$ cannot be negative, hence $$x=\frac{2}{3}$$ hours

=> Ans - (A)

Out of first 50 balls, number of blue balls = 49

From now, for each $$x$$ balls, number of blue balls = $$\frac{7x}{8}$$

Total number of balls = $$m=(x+50)$$

According to ques,

=> $$\frac{\frac{7x}{8}+49}{x+50}\geq \frac{9}{10}$$

=> $$\frac{70x}{8}+490\geq9x+450$$

=> $$40\geq\frac{x}{4}$$

=> $$x\leq160$$

$$\therefore$$ To maximize $$m$$, we need to maximize $$x$$, which has a maximum value of 160

=> Maximum number of balls = $$160+50=210$$

=> Ans - (C)

Shortcut : SP = Rs. 636 and CP = Rs. 600

=> Profit % = $$\frac{636-600}{600}\times100$$

= $$\frac{36}{6}=6\%$$

=> Ans - (A)

Let the numbers be $$a$$ and $$b$$

According to ques, => $$ab:(a+b):(a-b)=24:7:1$$

Thus, $$\frac{a+b}{a-b}=\frac{7}{1}$$

=> $$a+b=7a-7b$$

=> $$6a=8b$$

=> $$\frac{a}{b}=\frac{4}{3}$$

Let $$a=4y$$ and $$b=3y$$

Also, $$\frac{ab}{a-b}=\frac{24}{1}$$

=> $$\frac{4y\times3y}{4y-3y}=24$$

=> $$12y^2=24y$$

=> $$y=2$$

$$\therefore$$ Numbers are $$a=8$$ and $$b=6$$

=> Product = $$ab=8\times6=48$$

=> Ans - (B))

Let price paid be each individual be Rs. $$a,b,c,d$$ respecitvely.

=> $$(a+b+c+d)=6000$$ -------------(i)

Also, $$2a=b+c+d$$ --------------(ii)

Solving above equations, => $$a=2000$$ and $$b+c+d=4000$$

Similarly, $$3b=a+c+d$$, => $$b+1500$$ and $$c+d=2500$$

and $$4c=a+b+d$$, => $$c=1200$$

$$\therefore$$ Amount paid by 4th person = Rs. $$1300$$

=> Ans - (D)

Since, the jars are identical (have same capacity). Let quantity of each jar be L.C.M. (2,3) = 6 units

=> Acid in jar one  = 3 units and acid of water in jar 1 = 3 untis

Similarly, Acid in jar two = 4 units and water in jar two = 2 units

When mixed together, ratio of water to acid = $$(3+2):(3+4)=5:7$$

=> Ans - (A)

Let the whole numbers be $$a,b,c,d$$

According to ques, => $$a+b+c=180$$ -------(i)
$$a+b+d=197$$ ------------(ii)
$$a+c+d=208$$ ------------(iii)
$$b+c+d=222$$ -----------(iv)

Adding above equations, we get : $$3(a+b+c+d)=180+197+208+222$$

=> $$(a+b+c+d)=\frac{807}{3}=269$$

Substituting value from equation (i) in above equation,

=> $$d=269-180=89$$

$$\therefore$$ Largest number = 89

=> Ans - (A)

Radius of small pipes = 0.5 cm and big pipes = 3 cm

=> Number of circular pipes required = $$\frac{\pi R^2}{\pi r^2}$$

= $$\frac{3^2}{0.5^2}=\frac{9}{0.25}$$

= $$9\times\frac{4}{1}=36$$

=> Ans - (D)

Dimensions of city after rainfall = 10km x 10km x 1 cm

=> Volume = $$10^7\times10^7\times10$$ mm

= $$10^{15}$$ mm

Volume of raindrop = $$10$$ $$mm^3$$

$$\therefore$$ Number of raindrops = $$\frac{10^{15}}{10}=10^{14}$$

=> Ans - (D)

