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61
DRDO CSE 2022 Paper 1 | Question: 19
How many seven digit numbers are possible with exactly four $4 \mathrm{s}?$
How many seven digit numbers are possible with exactly four $4 \mathrm{s}?$
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1 votes
1 answer
62
DRDO CSE 2022 Paper 1 | Question: 22
How many minimum number of $\text{NOR}$ gates are required to implement the function $F=A^{\prime} B^{\prime} C^{\prime}+A B C^{\prime}$
How many minimum number of $\text{NOR}$ gates are required to implement the function $F=A^{\prime} B^{\prime} C^{\prime}+A B C^{\prime}$
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1 votes
0 answers
64
DRDO CSE 2022 Paper 1 | Question: 24
Given a truth table of the full adder for three inputs. Draw a full adder circuit with a decoder and two $\text{OR}$ ...
Given a truth table of the full adder for three inputs. Draw a full adder circuit with a decoder and two $\text{OR}$ gates.$$\begin{array}{|c|c|c|c|c|}\hline \mathrm{X} &...
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1 votes
1 answer
65
DRDO CSE 2022 Paper 1 | Question: 25
Simplify the Boolean function $F=W^{\prime} X^{\prime} Y^{\prime}+W X^{\prime} Y^{\prime}+W^{\prime} X Y Z^{\prime}+X^{\prime} Y Z^{\prime}$
Simplify the Boolean function $F=W^{\prime} X^{\prime} Y^{\prime}+W X^{\prime} Y^{\prime}+W^{\prime} X Y Z^{\prime}+X^{\prime} Y Z^{\prime}$
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1 votes
1 answer
66
DRDO CSE 2022 Paper 1 | Question: 27
Find the number of binary tree(s) with $3$ nodes (i.e., $\text{A, B,}$ and $\text{C})$ which when traversed by pre-order gives the sequence $\textbf{C B A}$. You also need to draw each such tree.
Find the number of binary tree(s) with $3$ nodes (i.e., $\text{A, B,}$ and $\text{C})$ which when traversed by pre-order gives the sequence $\textbf{C B A}$. You also nee...
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1 votes
2 answers
67
DRDO CSE 2022 Paper 1 | Question: 28
If the maximum height of a binary tree is $\mathrm{N},$ then how many number of nodes will there be?
If the maximum height of a binary tree is $\mathrm{N},$ then how many number of nodes will there be?
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1 votes
0 answers
69
DRDO CSE 2022 Paper 1 | Question: 30
If the prefix traversal order of a tree is $*+\mathbf{a} \mathbf{b}-\mathbf{c} \mathbf{d}$. Then, find the equivalent postfix order of the that tree.
If the prefix traversal order of a tree is $*+\mathbf{a} \mathbf{b}-\mathbf{c} \mathbf{d}$. Then, find the equivalent postfix order of the that tree.
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2 votes
0 answers
70
DRDO CSE 2022 Paper 1 | Question: 31
How many topological sortings (or topological orderings) does the given directed graph have?
How many topological sortings (or topological orderings) does the given directed graph have?
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1 votes
0 answers
72
DRDO CSE 2022 Paper 1 | Question: 33 (a)
Consider the following graph. How many nodes (apart from $s$) does the Breadth First Search algorithm discover before discovering $t$ when starting from $s$.
Consider the following graph.How many nodes (apart from $s$) does the Breadth First Search algorithm discover before discovering $t$ when starting from $s$.
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0 votes
1 answer
74
Provided by teacher, topic -arguments
Show that: (r → ~ q, r ∪ S, S → ~ q, p → q) ↔ ~ p are inconsistent.
Show that: (r → ~ q, r ∪ S, S → ~ q, p → q) ↔ ~ pare inconsistent.
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0 answers
78
ISI 2020 | PCB Mathematics | Question: 5.2
Deduce that if $N, H, K$ are normal subgroups of a group $G$ such that $ N \bigcap H=N \bigcap K=H \bigcap K=\left\{e_{G}\right\} $ and $G=H K$, then $N$ is an Abelian group.
