aptitude overflow book

Aptitude Overflow Book

December 13, 2015 by Arjun Suresh 1 Comment

Updated April 2016 April 2016 (excluding General Awareness and Computer Knowledge) 86,502 total views, 52 views today

86,502 total views, 52 views today

GATE Overflow
Aptitude Overflow

Answered: GATE CSE 2010 | Question: 3

The number of reflexive relations is given by $2^{n^{2}-n}$. The reasoning is not always very clear so here is the explanation: If the relation must be reflexive means we need to have all the self-pairs, e.g. (1,1) for all elements in the set. So choice for these is one as they have to be included, no matter what. Now come the other pairs left. These may or may not be included and it will not affect the overall reflexivity of the relation, as all self-pairs are already selected. So, total self-pairs = $n$, and remaining pairs = ${n^2}-n$ , which is total… [...]

Answered: GATE CSE 2021 Set 1 | Question: 52

Let $A = \begin{pmatrix} 0 & 1 & 1 & 1\\ 1& 0& 1 & 1\\ 1& 1 & 0 & 1 \\1 & 1 & 1 & 0 \end{pmatrix}$ Characteristic equation $ \mid A – \lambda I \mid = 0$ $\implies \begin{vmatrix} -\lambda & 1 & 1 & 1\\ 1& -\lambda & 1 & 1\\ 1& 1 & -\lambda & 1 \\1 & 1 & 1 & -\lambda \end{vmatrix} = 0$ Perform the operation, $C_{4} \rightarrow C_{1} + C_{2} + C_{3} + C_{4}$, we get $\implies \begin{vmatrix} -\lambda & 1 & 1 & 3-\lambda\\ 1& -\lambda & 1 &… [...]

Answered: CMI2016-A-6

Let start = 4 & end = 4 ; therefore m =4 , we know 4 is not a Prime hence goes to else part. Now, j becomes -4 & k becomes 4. & loop stops. If we check options now, option b) is eliminated while a) & b) come as true. Lets now take start =4 & end =5. Therefore m = 4, same happens as above & values in j=-4 &. k=4. Now m++, & m becomes 5, for m=5, we will get True as m is a prime, so if() part works. Now, i becomes 5 &… [...]

Answered: TIFR-2019-Maths-B: 5

True By the property: Rank(AB) [...]

Answered: GATE CSE 2021 Set 2 | Question: 44

The way the question is framed, I do not agree with the concept at all. A number is after all a number, be it big endian or little endian. The main concept of Big endian or little endian is as follows: Big Endian: In computer system which is big endian, the lower order byte of the data in the memory maps to the higher (big) order byte of the registers in CPU. (see figure below) Little Endian: In computer system which is little endian, the lower order byte of the data in the memory maps to the lower (little)… [...]

Answered: ISI2018-MMA-3

This is a direct application of Legendre's formula. For any factorial, the largest exponent of a prime number say ‘p’ in the factorial of any number say ‘x’ can be found out using the formula shown below: $\left \lfloor \dfrac{x}{p} \right \rfloor + \left \lfloor \dfrac{x}{p^{2}} \right \rfloor + \left \lfloor \dfrac{x}{p^{3}} \right \rfloor+ …. until \: becomes \:zero$ Logical Proof: Suppose you want to find exponent of 2 in 10! i.e. $1.2.3.4.5.6.7.9.10$ Then 2,4,6,8 and 10 will contribute single 2. Therefore we have 5 twos. BUT BUT BUT, 4 has one more 2 to contribute. And similarly, 8 has 2 more twos to contribute,… [...]

Answered: NIELIT 2019 Feb Scientist C - Section A: 19

Since, Seetha is $7^{th}$ from the left and Leena is $9^{th}$ from the right, when Seetha replace Leena, the position of Seetha from the right = $9.$ As per question, Seetha’s position from the left after interchanging $=11.$ Hence, the no. of girls in the row $$\begin{align}&=\text{(Seetha’s position from the left + Seetha’s position from the right)-1}\\&=(9+11) -1\\&= 20-1\\&= 19\end{align}$$ So, answer is None of the above. [...]

Answered: NIELIT 2017 DEC Scientific Assistant A - Section A: 6

All of the girls agree that the first three numbers are 995. Three of them agree that the fourth number is 9. Three agree that the fifth number is 2. Three agree that the sixth number is 6; three others agree that the seventh number is also 6. "Option A" is the best choice because it is made up of the numbers that most of the girls agree they saw. [...]

Answered: NIELIT 2016 MAR Scientist D: 8

Correct Answer: (D) Explanation: This game introduces the idea of reciprocal causation. For example, the constraint that says “If A, then B, and if B, then A” should be transcribed in one of the following two ways, based on the configurations of the other variables in the diagram: You will run into reciprocal causation in the final constraint of this logic game. Here are the final diagrams that you should create: Notice how the reciprocal causation constraints are diagrammed. Be aware of the implications of these constraints. For instance, if $B$ is not sent (diagram B), then $A$ cannot… [...]

Answered: NIELIT 2016 MAR Scientist D: 7

Answered: NIELIT 2016 MAR Scientist D: 6

Correct Answer: (A) Explanation: This game introduces the idea of reciprocal causation. For example, the constraint that says “If $A$, then $B$, and if $B$, then $A$” should be transcribed in one of the following two ways, based on the configurations of the other variables in the diagram: You will run into reciprocal causation in the final constraint of this logic game. Here are the final diagrams that you should create: Notice how the reciprocal causation constraints are diagrammed. Be aware of the implications of these constraints. For instance, if $B$ is not sent (diagram B), then $A$ cannot be sent… [...]

Answered: NIELIT 2016 MAR Scientist D: 33

The answer is (C). three [...]

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