Jamia Millia Islamia MCA 2024 Previous Year Questions (PYQs) – Page 8 of 10
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The compound statement with ‘And’ is false if ______ of its component statements are.
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Solution
In logic, a conjunction $p \land q$ is true only if both $p$ and $q$ are true.
Hence, it is false if any one is false.
If $_nP_3 = 4 \times {_nP_2}$, find $n$.
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Solution
${_nP_3} = \dfrac{n!}{(n - 3)!},\quad {_nP_2} = \dfrac{n!}{(n - 2)!}$
Given, $\dfrac{n!}{(n - 3)!} = 4 \times \dfrac{n!}{(n - 2)!}$
$\Rightarrow \dfrac{n(n - 1)(n - 2)!}{(n - 3)!} = 4 \times \dfrac{n!}{(n - 2)!}$
Simplify: $(n - 2) = 4 \Rightarrow n = 6$
${_nP_r} = {_nC_r} \times$ ______
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Solution
${_nP_r} = {_nC_r} \times r!$
. Find the variance of the observation values taken in the lab: $4.2,\ 4.3,\ 4.0,\ 4.1$.
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Solution
Mean $,\bar x=\dfrac{4.2+4.3+4.0+4.1}{4}=4.15$.
Deviations: $0.05,,0.15,,-0.15,,-0.05$.
Sum of squares $=0.0025+0.0225+0.0225+0.0025=0.05$.
Population variance $,s^2=\dfrac{0.05}{4}=0.0125$.
Sample variance $,s^2=\dfrac{0.05}{3}\approx0.0167$.
If the coefficient of variation is $100$ and the mean of the data is $25$, then find the standard deviation.
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Solution
Coefficient of variation $=$ $\dfrac{\sigma}{\bar{x}}\times100$
$\Rightarrow 100 = \dfrac{\sigma}{25} \times 100$
$\Rightarrow \sigma = 25$
One Gigabyte is approximately equal to —
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Solution
$1\ \text{GB} \approx 10^9\ \text{bytes} = 1{,}000{,}000{,}000\ \text{bytes}$
In computer world, Trojan Horse refers to —
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Solution
A Trojan Horse is a type of malicious software disguised as a legitimate program.
Computer resolution measures —
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Solution
Resolution determines the number of pixels displayed on the screen (horizontal × vertical).
A collection of programs that controls how your computer system runs and processes information is called —
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Solution
The Operating System (OS) manages hardware, software, memory, and tasks.
__________ is the application of investigation and analysis techniques to gather and preserve evidence from a computing device in a way suitable for presentation in court.
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Solution
Computer Forensics involves collecting and analyzing digital evidence for legal cases.
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