Let price of each pencil = Rs. $$x$$ and price of each pen = Rs. $$2x$$

Let number of pencils ordered = $$y$$ and number of pens ordered = $$4$$

=> Original cost price = Rs. $$(xy+8x)$$

After interchanging the price, => New price of bill = Rs. $$(4x+2xy)$$

According to ques,

=> $$\frac{4x+2xy}{xy+8x}=1.5$$

=> $$4x+2xy=1.5xy+12x$$

=> $$4+2y=1.5y+12$$

=> $$0.5y=12-4=8$$

=> $$y=\frac{8}{0.5}=16$$

$$\therefore$$ Ratio of pens to pencils = $$\frac{4}{16}=1:4$$

=> Ans - (B)

Let side of square inscribed in the semi circle be $$a$$ cm and radius of semi circle = $$r$$ cm

In right $$\triangle$$, => $$r^2=a^2+(\frac{a}{2})^2$$

=> $$r^2=a^2+\frac{a^2}{4}$$

=> $$r^2=\frac{5a^2}{4}$$

=> $$a^2=\frac{4r^2}{5}$$ --------------(i)

Similarly, let side of another square be $$b$$ cm and radius of same circle = $$r$$ cm

=> $$b^2+b^2=(2r)^2$$

=> $$b^2=2r^2$$ --------------(ii)

$$\therefore$$ Ratio of area of first square to area of second square = $$\frac{a^2}{b^2}$$

Substituting values from equation (i) and (ii), => $$\frac{\frac{4r^2}{5}}{2r^2}$$

= $$2:5$$

=> Ans - (C)

Let original price = Rs. $$x$$

Price after $$p\%$$ increase = $$x+\frac{p}{100}\times x=Rs.$$ $$(x+\frac{px}{100})$$

Price after $$p\%$$ decrease = $$(x+\frac{px}{100})-(\frac{p}{100})(x+\frac{px}{100})$$

According to ques, => $$x+\frac{px}{100}-\frac{px}{100}-\frac{p^2x}{10000}=100$$

=> $$x(1-\frac{p^2}{10000})=100$$

=> $$x=Rs.$$ $$\frac{100}{1-\frac{p^2}{100^2}}$$

=> Ans - (A)

We are given the area of ABCD rectangle = 40 sq. cm and the length of the rectangle i.e. AD to be 10 cm.
This gives the length of the breadth of rectangle = 40/10 = 4 cm. 
The breadth i.e. CD is a chord on the circular face. 
However, there are 2 cases when the chord could be of length = 4 cm :

Now, the perpendicular distance of either of the chord from the center can be calculated using Pythagoras theorem in the triangle OPC. This gives OP = $$\sqrt{\ 5}$$ cm.

Thus, the depth of the water could either be R - $$\sqrt{\ 5}$$ OR R + $$\sqrt{\ 5}$$ i.e. $$3-\sqrt{\ 5}\ or\ 3+\sqrt{\ 5}$$ cm.

Let the common perimeter be $$c$$

So, each side of square = $$\frac{c}{4}$$

=> Circum radius of square = $$r_s=\frac{s}{\sqrt2}=\frac{c}{4\sqrt2}$$

Thus, area of circle circumscribed about the square will be

=> $$A=\pi (r_s)^2=\pi\frac{c^2}{32}$$ -------------(i)

Now, each side of triangle = $$\frac{c}{3}$$

=> Height of triangle = $$\frac{\sqrt3}{2}\times\frac{c}{3}$$

=> Circum radius of triangle = $$r_t=\frac{2}{3}\times(\frac{\sqrt3}{2}\times\frac{c}{3})=\frac{c}{3\sqrt3}$$

So area of the circle circumscribed about the triangle 

=> $$B=\pi (r_t)^2=\pi\frac{c^2}{27}$$ -----------(ii)

$$\therefore$$ Required ratio $$A:B=27:32$$

=> Ans - (C)

Let length, breadth and height be $$l,b,h$$ cm respectively.

