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Recent questions tagged number-theory
1
vote
1
answer
1
TIFR CSE 2021 | Part A | Question: 7
Let $d$ be the positive square integers (that is, it is a square of some integer) that are factors of $20^{5} \times 21^{5}$. Which of the following is true about $d$? $50\leq d< 100$ $100\leq d< 150$ $150\leq d< 200$ $200\leq d< 300$ $300\leq d$
soujanyareddy13
asked
in
Quantitative Aptitude
Mar 25, 2021
by
soujanyareddy13
313
views
tifr2021
quantitative-aptitude
number-theory
4
votes
2
answers
2
GATE Electrical 2021 | GA Question: 4
Which one of the following numbers is exactly divisible by $\left ( 11^{13} +1\right )$? $11^{26} +1$ $11^{33} +1$ $11^{39} -1$ $11^{52} -1$
Arjun
asked
in
Quantitative Aptitude
Feb 20, 2021
by
Arjun
4.9k
views
gateee-2021
quantitative-aptitude
number-system
number-theory
3
votes
2
answers
3
TIFR CSE 2020 | Part A | Question: 15
The sequence $s_{0},s_{1},\dots , s_{9}$ is defined as follows: $s_{0} = s_{1} + 1$ $2s_{i} = s_{i-1} + s_{i+1} + 2 \text{ for } 1 \leq i \leq 8$ $2s_{9} = s_{8} + 2$ What is $s_{0}$? $81$ $95$ $100$ $121$ $190$
Lakshman Patel RJIT
asked
in
Quantitative Aptitude
Feb 11, 2020
by
Lakshman Patel RJIT
605
views
tifr2020
quantitative-aptitude
number-theory
3
votes
2
answers
4
TIFR CSE 2020 | Part A | Question: 9
A contiguous part, i.e., a set of adjacent sheets, is missing from Tharoor's GRE preparation book. The number on the first missing page is $183$, and it is known that the number on the last missing page has the same three digits, but in a different ... the front and one at the back. How many pages are missing from Tharoor's book? $45$ $135$ $136$ $198$ $450$
Lakshman Patel RJIT
asked
in
Quantitative Aptitude
Feb 11, 2020
by
Lakshman Patel RJIT
677
views
tifr2020
quantitative-aptitude
number-theory
2
votes
1
answer
5
TIFR CSE 2020 | Part A | Question: 6
What is the maximum number of regions that the plane $\mathbb{R}^{2}$ can be partitioned into using $10$ lines? $25$ $50$ $55$ $56$ $1024$ Hint: Let $A(n)$ be the maximum number of partitions that can be made by $n$ lines. Observe that $A(0) = 1, A(2) = 2, A(2) = 4$ etc. Come up with a recurrence equation for $A(n)$.
Lakshman Patel RJIT
asked
in
Quantitative Aptitude
Feb 10, 2020
by
Lakshman Patel RJIT
615
views
tifr2020
general-aptitude
quantitative-aptitude
number-theory
2
votes
5
answers
6
ISI2018-MMA-3
The number of trailing zeros in $100!$ is $21$ $23$ $24$ $25$
akash.dinkar12
asked
in
Quantitative Aptitude
May 11, 2019
by
akash.dinkar12
544
views
isi2018-mma
general-aptitude
quantitative-aptitude
number-theory
0
votes
2
answers
7
Number theory
Why does a perfect square number have odd number of factors?
Sammohan Ganguly
asked
in
Mathematical Logic
Apr 20, 2018
by
Sammohan Ganguly
235
views
number-theory
1
vote
2
answers
8
Number Theory
A prison houses 100 inmates, one in each of 100 cells, guarded by a total of 100 warders. One evening, all the cells are locked and the keys left in the locks. As the first warder leaves, she turns every key, unlocking all the doors. The second warder ... every third key and so on. Finally the last warder turns the key in just the last cell. Which doors are left unlocked and why?
