# Recent exams in GATE Overflow Tests

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50 Marks, 90 Minutes, 30 Questions
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Fourier series of the periodic function (period 2π) defined by $f(x) = \begin{cases} 0, -p < x < 0\\x, 0 < x < p \end{cases} \text { is }\\ \frac{\pi}{4} + \sum \left [ \frac{1}{\pi n^2} \left(\cos n\pi - 1 \right) \cos nx - \frac{1}{n} \cos n\pi \sin nx \right ]$ ... $\frac{{\pi }^2 }{4}$ $\frac{{\pi }^2 }{6}$ $\frac{{\pi }^2 }{8}$ $\frac{{\pi }^2 }{12}$
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Many microprocessors have a specified lower limit on clock frequency (apart from the maximum clock frequency limit) because ?
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We can simply do a binary search in the array of natural numbers from $1..n$ and check if the cube of the number matches $n$ (i.e., check if $a[i] * a[i] * a[i] == n$). This check takes $O(\log n)$ ... cannot be lower than $\log n$. (It must be $\Omega \left( \log n \right)$). So, (D) is also false and (C) is the correct answer.
5
Consider a file of $16384$ records. Each record is $32$ $bytes$ long and its key field is of size $6$ $bytes$. The file is ordered on a non-key field, and the file organization is unspanned. The file is stored in a file system with block size $1024$ $bytes$, and the size of ... and second-level blocks in the multi-level index are respectively $8$ and $0$ $128$ and $6$ $256$ and $4$ $512$ and $5$
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The cube root of a natural number $n$ is defined as the largest natural number $m$ such that $(m^3 \leq n)$ . The complexity of computing the cube root of $n$ ($n$ is represented by binary notation) is $O(n)$ but not $O(n^{0.5})$ $O(n^{0.5})$ but not $O((\log n)^k)$ for any constant ... $m>0$ $O( (\log \log n)^k )$ for some constant $k > 0.5$, but not $O( (\log \log n)^{0.5} )$
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The corresponding English meaning: If $P(x)$ is true for all $x$, or if $Q(x)$ is true for all $x$, then for all $x$, either $P(x)$ is true or $Q(x)$ is true. This is always true and hence valid. To understand deeply, consider $X = \{3,6,9,12\}$. For ... in proving validity of many statements as is its converse given below: $\exists(x)(P(x)) \equiv \neg \forall (x)(\neg P(x))$ Correct Answer: $A$
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Which of the following predicate calculus statements is/are valid? $(\forall (x)) P(x) \vee (\forall(x))Q(x) \implies (\forall (x)) (P(x) \vee Q(x))$ $(\exists (x)) P(x) \wedge (\exists (x))Q(x) \implies (\exists (x)) (P(x) \wedge Q(x))$ ... $(\exists (x)) (P(x) \vee Q(x)) \implies \sim (\forall (x)) P(x) \vee (\exists (x)) Q(x)$
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so D or E ?
11
Both the programs are equivalent in the sense that the output will be the same at the end of execution. Q just writes 1 to u but this will be overwritten by the following write of 0. So, in any computer both P and Q should produce the same result at the end of execution. Correct Answer: $D$
12
I assume 2^2^k is evaluated as 2^(2^k) In each iteration of while loop j is becomeing 2^2^l (where l is the loop iteration count) and loop terminates when j = 2^2^k. So, l must be equal to k when loop terminates. So, complexity of while loop is $\Theta(k)$. Now, the outher for loop runs for $n$ iterations and hence the complexity of the entire code is $\Theta(nk)\\ =\Theta(n\log \log n)$
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What is the time complexity? main() { n=2^2^k, k>0 for(i = 1 to n) { j=2 while(j ≤ n) { j=j^2 } } }
14
Yeap, that is what I meant...thanks
15
their is the second option is true. Option 2 : Code A uses lesser memory and is faster than Code B If we are define 3 variable then low memory used. and if go with the 4 variable then every time d=(a-b) firstly. so the code becomes slow. so the I m go with Option 2 : Code A uses lesser memory and is faster than Code B.
16
Lets take the English meaning Government will not be unpopular $\implies$ People will not suffer $\implies$ Either no inflation or government regulates it $\implies$ If no regulation then no inflation $\implies$ if no regulation then no wage or price rise In your statement, (W+P)->G ... rt? So, a, b and d are answers. I misread the first sentence earlier. That is why I posted only (a) as answer.
