CAT Questions

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Let A, B, C be the respective events of solving the problem and A , B, C be the respective events of not solving the problem. Then A, B, C are independent event

∴A, B, C are independent events

Now,  P(A) = 1/2 , P(B) = 1/3 and P(C)=1/4

 PA=12, PB=23, PC= 34

∴ P( none  solves the problem) = P(not A) and (not B) and (not C)  

                  = PA∩B∩C 

                  = PAPBPC         ∵ A, B, C are Independent                       

                  =  12×23×34  

                  = 14  

Hence, P(the problem will be solved) = 1 - P(none solves the problem) 

                = 1-14= 3/4

Given 373+353+283-3x37x35x28372+352+282-37x35-35x28-37x28

It is in the form of

 a3+b3+c3-3abca2+b2+c2-ab-bc-ca= a + b + c

Here a = 37, b = 35 & c = 28 

=> a + b + c = 37 + 35 + 28 = 100

Therefore,   = 100

A conjunction is a word that joins words, clauses, phrases or sentences.

For example but, and, or, nor, yet for, so, although, since, because, unless, when, where, while, etc.

There are four types of conjunctions:

1. Subordinating Conjunction

2. Correlative Conjunction

3. Phrasal Conjunction

4. Coordinating Conjunction

In the given sentence, "She is not only a great singer but also an exceptional dancer" Not Only But Also is a type of Correlative conjunction.

Here all the given options are Exothermic reactions. Exothermic reactions are those reactions which involves the release of heat.

Generally all the combining reactions are exothermic in nature.

From all the hints given, 

only 042 satisfies and it unlocks the key.