Recent questions tagged modular-arithmetic / GATE Overflow for GATE CSE

2 votes

2 answers

1

GATE Electrical 2023 | GA Question: 9
The digit in the unit's place of the product $3^{999} \times 7^{1000}$ is _________. $7$ $1$ $3$ $9$

The digit in the unit's place of the product $3^{999} \times 7^{1000}$ is _________.$7$$1$$3$$9$

admin

999 views

admin asked May 20, 2023

1 votes

0 answers

2

GO Classes 2024 | IIITH Mock Test 5 | Question: 61
What are the last two digits of $1! + 2! + \dots +100!?$ $00$ $13$ $30$ $33$

What are the last two digits of $1! + 2! + \dots +100!?$$00$$13$$30$$33$

GO Classes

266 views

GO Classes asked Apr 30, 2023

17 votes

2 answers

3

GO Classes CS/DA 2025 | Weekly Quiz 3 | Fundamental Course and Linear Algebra | Question: 2
If $n!$ denotes the product of the integers $1$ through $n,$ what is the remainder when $(1 !+2 !+3 !+4 !+5 !+6 !+\ldots +9 ! )$ is divided by $9 ?$

If $n!$ denotes the product of the integers $1$ through $n,$ what is the remainder when $(1 !+2 !+3 !+4 !+5 !+6 !+\ldots +9 ! )$ is divided by $9 ?$

GO Classes

812 views

GO Classes asked Mar 14, 2023

2 votes

1 answer

4

TIFR CSE 2023 | Part B | Question: 11
Let $m=2877426671$. It is known that $p=5754853343=2 m+1$ is a $10$ -digit prime number. What is $16^{m}(\bmod p)$ ? $1$ $4$ $16$ $2877426671$ $5754853342 \;($ which is actually $-1(\bmod p))$

Let $m=2877426671$. It is known that $p=5754853343=2 m+1$ is a $10$ -digit prime number. What is $16^{m}(\bmod p)$ ?$1$$4$$16$$2877426671$$5754853342 \;($ which is actua...

admin

408 views

admin asked Mar 14, 2023

5 votes

4 answers

5

GO Classes CS/DA 2025 | Weekly Quiz 1 | Fundamental Course | Question: 8
Let $k$ be some integer and it is given that $a \equiv b(\bmod n)$ then which of the following(s) is/are ALWAYS true? More than one option can be true. $a \equiv b-3 n(\bmod n)$ $a \equiv b+k(\bmod n)$ $a+k \equiv b+k(\bmod n)$ $a+5 n \equiv b-3 n(\bmod n)$

Let $k$ be some integer and it is given that $a \equiv b(\bmod n)$ then which of the following(s) is/are ALWAYS true?More than one option can be true.$a \equiv b-3 n(\bmo...

GO Classes

1.0k views

GO Classes asked Mar 1, 2023

5 votes

2 answers

6

GO Classes CS/DA 2025 | Weekly Quiz 1 | Fundamental Course | Question: 9
Which of the following(s) ALWAYS hold given that $a \equiv b(\bmod n)$ is true for some integers $a, b$ and $n.$ More than one option can be true. $a \bmod n=b \bmod n$ $n \mid(a-b)$ $n \mid a$ $n \mid b$

Which of the following(s) ALWAYS hold given that $a \equiv b(\bmod n)$ is true for some integers $a, b$ and $n.$More than one option can be true.$a \bmod n=b \bmod n$$n \...

GO Classes

808 views

GO Classes asked Mar 1, 2023

3 votes

3 answers

7

GO Classes CS/DA 2025 | Weekly Quiz 1 | Fundamental Course | Question: 10
Which of the following options is/are TRUE? $43 \equiv-2(\bmod 5)$ $5 \equiv-7(\bmod 3)$ $-10 \equiv-25(\bmod 7)$ $8 \equiv-8(\bmod 5)$

Which of the following options is/are TRUE?$43 \equiv-2(\bmod 5)$$5 \equiv-7(\bmod 3)$$-10 \equiv-25(\bmod 7)$$8 \equiv-8(\bmod 5)$

GO Classes

823 views

GO Classes asked Mar 1, 2023

2 votes

3 answers

8

DRDO CSE 2022 Paper 2 | Question: 24
Compute the following: $3^{32} \bmod 80$.

Compute the following: $3^{32} \bmod 80$.

admin

578 views

admin asked Dec 15, 2022

4 votes

3 answers

9

GO Classes Weekly Quiz 2 | Programming in C | Propositional Logic | Question: 1
What is the last digit in the decimal representation of $7^{19522}$?

What is the last digit in the decimal representation of $7^{19522}$?

GO Classes

993 views

GO Classes asked May 2, 2022

3 votes

2 answers

10

GO Classes Weekly Quiz 1 | General Aptitude | Question: 2
Compute the remainder of $3^{64}$ in the division by $67.$

Compute the remainder of $3^{64}$ in the division by $67.$

GO Classes

680 views

GO Classes asked May 1, 2022

3 votes

4 answers

11

GO Classes Weekly Quiz 1 | General Aptitude | Question: 3
Compute $2^{32} \; \mod \; 37$

Compute $2^{32} \; \mod \; 37$

GO Classes

666 views

GO Classes asked May 1, 2022

2 votes

1 answer

12

GO Classes Weekly Quiz 1 | General Aptitude | Question: 10
Which of the following is/are True? Suppose $na\equiv nb\; \mod\; m,$ then $a\equiv b \;\mod\; m$ holds $x^3$ is always congruent to one of $-1, 0, 1$ on $\mod\; 7$. Suppose $a\equiv b\; \mod \;m$ ... $aa'\equiv bb'\; \mod\; m$ Suppose $a\equiv b \; \mod\; m,$ then $a+m \equiv b \;\mod\; m$

Which of the following is/are True?Suppose $na\equiv nb\; \mod\; m,$ then $a\equiv b \;\mod\; m$ holds$x^3$ is always congruent to one of $-1, 0, 1$ on $\mod\; 7$.Suppose...

