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Recent questions tagged drdocse-2022-paper1

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Can anyone guide me for DRDO Scientist B interview, it will be very helpful Thanks

pppankajsaini asked in Job Queries Feb 6

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2

DRDO CSE 2022 Paper 1 | Question: 5 (b)
Consider rolling of a dice experiment. Let $\text{A}$ be the event of getting an even number and $\mathrm{B}$ be the event of getting a prime number. Write the sets representing the following events. $\mathrm{A}$ and $\mathrm{B}$

admin asked in Probability Jan 26

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3

DRDO CSE 2022 Paper 1 | Question: 5 (c)
Consider rolling of a dice experiment. Let $\text{A}$ be the event of getting an even number and $\mathrm{B}$ be the event of getting a prime number. Write the sets representing the following events. not $\text{B}$

admin asked in Probability Jan 26

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4

DRDO CSE 2022 Paper 1 | Question: 33 (b)
Consider the following graph. How many nodes (apart from $s$) does the Depth First Search algorithm discover before discovering $t$ when starting from $s.$

admin asked in Algorithms Dec 15, 2022

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DRDO CSE 2022 Paper 1 | Question: 32 (b)
Let us suppose we are given an integer $\text{N}$ in binary representation. Let us consider the following algorithm to check if $\text{N}$ is a prime. For every $i$ such that $2 \leq i \leq\lceil\sqrt{\text{N}}\rceil$ ... of the running time in terms of the input size? (Assume hypothetically that division can be done in $\text{O}(1)$ time).

admin asked in Algorithms Dec 15, 2022

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DRDO CSE 2022 Paper 1 | Question: 26 (b)
Provide the correct data structures for the following: Asynchronous data transfer and accessing shared resource involve _________.

admin asked in DS Dec 15, 2022

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DRDO CSE 2022 Paper 1 | Question: 6 (b)
Let $\oplus$ sign denote bitwise addition modulo $2$. Let $n$ and $m$ be integers. Consider the set of $m$ equations on $n$ variables as follows. \[\begin{array}{l} a_{1,1} x_{1} \oplus a_{1,2} x_{2} \oplus \ldots \oplus ... $\{0,1\}$. What is the expected number of equations that can be satisfied if $x_i$'s are picked uniformly and independently at random.

admin asked in Digital Logic Dec 15, 2022

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DRDO CSE 2022 Paper 1 | Question: 1
Compute $\left[M M^{T}\right]^{-1}$ for an orthogonal matrix where \[M=\left[\begin{array}{lll} \frac{1}{\sqrt{2}} & \frac{2}{\sqrt{2}} & \frac{-2}{\sqrt{2}} \\ \frac{-2}{\sqrt{2}} & \frac{2}{\sqrt{2}} & \frac{1}{\sqrt{2}} \\ \frac{2}{\sqrt{2}} & \frac{1}{\sqrt{2}} & \frac{2}{\sqrt{2}} \end{array}\right] .\]

admin asked in Linear Algebra Dec 15, 2022

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DRDO CSE 2022 Paper 1 | Question: 2
Calculate the eigenvalues of matrix $M, M^{-1}, M^{2}$ and $M+2 I$ where \[M=\left[\begin{array}{cc} 4 & 5 \\ 2 & -5 \end{array}\right].\]

admin asked in Linear Algebra Dec 15, 2022

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DRDO CSE 2022 Paper 1 | Question: 3
With no unique solution, solve for $n$ with the following system of equations $\begin{array}{r} a+b+2 c=3 \\ a+2 b+3 c=4 \\ a+4 b+n c=6 \end{array}$

admin asked in Linear Algebra Dec 15, 2022

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DRDO CSE 2022 Paper 1 | Question: 4
Let the function $f(x)$ be defined as follows. \[f(x)=\left\{\begin{array}{ll} x^{2} & x \leq 1 \\ 2 a x^{2}+bx + c & 1 < x \leq 2 \\ x + 2d & x>1 \end{array}\right.\] Find the values of $a, b, c$ and $d$ such that $f$ is continuous and differentiable everywhere.

admin asked in Calculus Dec 15, 2022

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DRDO CSE 2022 Paper 1 | Question: 5 (a)
Consider rolling of a dice experiment. Let $\text{A}$ be the event of getting an even number and $\mathrm{B}$ be the event of getting a prime number. Write the sets representing the following events. $\mathrm{A}$ or $\mathrm{B}$

admin asked in Probability Dec 15, 2022

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13

DRDO CSE 2022 Paper 1 | Question: 6 (a)
Let $\oplus$ sign denote bitwise addition modulo $2$. Let $n$ and $m$ be integers. Consider the set of $m$ equations on $n$ variables as follows. \[\begin{array}{l} a_{1,1} x_{1} \oplus a_{1,2} x_{2} \oplus \ldots \oplus a_{1, n} x_{n}=b_{1 ... $a_{1, n} x_{n}=b_{1}$ if all $x_{i}$'s are picked uniformly and independently at random from $\{0,1\}$.