=> Surface area of cuboid = $$2(lb+bh+hl)=22$$ -----------(i)

Sum of all edges = $$4(l+b+h)=24 \Rightarrow (l+b+h)=6$$

Squaring both sides, => $$(l^2+b^2+h^2)+2(lb+bh+hl)=36$$

Substituting value from equation (i), we get :

=> $$(l^2+b^2+h^2)+22=36$$

=> $$(l^2+b^2+h^2)=36-22 = 14$$

$$\therefore$$ Diagonal of cuboid = $$\sqrt{l^2+b^2+h^2}=\sqrt{14}$$

=> Ans - (D)

Let radius of cylinder = $$x$$ cm and its height = $$2x$$ cm

Height of cone = $$h=12$$ cm and radius of cone = $$r=5$$ cm

Since, the axes coincide, thus in the two similar triangles, we have : $$\frac{y}{h}=\frac{x}{r}$$

=> $$\frac{12-2x}{12}=\frac{x}{5}$$

=> $$60-10x=12x$$

=> $$12x+10x=22x=60$$

=> $$x=\frac{60}{22}=2\frac{8}{11}$$ cm

=> Ans - (A)

Cool and cold are two states that vary in intensity. For instance, cool is comfortable, but cold is not conducive to oneself. The same relation is displayed by sprain and fracture where sprain is lesser in intensity when compared with fracture. 

Unity and diversity are two opposite concepts altogether because diversity mainly overrides the concept of unity. The same relation is displayed by Lead and Follow, which are opposite poles as well. 

Easy way to look at this: Cow and Dog are two different kinds of animals. The same relation is exhibited by Forests and Mountains, which are two different forms of landscape/land forms. 

Crow : Horse : Shark represents a collection of items belonging to the same broad category of 'Animals'. To complete the analogy, the selected option should also present a set of three items that fall within a distinct common category.

Option D: History : Geography : Economics is the correct choice because all three terms represent a collection of items belonging to the single broader category of 'Academic Subjects' or 'Social Studies Fields'. The other options fail to meet this criterion: Option A mixes containers and an item; Option B presents related but distinct concepts (a location, a person, and an object); and Option C lists three different types of geographical features.
Thus, the correct answer is Option D.

The house has a fan, which is located inside the room. Similarly, pocket has money, which is kept in a purse. 

Here, the customer has expressed that the rate is too high for getting one single tooth pulled out, and that too for work that needs only a minute. 

Hence, statement 1 can be a funny punchline, wherein the dentist mocks the patient by asking her to get all the teeth pulled out, which is not a practical solution to secure a discount. 

Even the second statement is a good punchline that counters the argument made by the patient about the work needing only a minute. 

This makes both statements good punchlines.

The son was talking about the carburetor having some water. Hence, any reason against the practical notions shall be a good punchline. 

Statement 1 is not a funny line, considering the possibility of rain while he was checking the carburetor. It can actually be a valid reason. 

Statement 2 is funny, since the line seems to exaggerate the incident, and had the car fallen off the bride, it would not exist anymore.

The psychiatrist said that the man's wife would be completely different (in the sense that she would experience a major change in her personality) after the treatment. Hence, any line that uses the words 'different woman' in the context of having another person altogether shall be funny. 

1. This is a funny statement as it shows that the words of the psychiatrist were used in a different context altogether, and the man used a punchline in the context of having another woman and his wife finding it out. 

2. This is a funny statement as well as he uses the line in context of there being another woman. However, the two punchlines are opposite in nature as the man's attitude of having another woman is different in the two. 

Both options are apt punchlines are they change the course of discussion altogether by twisting the phrase 'new towels' by first mentioning them as gifts on the anniversary and second by mentioning them as the ones brought from the hotel. In both the cases, the towels won't be new, but the two statements are different ideas altogether. 