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To put these things in English sentences is the mistake I commited..to ammend it, W=wages raised,P=price raised,I=Inflation occured,G=government regulates it,PS=people suffer,GU=government becomes unpopular....here are relations...(W+P)->I , I->(G+Pe) , Pe-> GU....with the ... now, as given in the option B if we make value of G =0(not regulated) then both W and P has to be zero......thanks
18
@Shaun Patel : In option (b), if inflation is not regulated, then it is not necessary that wages are not raised, i.e. wages might have been raised, because then inf;ation would have occured, and still we could have said that inflation is not regulated, because then people will suffer. Similar case for option (d). So option (b) and (d) are incorrect.
19
A is surely corrrect but what about B and D...For B,D, as people will not suffer(concluded) and government has not regulated the inflation(given in options) then it can be concluded that there is no inflation and hence no price/wages are raised....isn't it?
20
Pankaj and Mythili were both asked to write the code to evaluate the following expression: $a - b + c/(a-b) + (a-b)^2$ Pankaj writes the following code statements (Code A): print (a-b) + c/(a-b) + (a-b)*(a-b) Mythili writes the following code statements (Code ... Code B Option 3 : Code A uses more memory and is faster than Code B Option 4 : Code A uses more memory and is slower than Code B Like
21
It is told in the question "If the people suffer, the government will be unpopular". And "government will not be unpopular" means, people will not suffer. It is like $A \rightarrow B$ is true and ~B is given. So, ~A must be true. So, (A) is valid (always true). Lets take ... if no regulation then no wage or price rise So, (B) and (D) are valid (always true) and (C) and (E) are not valid.
22
If either wages or prices are raised, there will be inflation. If there is inflation, then either the government must regulate it or the people will suffer. If the people suffer, the government will be unpopular. Government will not be unpopular. Which of the ... wages are not raised Prices are not raised If the inflation is not regulated, then the prices are not raised Wages are not raised
23
50 Marks, 90 Minutes, 30 Questions
24
50 Marks, 100 Minutes, 30 Questions
25
50 Marks, 90 Minutes, 30 Questions
26
50 Marks, 90 Minutes, 30 Questions
27
50 Marks, 90 Minutes, 30 Questions
28
50 Marks, 90 Minutes, 30 Questions
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50 Marks, 90 Minutes, 30 Questions
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50 Marks, 90 Minutes, 30 Questions
31
50 Marks, 90 Minutes, 30 Questions
32
From Wikipedia: When a connection is requested by an application, the application indicates to the network The Type of Service required The Traffic Parameters of each data flow in both directions The Quality of Service (QoS) Parameters requested in each direction These parameters form the traffic descriptor for the connection.
33
Need the clear concept of hierarchy of Page table.
34
To say P=NP which one of the following is sufficient? (All reductions in polynomial time) A. Reduction of a NP problem to a P problem B. Reduction of a NP-complete problem to a P problem C. Reduction of a P problem to an NP problem D. Reduction of a P problem to an NP-complete problem
35
The decimal value $0.5$ in IEEE single precision floating point representation has fraction bits of $000\dots 000$ and exponent value of $0$ fraction bits of $000\dots 000$ and exponent value of $−1$ fraction bits of $100\dots 000$ and exponent value of $0$ no exact representation
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The truth table ${\begin{array}{|c|c|c|}\hline \textbf{X}& \textbf{Y}& \textbf{(X,Y)} \\\hline 0& 0& 0 \\ \hline 0& 1&0\\ \hline 1& 0& 1 \\\hline 1& 1& 1 \\\hline \end{array}}$ represents the Boolean function $X$ $X + Y$ $X \oplus Y$ $Y$
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The worst case running time to search for an element in a balanced binary search tree with $n2^{n}$ elements is $\Theta(n\log n)$ $\Theta(n2^n)$ $\Theta(n)$ $\Theta(\log n)$
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Assuming $P \neq NP$, which of the following is TRUE? $NP- \ complete = NP$ $NP-complete \cap P = \phi$ $NP-hard = NP$ $P = NP-complete$
39
Consider the following logical inferences. $I_{1}$: If it rains then the cricket match will not be played. The cricket match was played. Inference: There was no rain. $I_{2}$: If it rains then the cricket match will not be played. It did not rain. Inference: The cricket match ... inference $I_{1}$ is not correct but $I_{2}$ is a correct inference Both $I_{1}$ and $I_{2}$ are not correct inferences
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60 Marks, 100 Minutes, 30 Questions
41
30 Marks, 60 Minutes, 30 Questions