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10 votes
4 answers
9221
GATE CSE 1997 | Question: 4.1
What is the maximum value of the function $f(x) = 2x^2 - 2x + 6$ in the interval $\left[0,2 \right]$? 6 10 12 5.5
What is the maximum value of the function $f(x) = 2x^2 - 2x + 6$ in the interval $\left[0,2 \right]$?610125.5
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24 votes
4 answers
9222
GATE CSE 1997 | Question: 3.3
In the lattice defined by the Hasse diagram given in following figure, how many complements does the element ‘$e$’ have? $2$ $3$ $0$ $1$
In the lattice defined by the Hasse diagram given in following figure, how many complements does the element ‘$e$’ have?$2$$3$$0$$1$
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17 votes
3 answers
9223
GATE CSE 1997 | Question: 3.2
Which of the following propositions is a tautology? $(p \vee q) \rightarrow p$ $p \vee (q \rightarrow p)$ $p \vee (p \rightarrow q)$ $p \rightarrow (p \rightarrow q)$
Which of the following propositions is a tautology?$(p \vee q) \rightarrow p$$p \vee (q \rightarrow p)$$p \vee (p \rightarrow q)$$p \rightarrow (p \rightarrow q)$
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18 votes
5 answers
9225
GATE CSE 1997 | Question: 1.3
The determinant of the matrix $\begin{bmatrix} 6 & -8 & 1 & 1 \\ 0 & 2 & 4 & 6 \\ 0 & 0 & 4 & 8 \\ 0 & 0 & 0 & -1 \end{bmatrix}$ $11$ $-48$ $0$ $-24$
The determinant of the matrix $\begin{bmatrix} 6 & -8 & 1 & 1 \\ 0 & 2 & 4 & 6 \\ 0 & 0 & 4 & 8 \\ 0 & 0 & 0 & -1 \end{bmatrix}$$11$$-48$$0$$-24$
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20 votes
2 answers
9226
GATE CSE 1997 | Question: 1.1
The probability that it will rain today is $0.5$. The probability that it will rain tomorrow is $0.6$. The probability that it will rain either today or tomorrow is $0.7$. What is the probability that it will rain today and tomorrow? $0.3$ $0.25$ $0.35$ $0.4$
The probability that it will rain today is $0.5$. The probability that it will rain tomorrow is $0.6$. The probability that it will rain either today or tomorrow is $0.7$...
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25 votes
5 answers
9227
GATE CSE 2011 | Question: 40
Consider the matrix as given below. $\begin{bmatrix} 1 & 2 & 3 \\ 0 & 4 & 7 \\ 0 & 0 & 3\end{bmatrix}$ Which one of the following options provides the CORRECT values of the eigenvalues of the matrix? $1, 4, 3$ $3, 7, 3$ $7, 3, 2$ $1, 2, 3$
Consider the matrix as given below.$$\begin{bmatrix} 1 & 2 & 3 \\ 0 & 4 & 7 \\ 0 & 0 & 3\end{bmatrix}$$Which one of the following options provides the CORRECT values of...
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25 votes
7 answers
9230
GATE CSE 2011 | Question: 31
Given $i = \sqrt{-1}$, what will be the evaluation of the definite integral $\int \limits_0^{\pi/2} \dfrac{\cos x +i \sin x} {\cos x - i \sin x} dx$ ? $0$ $2$ $-i$ $i$
Given $i = \sqrt{-1}$, what will be the evaluation of the definite integral $\int \limits_0^{\pi/2} \dfrac{\cos x +i \sin x} {\cos x - i \sin x} dx$ ?$0$$2$$-i$$i$
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55 votes
6 answers
9231
GATE CSE 2011 | Question: 30
Which one of the following options is CORRECT given three positive integers $x, y$ and $z$ ... always true irrespective of the value of $x$ $P(x)$ being true means that $x$ has exactly two factors other than $1$ and $x$
Which one of the following options is CORRECT given three positive integers $x, y$ and $z$, and a predicate$$P\left(x\right) = \neg \left(x=1\right)\wedge \forall y \left...
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17 votes
2 answers
9233
GATE CSE 2011 | Question: 17
K4 and Q3 are graphs with the following structures. Which one of the following statements is TRUE in relation to these graphs? K4 is a planar while Q3 is not Both K4 and Q3 are planar Q3 is planar while K4 is not Neither K4 nor Q3 is planar
K4 and Q3 are graphs with the following structures.Which one of the following statements is TRUE in relation to these graphs?K4 is a planar while Q3 is notBoth K4 and Q3 ...
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27 votes
4 answers
9234
GATE CSE 2011 | Question: 3
If two fair coins are flipped and at least one of the outcomes is known to be a head, what is the probability that both outcomes are heads? $\left(\dfrac{1}{3}\right)$ $\left(\dfrac{1}{4}\right)$ $\left(\dfrac{1}{2}\right)$ $\left(\dfrac{2}{3}\right)$
If two fair coins are flipped and at least one of the outcomes is known to be a head, what is the probability that both outcomes are heads?$\left(\dfrac{1}{3}\right)$$\le...
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57 votes
11 answers
9237
GATE CSE 2014 Set 3 | Question: 51
If $G$ is the forest with $n$ vertices and $k$ connected components, how many edges does $G$ have? $\left\lfloor\frac {n}{k}\right\rfloor$ $\left\lceil \frac{n}{k} \right\rceil$ $n-k$ $n-k+1$
If $G$ is the forest with $n$ vertices and $k$ connected components, how many edges does $G$ have?$\left\lfloor\frac {n}{k}\right\rfloor$$\left\lceil \frac{n}{k} \right\r...
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35 votes
5 answers
9240
GATE CSE 2014 Set 3 | Question: 48
Let $S$ be a sample space and two mutually exclusive events $A$ and $B$ be such that $A \cup B = S$. If $P(.)$ denotes the probability of the event, the maximum value of $P(A)P(B)$ is_____.
Let $S$ be a sample space and two mutually exclusive events $A$ and $B$ be such that $A \cup B = S$. If $P(.)$ denotes the probability of the event, the maximum value of ...
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