Statement 1 is a punchline as B induced humor by saying that the interaction with J got him money and J got experience. The tradeoff is shown with a funny statement in this. 

Statement 2 is a punchline as well, because it is presented in an unusual manner. However, the two statements are entirely different in the way they are presented. 

For the sake of clarity, we shall know that ABCDE represents A as the starting point, and on moving anticlockwise we get B. On the other hand, clockwise movement gives E. 

The following conclusions can be made: 

A and B: The order shall be Q_ZST

Now, Y sits third to the left of X, which means Y's position is third to the left of X (clockwise). 

Also, P is not an immediate neighbor of Q. 

Hence, a possible combination can be: Y_QXZSTP

R can occupy the blank. Hence, the combination, in a clockwise direction, can be YRQXZSTP

Now, Z is third to the left of P. Hence, Third to the left of Q is P.  

For the sake of clarity, we shall know that ABCDE represents A as the starting point, and on moving anticlockwise we get B. On the other hand, clockwise movement gives E.

The following conclusions can be made:

A and B: The order shall be Q_ZST

Now, Y sits third to the left of X, which means Y's position is third to the left of X (clockwise).

Also, P is not an immediate neighbor of Q.

Hence, a possible combination can be: Y_QXZSTP

R can occupy the blank. Hence, the combination, in a clockwise direction, can be YRQXZSTP

Immediate right of S is T.

For the sake of clarity, we shall know that ABCDE represents A as the starting point, and on moving anticlockwise we get B. On the other hand, clockwise movement gives E.

The following conclusions can be made:

A and B: The order shall be Q_ZST

Now, Y sits third to the left of X, which means Y's position is third to the left of X (clockwise).

Also, P is not an immediate neighbor of Q.

Hence, a possible combination can be: Y_QXZSTP

R can occupy the blank. Hence, the combination, in a clockwise direction, can be YRQXZSTP

Third to the left of Z is R. 

For the sake of clarity, we shall know that ABCDE represents A as the starting point, and on moving anticlockwise we get B. On the other hand, clockwise movement gives E.

The following conclusions can be made:

A and B: The order shall be Q_ZST

Now, Y sits third to the left of X, which means Y's position is third to the left of X (clockwise).

Also, P is not an immediate neighbor of Q.

Hence, a possible combination can be: Y_QXZSTP

R can occupy the blank. Hence, the combination, in a clockwise direction, can be YRQXZSTP

Between P and Q (anti clockwise from Q), we have XZST. Hence, four people. 

For the sake of clarity, we shall know that ABCDE represents A as the starting point, and on moving anticlockwise we get B. On the other hand, clockwise movement gives E.

The following conclusions can be made:

A and B: The order shall be Q_ZST

Now, Y sits third to the left of X, which means Y's position is third to the left of X (clockwise).

Also, P is not an immediate neighbor of Q.

Hence, a possible combination can be: Y_QXZSTP

R can occupy the blank. Hence, the combination, in a clockwise direction, can be YRQXZSTP

Here, R is sitting to the immediate left of Q. 

The passage only mentions NIN and NNMB. However, we cannot say anything about the number of institutes that collected data on heights. Hence, the data is inadequate to corroborate the statement. 

The passage states: At age 13, the average height recorded for boys in 2010 is lower than the average for 2005-10 in only one state; Karnataka.

Hence, it is clear that there is data about Karnataka in both the time brackets, and hence we can say for sure that both the agencies have collected data from Karnataka. 

The survey was intended to measure the average height of people in different age groups. However, the passage is silent over the average age of the states. Hence, there is no adequate data to corroborate the statement. 

The passage talks about specific groups (say female in age group of 13 years, or boys at age 13). However, we cannot say anything about the cumulative average of the states. Also, we have no information about the overall average of other states. Hence, data inadequate. 

The passage specifically talks about boys/girls at the age of 13. However, it is silent over the other age groups. Hence, there is no adequate data to corroborate the statement. 