GO Classes

525 views

GO Classes asked May 1, 2022

2 votes

1 answer

13

GO Classes Weekly Quiz 1 | General Aptitude | Question: 11
What is the remainder of $62831853$ modulo $11$?

What is the remainder of $62831853$ modulo $11$?

GO Classes

501 views

GO Classes asked May 1, 2022

1 votes

3 answers

14

TIFR CSE 2021 | Part A | Question: 13
What are the last two digits of $7^{2021}$? $67$ $07$ $27$ $01$ $77$

What are the last two digits of $7^{2021}$?$67$$07$$27$$01$$77$

soujanyareddy13

545 views

soujanyareddy13 asked Mar 25, 2021

19 votes

18 answers

15

GATE CSE 2019 | Question: 21
The value of $3^{51} \text{ mod } 5$ is _____

The value of $3^{51} \text{ mod } 5$ is _____

Arjun

18.4k views

Arjun asked Feb 7, 2019

3 votes

4 answers

16

GATE Overflow | Mock GATE | Test 1 | Question: 4
What is the value of $(x \% \text{ of } y) + (y \% \text{ of } x)$? $20 \% \text{ of } x/y$ $2 \% \text{ of } x/y$ $2 \% \text{ of } xy$ $20 \% \text{ of } xy$

What is the value of $(x \% \text{ of } y) + (y \% \text{ of } x)$?$20 \% \text{ of } x/y$$2 \% \text{ of } x/y$$2 \% \text{ of } xy$$20 \% \text{ of } xy$

Ruturaj Mohanty

944 views

Ruturaj Mohanty asked Dec 27, 2018

7 votes

2 answers

17

GATE Overflow | Mock GATE | Test 1 | Question: 6
The remainder when $'m+n'$ is divided by $12$ is $8$, and the remainder when $'m-n'$ is divided by $12$ is $6$. If $m>n$, then what is the remainder when $'mn'$ is divided by $6$?

The remainder when $'m+n'$ is divided by $12$ is $8$, and the remainder when $'m-n'$ is divided by $12$ is $6$. If $m>n$, then what is the remainder when $'mn'$ is divide...

Ruturaj Mohanty

1.4k views

Ruturaj Mohanty asked Dec 27, 2018

5 votes

2 answers

18

TIFR CSE 2019 | Part A | Question: 2
How many proper divisors (that is, divisors other than $1$ or $7200$) does $7200$ have ? $18$ $20$ $52$ $54$ $60$

How many proper divisors (that is, divisors other than $1$ or $7200$) does $7200$ have ?$18$$20$$52$$54$$60$

Arjun

1.6k views

Arjun asked Dec 18, 2018

12 votes

2 answers

19

TIFR CSE 2019 | Part A | Question: 7
What are the last two digits of $1! + 2! + \dots +100!$? $00$ $13$ $30$ $33$ $73$

What are the last two digits of $1! + 2! + \dots +100!$?$00$$13$$30$$33$$73$

Arjun

1.5k views

Arjun asked Dec 18, 2018

3 votes

2 answers

20

TIFR CSE 2019 | Part B | Question: 14
Let $m$ and $n$ be two positive integers. Which of the following is NOT always true? If $m$ and $n$ are co-prime, there exist integers $a$ and $b$ such that $am + bn=1$ $m^{n-1} \equiv 1 (\text{ mod } n)$ ... $m+1$ is a factor of $m^{n(n+1)}-1$ If $2^n -1$ is prime, then $n$ is prime

Let $m$ and $n$ be two positive integers. Which of the following is NOT always true?If $m$ and $n$ are co-prime, there exist integers $a$ and $b$ such that $am + bn=1$$m^...

Arjun

1.3k views

Arjun asked Dec 18, 2018

4 votes

3 answers

21

GATE2017 CE-1: GA-8
The last digit of $(2171)^{7}+(2172)^{9}+(2173)^{11}+(2174)^{13}$ is $2$ $4$ $6$ $8$

The last digit of $(2171)^{7}+(2172)^{9}+(2173)^{11}+(2174)^{13}$ is$2$$4$$6$$8$

Milicevic3306

3.1k views

Milicevic3306 asked Mar 26, 2018

2 votes

1 answer

22

MadeEasy Test Series 2018: General Aptitude - Modular Arithematic
The value of the expression $13^{88} \text{(mod 19)},$ in the range $0$ to $18,$ is ________.

The value of the expression $13^{88} \text{(mod 19)},$ in the range $0$ to $18,$ is ________.

sumit chakraborty

615 views

sumit chakraborty asked Jan 27, 2018

2 votes

0 answers

23

Modular arithmetic. Solve for x : (103*x) mod 360 = 1.
Solve for x : (103*x) mod 360 = 1. Please explain how to solve this step by step. The answer is 7.

Solve for x :(103*x) mod 360 = 1.Please explain how to solve this step by step.The answer is 7.

Rohit Gupta 8

1.6k views

Rohit Gupta 8 asked Jan 14, 2018

17 votes

12 answers

24

TIFR CSE 2018 | Part B | Question: 1
What is the remainder when $4444^{4444}$ is divided by $9?$ $1$ $2$ $5$ $7$ $8$

What is the remainder when $4444^{4444}$ is divided by $9?$$1$$2$$5$$7$$8$

Arjun

3.4k views

Arjun asked Dec 10, 2017

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