admin asked in Digital Logic Dec 15, 2022

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DRDO CSE 2022 Paper 1 | Question: 7
Let $T$ be a subset of $\{1,2, \ldots, n\}$ of size $\frac{n}{2}$, sampled uniformly at random from all subsets of size $\frac{n}{2}$ of the same set $\{1,2, \ldots, n\}$. Let $S \subseteq\{1,2, \ldots, n\}$ be an arbitrary subset of size $\frac{n}{2}$. What is the probability that $|S \cap T|=\frac{n}{4}$.

admin asked in Probability Dec 15, 2022

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DRDO CSE 2022 Paper 1 | Question: 8
Given a powerset $S$ of $\{1,2,3\}$, its partial order $\leq$ is given by set inclusion. That is, for any subsets $T_{1} \neq T_{2}$ of $\{1,2,3\}$ we have $T_{1} \leq T_{2}$ if and only if $T_{1} \subset T_{2}$. Construct the Hasse diagram on $S$ under this partial order definition.

admin asked in Set Theory & Algebra Dec 15, 2022

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DRDO CSE 2022 Paper 1 | Question: 9
Count the number of perfect matchings in the bipartite graph whose adjacency matrix $\text{A}$ is as follows. \[\left[\begin{array}{lll} 1 & 1 & 0 \\ 0 & 1 & 1 \\ 1 & 1 & 1 \end{array}\right]\]

admin asked in Graph Theory Dec 15, 2022

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DRDO CSE 2022 Paper 1 | Question: 10
Given a tree $\text{T}$ and $\lambda \geq 2$ colours $\left(c_{1}, c_{2}, \ldots, c_{\lambda}\right),$ how many proper colourings of the tree $\text{T}$ are possible?

admin asked in Graph Theory Dec 15, 2022

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DRDO CSE 2022 Paper 1 | Question: 11
Consider the following graph. Find closeness centrality of $\text{‘A’}$ node.

admin asked in Graph Theory Dec 15, 2022

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19

DRDO CSE 2022 Paper 1 | Question: 12
Given two propositions $P$ and $Q$. "if $P$ then $Q$" denoted by $P \rightarrow Q$ is called Implication. Such implication and its ____________ are logically equivalent.

admin asked in Mathematical Logic Dec 15, 2022

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DRDO CSE 2022 Paper 1 | Question: 13
Consider the following graph. Which nodes form the cliques of size $3?$

admin asked in Graph Theory Dec 15, 2022

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DRDO CSE 2022 Paper 1 | Question: 14
Derangements are permutations $\pi$ of the set $\{1,2, \ldots, n\}$ such that $\pi(i) \neq i.$ Compute the number of derangements on the set $1,2, \ldots, n$.

admin asked in Combinatory Dec 15, 2022

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DRDO CSE 2022 Paper 1 | Question: 15
What is the generating function corresponding to Fibonacci series. \[F_{n}=F_{n-1}+F_{n-2} .\] Note that $F_{0}=F_{1}=1$.

admin asked in Combinatory Dec 15, 2022

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DRDO CSE 2022 Paper 1 | Question: 16
Let us say we have a supply of $1$ rupee and $2$ rupee coins in large quantities. What is the generating function for the number of ways of giving change with $1$ rupee and $2$ rupee coins.

admin asked in Combinatory Dec 15, 2022

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DRDO CSE 2022 Paper 1 | Question: 17
Total number of functions from set $B$ to set $A$ with $n$ and $m$ elements, respectively are ___________.

admin asked in Set Theory & Algebra Dec 15, 2022

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25

DRDO CSE 2022 Paper 1 | Question: 18
A gardener wants to buy $3$ neem plants, $5$ rose plants and $1$ banyan plant from a nursery having $7$ neem, $10$ rose and $6$ banyan plants. How many choices does a gardener have?

admin asked in Combinatory Dec 15, 2022

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DRDO CSE 2022 Paper 1 | Question: 19
How many seven digit numbers are possible with exactly four $4 \mathrm{s}?$

admin asked in Combinatory Dec 15, 2022

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27

DRDO CSE 2022 Paper 1 | Question: 20
A partially ordered set $S=(\{3,4,12,24,48,72\}, /)$ is a _________ with _________ cycle$(s).$

admin asked in Set Theory & Algebra Dec 15, 2022

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28

DRDO CSE 2022 Paper 1 | Question: 21
For decimal number $-30$, the $16$-bit $2$'s complement representation is _________

admin asked in Digital Logic Dec 15, 2022

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29

DRDO CSE 2022 Paper 1 | Question: 22
How many minimum number of $\text{NOR}$ gates are required to implement the function $F=A^{\prime} B^{\prime} C^{\prime}+A B C^{\prime}$

admin asked in Digital Logic Dec 15, 2022

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DRDO CSE 2022 Paper 1 | Question: 23
For two flip-flops $F_{1}$ and $F_{2}$ and input $\mathrm{X}$, the next state and output is given as \[ \begin{array}{c} F_{1}(t+1)=\sum(1,2,5,6) \\ F_{2}(t+1)=\sum(3,7) \\ Y\left(F_{1}, F_{2}, X\right)=\sum(4,6) \end{array} \] Write functions for the next state and output of the circuit.

admin asked in Digital Logic Dec 15, 2022

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