If the word is of 4 letters,
1. Consonants and Vowels are arranged as CVCV, then the code will be : 5 25 5 25
2. Consonants and vowels are arranged as VCVC, then the code will be : 30 5 30 5
3. Consonants and vowels are arranged as CVVC, then the code will be : 5 20 20 5

If the word has 3 letters,
1. Consonants and vowels are arranged as VCV, then the code will be : 0 5 0
2. Consonants and vowels are arranged as CVC, then the code will be : 5 10 5

This is what we can infer from all the codes given to us.
Now, the word is MODE and the consonants and vowels are arranged as CVCV, then the code will be 5 25 5 25 i.e. Option C.

If the word is of 4 letters,
1. Consonants and Vowels are arranged as CVCV, then the code will be : 5 25 5 25
2. Consonants and vowels are arranged as VCVC, then the code will be : 30 5 30 5
3. Consonants and vowels are arranged as CVVC, then the code will be : 5 20 20 5

If the word has 3 letters,
1. Consonants and vowels are arranged as VCV, then the code will be : 0 5 0
2. Consonants and vowels are arranged as CVC, then the code will be : 5 10 5

This is what we can infer from all the codes given to us.
Now, the word is RUN and the consonants and vowels are arranged as CVC, so the code will be 5 10 5 i.e. Option B.

If the word is of 4 letters, 
1. Consonants and Vowels are arranged as CVCV, then the code will be : 5 25 5 25
2. Consonants and vowels are arranged as VCVC, then the code will be : 30 5 30 5
3. Consonants and vowels are arranged as CVVC, then the code will be : 5 20 20 5

If the word has 3 letters,
1. Consonants and vowels are arranged as VCV, then the code will be : 0 5 0
2. Consonants and vowels are arranged as CVC, then the code will be : 5 10 5

This is what we can infer from all the codes given to us.
Now, ICON has 4 letters and consonants and vowels are arranged as VCVC, so the code will be 30 5 30 5 i.e. Option A.

The code for AGE is directly given to be 0 5 0 i.e. Option D.

If the word is of 4 letters,
1. Consonants and Vowels are arranged as CVCV, then the code will be : 5 25 5 25
2. Consonants and vowels are arranged as VCVC, then the code will be : 30 5 30 5
3. Consonants and vowels are arranged as CVVC, then the code will be : 5 15 15 5 and if the vowels are identical, then the code will be 5 20 20 5.

If the word has 3 letters,
1. Consonants and vowels are arranged as VCV, then the code will be : 0 5 0
2. Consonants and vowels are arranged as CVC, then the code will be : 5 10 5

This is what we can infer from all the codes given to us.
Now, the word is REAL and the consonants and vowels are arranged as CVVC with distinct vowels, then the code will be 5 15 15 5 i.e. Option B.

In the given arrangement, the next batch's code is written by first writing previous batch's last word, then next words from the beginning, then next 2 words from the end, then next 3 letters from the beginning.

So, if the previous batch's code is 12345678 (as there are 8 words and we assign them numbers for easier calculation), the next batch's code will be 8 12 76 345.

3rd batch will have 5 81 43 276

4th batch will have 6 58 72 143.
If 2nd batch's code i.e. 8 12 76 345 is "to confidence hard you leads work and success", 4th batch's code i.e. 6 58 72 143 will be: "leads success to you hard confidence and work" i.e. Option C.

In the given arrangement, the next batch's code is written by first writing previous batch's last word, then next words from the beginning, then next 2 words from the end, then next 3 letters from the beginning.
So, if the previous batch's code is 12345678 (as there are 8 words and we assign them numbers for easier calculation), the next batch's code will be 8 12 76 345.
3rd batch will have 5 81 43 276
4th batch will have 6 58 72 143
5th batch will have 3 65 41 872 and,
6th batch will have 2 36 78 541. If this code is "and pencil by all boys used are pen", then 1st  batch's code i.e. 12345678 will be "pen and pencil are used by all boys" i.e. Option D.

