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#58781
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3 answers
29 votes
GATE CSE 2007 | Question: 13
The maximum number of binary trees that can be formed with three unlabeled nodes is:$1$5$4$3$
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#58782
26.2k
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4 answers
27 votes
GATE CSE 2007 | Question: 12
The height of a binary tree is the maximum number of edges in any root to leaf path. The maximum number of nodes in a binary tree of height $h$ is:$2^h -1$2^{h-1} -1$2^{h+1} -1$2^{h+1}$
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#58783
21.3k
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4 answers
26 votes
GATE CSE 2007 | Question: 11, ISRO2009-36, ISRO2016-21
Consider a disk pack with $16$ surfaces, $128$ tracks per surface and $256$ sectors per track. $512$ bytes of data are stored in a bit serial manner in a sector. The ... bits$256$ Mbyte, $28$ bits$512$ Mbyte, $20$ bits$64$ Gbyte, $28$ bits
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#58784
13.5k
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1 answers
22 votes
GATE CSE 2007 | Question: 10
Consider a $4$-way set associative cache consisting of $128$ lines with a line size of $64$ words. The CPU generates a $20-bit$ address of a word in main memory. The number of ... $7, 7, 6$7, 5, 8$9, 5, 6$
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#58785
3.4k
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1 answers
19 votes
GATE CSE 2007 | Question: 9
Consider the following Boolean function of four variables:$f(w, x, y, z) = \Sigma(1, 3, 4, 6, 9, 11, 12, 14)$The function isindependent of one variables.independent of two variables.independent of three variables.dependent on all variables
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#58786
21.7k
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6 answers
36 votes
GATE CSE 2007 | Question: 8, ISRO2011-31
How many $3$-to-$8$ line decoders with an enable input are needed to construct a $6$-to-$64$ line decoder without using any other logic gates?$7$8$9$10$
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#58787
15.7k
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3 answers
38 votes
GATE CSE 2007 | Question: 7
Which of the following is TRUE?Every subset of a regular set is regularEvery finite subset of a non-regular set is regularThe union of two non-regular sets is not regularInfinite union of finite sets is regular
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#58788
5.8k
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2 answers
25 votes
GATE CSE 2007 | Question: 6
Which of the following problems is undecidable?Membership problem for CFGsAmbiguity problem for CFGsFiniteness problem for FSAsEquivalence problem for FSAs
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#58789
10.5k
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3 answers
19 votes
GATE CSE 2007 | Question: 4
Let $G$ be the non-planar graph with the minimum possible number of edges. Then $G$ has9 edges and 5 vertices9 edges and 6 vertices10 edges and 5 vertices10 edges and 6 vertices
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#58790
10.5k
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4 answers
37 votes
GATE CSE 2007 | Question: 3
What is the maximum number of different Boolean functions involving $n$ Boolean variables?$n^2$2^n$2^{2^n}$2^{n^2}$
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#58791
8.9k
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3 answers
27 votes
GATE CSE 2007 | Question: 2
Let $S$ be a set of $n$ elements. The number of ordered pairs in the largest and the smallest equivalence relations on $S$ are:$n$ and $n$n^2$ and $n$n^2$ and $0$n$ and $1$
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#58792
6.7k
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2 answers
17 votes
GATE CSE 2007 | Question: 1
Consider the following two statements about the function $f(x)=\left\vert x\right\vert$:P. $f(x)$ is continuous for all real values of $x$.Q. $f(x)$ is differentiable for ... $P$ and $Q$ are true.Both $P$ and $Q$ are false.
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#58793
9.1k
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11 answers
27 votes
GATE CSE 2005 | Question: 52
A random bit string of length n is constructed by tossing a fair coin n times and setting a bit to 0 or 1 depending on outcomes head and tail, respectively. The probability that two such ... $1 - \frac{1}{2^n}$
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#58794
6.2k
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9 answers
23 votes
GATE CSE 2005 | Question: 51
Box $P$ has $2$ red balls and $3$ blue balls and box $Q$ has $3$ red balls and $1$ blue ball. A ball is selected as follows: (i) select a box (ii) choose a ball from ... $ is:$\dfrac{4}{19}$\dfrac{5}{19}$\dfrac{2}{9}$\dfrac{19}{30}$
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#58795
8.6k
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8 answers
28 votes
GATE CSE 2005 | Question: 50
Let $G(x) = \frac{1}{(1-x)^2} = \sum\limits_{i=0}^\infty g(i)x^i$, where $|x| < 1$. What is $g(i)$?$i$i+1$2i$2^i$
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#58796
6.3k
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3 answers
21 votes
GATE CSE 2005 | Question: 49
What are the eigenvalues of the following $2\times 2$ matrix? $\left( \begin{array}{cc} 2 & -1\\ -4 & 5\end{array}\right)$$-1$ and $1$1$ and $6$2$ and $5$4$ and $-1$
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#58797
7.8k
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4 answers
20 votes
GATE CSE 2005 | Question: 48
Consider the following system of linear equations : $2x_1 - x_2 + 3x_3 = 1$ $3x_1 + 2x_2 + 5x_3 = 2$ $-x_1+4x_2+x_3 = 3$ The ... hasno solutiona unique solutionmore than one but a finite number of solutionsan infinite number of solutions
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#58798
8.5k
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2 answers
16 votes
GATE CSE 2005 | Question: 47
Which one of the following graphs is NOT planar? G1G2G3G4
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#58799
7.9k
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4 answers
32 votes
GATE CSE 2005 | Question: 46
Consider the set $H$ of all $3 * 3$ ... $H$ is:a groupa monoid but not a groupa semi group but not a monoidneither a group nor a semi group
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#58800
14.0k
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9 answers
63 votes
GATE CSE 2005 | Question: 44
What is the minimum number of ordered pairs of non-negative numbers that should be chosen to ensure that there are two pairs $(a,b)$ and $(c,d)$ in the chosen set such that, $a \equiv c\mod 3$ and $b \equiv d \mod 5$4$6$16$24$
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