CAT 1998 Question Paper

The last digit of powers of 2 follow a pattern as given below.

The last digit of $$2^1$$ is 2
The last digit of $$2^2$$ is 4
The last digit of $$2^3$$ is 8
The last digit of $$2^4$$ is 6

The last digit of $$2^5$$ is 2
The last digit of $$2^6$$ is 4
The last digit of $$2^7$$ is 8
The last digit of $$2^8$$ is 6

Hence, the last digit of $$2^{51}$$ is 8

Let the volume of the cup be V.
Hence, after removing three cups of alcohol from the first container,

Volume of alcohol in the first container is 500-3V
Volume of water in the second container is 500 and volume of alcohol in the second container is 3V.
So, in each cup, the amount of water contained is $$\frac{500}{500+3V}*V$$

Hence, after adding back 3 cups of the mixture, amount of water in the first container is $$0+\frac{1500V}{500+3V} $$
Amount of alcohol contained in the second container is $$3V - \frac{9V^2}{500+3V} = \frac{1500V}{500+3V}$$

So, the required proportion of water in the first container and alcohol in the second container are equal.

For a number to be divisible by 8, last 3 digits must be divisible by 8.

Last 3 digits of this number are 354.

354 mod 8 = 2

Hence, 2 is the remainder.

The ranking list would be in the order A, B, C, D......., X, Y, Z. Now the A wins all his 25 matches, B wins 24 matches and lost to A. C wins 23 matches and lost to A and B. In this way N 12 matches and looses 13 matches to A,B,C,D....,M

The best word to use for "links" is "forging".

Hence, "focusing on forging European links" is the correct phrase.

Bank deposits are countable. So they swell. They don't flourish. "To flourish" means to develop. The correct answer is option b.

There is no error in the given sentence. "An inexplicable phenomenon" means a phenomenon which cannot be explained. So the usage is contextually as well as grammatically correct.

"cannot scold freely" means "cannot scold whenever the management want". This can be replaced by "cannot scold at will."

Option C and Option D are incorrect as the author talks about writing without affectation i.e. writing without any pretension. Hence, it can be mistaken for writing without consideration or care and not writing fast. 

Between options A and B, A contains the correct phrase 'at random'. The phrase means without a care and in a disorderly manner. "Writing  randomly" does not carry the same implication. Also, here the modifier 'random' is a misplaced modifier. It is modifying the way of writing instead of modifying what is written. 

Lukewarm is the correct usage in the first blank as it means not entusiastic. "Electifies" correctly matches the second blank. Hence the correct option is B.