In the given arrangement, the next batch's code is written by first writing previous batch's last word, then next words from the beginning, then next 2 words from the end, then next 3 letters from the beginning.
So, if the previous batch's code is 12345678 (as there are 8 words and we assign them numbers for easier calculation), the next batch's code will be 8 12 76 345.
3rd batch will have 5 81 43 276
4th batch will have 6 58 72 143
5th batch will have 3 65 41 872 and,
6th batch will have 2 36 78 541.
If 3rd batch's code i.e. 5 81 43 276 is "night succeed day and hard work to for", then passcode for 6th batch i.e. 2 36 78 541 is "work hard for to succeed night and day".
Thus, the correct answer is Option B.

In the given arrangement, the next batch's code is written by first writing previous batch's last word, then next words from the beginning, then next 2 words from the end, then next 3 letters from the beginning.
So, if the previous batch's code is 12345678 (as there are 8 words and we assign them numbers for easier calculation), the next batch's code will be 8 12 76 345.
3rd batch will have 5 81 43 276
4th batch will have 6 58 72 143
5th batch will have 3 65 41 872 and,
6th batch will have 2 36 78 541. 
So, if 5th batch's code i.e. 3 65 41 872 is "visit in zoo should the we time day", then "zoo we the should visit day time in" is 5 81 43 276 i.e. the code for 3rd batch.
Thus, the correct answer is Option A.

We shall test each of the options and try to negate by coming up with a scenario where the particular conclusion won't hold true. If we cannot do that for a particular conclusion, that shall be the valid one.

1. Some students are chairs: We don't have any information about the connection between Books and Chairs. There can be an instance where students who are not books can come under the header of chairs. However, the other instance where chairs and students are disjoint sets can hold true as well. Hence, an invalid conclusion. 

2. No college is a chair: Since it is clearly given that all colleges are books, and no book can be classified as a chair, we can definitely say that no college is a chair. 

3. Some students are books: We know that all colleges are books, and at the same time, some students are college as well. Hence, we can definitely conclude that students which are classified as college are books as well. 

4. Some students are not chairs: We definitely know that some students are college, which in turn are books. Further, it is also given that no book is a chair. Hence, students which are college cannot be chair. 

Only stars are moons, which shall be interpreted in this way: All moons are stars. 

We shall verify each option:

1. Some moons are not planets: Since we know that only stars can be classified as moons, it is always true that some moons are not planets. 

2. No moon is a cosmos: We know that only stars are moons; this is again, a valid conclusion. 

3. No cosmos is a planet: We have no relation given for planet and cosmos; hence, we cannot say for sure whether some cosmos are planets or not. 

4. No star is a planet: We have no relation given for stars and planets. We only know that no planets are moons. However, there might or might not be stars which are not moon but are planet indeed. 

Testing each of the options: 

1. All hospitals are medicines: This is directly given in the question.

2. Some colleges are medicines: We know that some colleges are hospitals, and all hospitals are medicines. Hence, the colleges which are hospitals are definitely medicines. 

3 and 4: We don't have any relation given between colleges and machines. Hence, either of the statements shall hold true. 

We shall verify each of the options:

1. Some bags are plates: We don't have any relation given for bags and plates. Hence, an invalid conclusion. 

2. Some bags are not plates: We know that some chairs are bags, and none of the chairs are plates. Hence, the chairs that come under bags are not plates. This is a valid conclusion. 

3 and 4: We don't have any relation given about books and chairs, hence either of these shall be true. 

Let us verify each of the options: 

1. Some dancers are not players: There can be an instance where players are a bigger set, only some of them fall within heroes and musicians, and in the rest of the set of players, all dancers are classified. Hence, this is an invalid conclusion.

2. No dancer is a musician: Since all dancers are heroes, and none of the dancers are heroes, we can say that none of the dancers are musicians. 