Deduce that if $N, H, K$ are normal subgroups of a group $G$ such that $$ N \bigcap H=N \bigcap K=H \bigcap K=\left\{e_{G}\right\} $$ and $G=H K$, then $N$ is an Abelian ...
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0 answers
79
ISI2020-PCB-CS: 8.2
Consider the following state diagram of a sequential circuit, where each of a, b, c, d, e, f and g represents a state. Represent the state diagram with minimum number of states without altering the input-output relationships. Justify your answer.
Consider the following state diagram of a sequential circuit, where each of a, b, c, d, e, f and g represents a state. Represent thestate diagram with minimum number of s...
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1 votes
3 answers
81
ISI2020-PCB-CS: 1.3
What does the following function compute for $x \neq 0?$ float isi1(float x, int y) { if (y==0) { return 1; } else if (y>0) { return isi1(x,-y); } else { return isi1(x, y+1)/x; } }
What does the following function compute for $x \neq 0?$float isi1(float x, int y) { if (y==0) { return 1; } else if (y>0) { return isi1(x,-y); } else { return isi1(x, y+...
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0 votes
0 answers
83
ISI 2019 | PCB Mathematics | Question: 1
Let $\left\{a_{n}\right\}$ be a decreasing sequence such that $\displaystyle{}\sum_{n=1}^{\infty} a_{n}$ is convergent. Prove that the sequence $\left\{n a_{n}\right\}$ goes to zero as $n \rightarrow \infty$.
Let $\left\{a_{n}\right\}$ be a decreasing sequence such that $\displaystyle{}\sum_{n=1}^{\infty} a_{n}$ is convergent. Prove that the sequence $\left\{n a_{n}\right\}$ g...
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0 votes
1 answer
84
ISI 2019 | PCB Mathematics | Question: 2
Consider an $n \times n$ matrix $A=I_{n}-\alpha \alpha^{T}$, where $I_{n}$ is the identity matrix of order $n$ and $\alpha$ is an $n \times 1$ column vector such that $\alpha^{T} \alpha=1$. Prove that $A^{2}=A.$
Consider an $n \times n$ matrix $A=I_{n}-\alpha \alpha^{T}$, where $I_{n}$ is the identity matrix of order $n$ and $\alpha$ is an $n \times 1$ column vector such that $\a...
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1 votes
0 answers
85
ISI 2019 | PCB Mathematics | Question: 3
Let $A$ and $B$ be two invertible real matrices of order $n$. Show that $\det(x A+(1-x) B)=0$ has finitely many solutions for $x.$
Let $A$ and $B$ be two invertible real matrices of order $n$. Show that $\det(x A+(1-x) B)=0$ has finitely many solutions for $x.$
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0 votes
0 answers
86
ISI 2019 | PCB Mathematics | Question: 4
Show that for every $\theta \in\left(0, \frac{\pi}{2}\right),$ there exists a unique real number $x_{\theta}$ such that $ (\sin \theta)^{x_{\theta}}+(\cos \theta)^{x_{\theta}}=\frac{3}{2} . $
Show that for every $\theta \in\left(0, \frac{\pi}{2}\right),$ there exists a unique real number $x_{\theta}$ such that $$ (\sin \theta)^{x_{\theta}}+(\cos \theta)^{x_{\t...
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0 votes
0 answers
89
ISI 2019 | PCB Mathematics | Question: 7
Solve the differential equation $ x^{2}\left(x^{2}-1\right) \frac{d y}{d x}+x\left(x^{2}+1\right) y=x^{2}-1 . $
Solve the differential equation $$ x^{2}\left(x^{2}-1\right) \frac{d y}{d x}+x\left(x^{2}+1\right) y=x^{2}-1 . $$
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0 votes
0 answers
90
ISI 2019 | PCB Mathematics | Question: 8
Let $f$ be a real valued function on $\mathbb{R}$. If for all real $x$, $ f(x)+3 f(1-x)=5 $ holds, then show that $f$ is a constant function.
Let $f$ be a real valued function on $\mathbb{R}$. If for all real $x$, $$ f(x)+3 f(1-x)=5 $$ holds, then show that $f$ is a constant function.
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