3. Some players are heroes: Since some musicians are players, and all musicians are heroes, we can say the players that can be classified as musicians are heroes. 

4. Some players are not dancers: Since some musicians are players, all musicians are heroes, and no dancer is a hero, we can say that players which are musicians are definitely not dancers. 

We know: 

P>R

Q>S and T

U>S (2 years)

P- 2007/2008

Oldest in 2005

Now, we can see that P is not the oldest. Hence, the oldest shall be either U or Q. 

The birth years shall be: 2005, 2006, 2007, 2008, 2009, 2010.

Case 1: When the oldest is U

Hence, U (2005), S (2007), Q (2006), P (2008), R/T (2009/2010)

Case 2: When Q is the oldest

Hence, Q (2005), U (2006), S (2008), P (2007), R/T (2009/2010)

It has to be case 1, where P is younger than S. Hence, all the options must be true except for D, as either R or T can take 2009.

We know:

P>R

Q>S and T

U>S (2 years)

P- 2007/2008

Oldest in 2005

Now, we can see that P is not the oldest. Hence, the oldest shall be either U or Q.

The birth years shall be: 2005, 2006, 2007, 2008, 2009, 2010.

Case 1: When the oldest is U

Hence, U (2005), S (2007), Q (2006), P (2008), R/T (2009/2010)

Case 2: When Q is the oldest

Hence, Q (2005), U (2006), S (2008), P (2007), R/T (2009/2010)

It is case 1 where U is the oldest. There, Q has to be from 2006.

We know:

P>R

Q>S and T

U>S (2 years)

P- 2007/2008

Oldest in 2005

Now, we can see that P is not the oldest. Hence, the oldest shall be either U or Q.

The birth years shall be: 2005, 2006, 2007, 2008, 2009, 2010.

Case 1: When the oldest is U

Hence, U (2005), S (2007), Q (2006), P (2008), R/T (2009/2010)

Case 2: When Q is the oldest

Hence, Q (2005), U (2006), S (2008), P (2007), R/T (2009/2010)

Hence, the cases can be (youngest to oldest): R/T, P, S, Q, U or R/T, S, P. U, Q.

We know:

P>R

Q>S and T

U>S (2 years)

P- 2007/2008

Oldest in 2005

Now, we can see that P is not the oldest. Hence, the oldest shall be either U or Q.

The birth years shall be: 2005, 2006, 2007, 2008, 2009, 2010.

Case 1: When the oldest is U

Hence, U (2005), S (2007), Q (2006), P (2008), R/T (2009/2010)

Case 2: When Q is the oldest

Hence, Q (2005), U (2006), S (2008), P (2007), R/T (2009/2010)

It is case 2 where P is older than U. And there, two cases can be made depending on the year of R/T.

If the eldest child was born in 2005, then all the children were born in the years ranging from 2005 to 2010.
Case 1: P was born in 2007.
As U is 2 years older than S, U was either born in 2008 or 2006.
Case 1A: U was born in 2008. S was born in 2010. As P is older than R, R must be born in 2009. Also, as Q is older than T, T must be born in 2006 and Q must be born in 2005.
Case 1B: U was born in 2006. S was born 2 years later i.e. 2008. Now, Q must be older than S which means that Q was born in 2005. R and T are born in either 2009 or 2010.

Case 2: P was born in 2008. 
As U is 2 years older than S, U was either born in 2005 or 2007.
Case 2A: U was born in 2005. S was born in 2007. As Q is older than S, Q was born in 2006. R and T are born in either of 2009 or 2010.
Case 2B: U was born in 2007 so S was born in 2009. As P is older than R, R must be born in 2010. And as Q is older than T, Q must be born in 2005 and T must be born in 2006.

The possibilities when T is older than S are cases 1A and 2B.
In both the cases Q was born in 2005 and T was born in 2006.
So, only I and II statements are definitely true.