Mk Utkarsh
asked
in
Numerical Methods
Apr 13, 2018
by
Mk Utkarsh
465
views
number-theory
1
vote
0
answers
9
Self doubt
Why floating point in de-normalized normal form has range between : $\pm1\times2^{-149}$ and $\pm(1 - 2 ^{-23})\times2^{-126}$
Durgesh Singh
asked
in
Digital Logic
Jan 13, 2018
by
Durgesh Singh
313
views
floating-point-representation
number-theory
digital-logic
0
votes
0
answers
10
Kenneth Rosen section 3.4 Exercise question 12
Is this approach right in proving a theorem Ques: show that a mod m = b mod m if a is congruent to b (mod m) Proof: given a is congruent to b(mod m) According to definition: a - b / m i.e a - b = mx (for some integer x). ....(1) Also a = ... by equation (3) then we get a mod m = my + a my + a can also be written as b mod m Therefore, a mod m = b mod m
Jaspreet Singh 4
asked
in
Set Theory & Algebra
Aug 19, 2017
by
Jaspreet Singh 4
264
views
number-theory
2
votes
1
answer
11
Question on Number System
Find the remainder of $\frac{9^{1}+9^{2}+...+9^{n}}{6}$ where $n$ is multiple of 11. I am getting $0$ or $3$. But given answer is 3. Can anyone check?
Aghori
asked
in
Combinatory
Jul 13, 2017
by
Aghori
1.8k
views
number-theory
3
votes
1
answer
12
Question on Number System.
If $N = 1!+2!+3!+...+10!$. What is the last digit of $N^{N}$?
Aghori
asked
in
Combinatory
Jul 13, 2017
by
Aghori
399
views
number-theory
5
votes
1
answer
13
Series Summation
Series summation of $S_n$ in closed form? $\begin{align*} &S_n = \frac{1}{1.2.3.4} + \frac{1}{2.3.4.5} + \frac{1}{3.4.5.6} + \dots + \frac{1}{n.(n+1).(n+2).(n+3)} \end{align*}$
dd
asked
in
Set Theory & Algebra
Jun 11, 2017
by
dd
555
views
number-theory
summation
discrete-mathematics
0
votes
1
answer
14
Divisibility Test of 11
This is the statement for Divisibility test of 11. Add and subtract digits in an alternating pattern (add digit, subtract next digit, add next digit, etc). Then check if that answer is divisible by 11. This is the proof that I found : If x is divisible by 11, then x ≡ 0 (mod 11). ... -------------------------------------- Now, I didn't understand the proof starting from But.
Uzumaki Naruto
asked
in
Mathematical Logic
May 12, 2017
by
Uzumaki Naruto
474
views
number-theory
divisibility
proof
7
votes
1
answer
15
ISI2004-MIII: 11
If $\alpha 1,\alpha 2,\dots,\alpha n$ are the positive numbers then $\frac{a1}{a2}+\frac{a2}{a3}+\dots+\frac{an-1}{an}+\frac{an}{a1}$ is always $\geq n$ $\leq n$ $\leq n^{\frac{1}{2}}$ None of the above
Tesla!
asked
in
Set Theory & Algebra
Apr 4, 2017
by
Tesla!
630
views
isi2004
set-theory&algebra
number-theory
3
votes
3
answers
16
GATE2017 ME-2: GA-3
If $a$ and $b$ are integers and $a-b$ is even, which of the following must always be even? $ab$ $a^{2}+b^{2}+1$ $a^{2}+b+1$ $ab-b$
Arjun
asked
in
Quantitative Aptitude
Feb 27, 2017
by
Arjun
1.1k
views
gate2017-me-2
general-aptitude
quantitative-aptitude
number-theory
3
votes
2
answers
17
GATE2016 ME-2: GA-9
The binary operation $\square$ is defined as $a\square b = ab+(a+b),$ where $a$ and $b$ are any two real numbers. The value of the identity element of this operation, defined as the number $x$ such that $a\square x = a,$ for any $a$, is $0$ $1$ $2$ $10$
makhdoom ghaya
asked
in
Quantitative Aptitude
Jan 20, 2017
by
makhdoom ghaya
1.7k
views
gate2016-me-2
quantitative-aptitude
number-theory
easy
0
votes
1
answer
18
UGC NET CSE | June 2010 | Part 2 | Question: 9
What is decimal equivalent of BCD $11011.1100$? $22.0$ $22.2$ $20.2$ $21.2$
makhdoom ghaya
asked
in
Digital Logic
Sep 15, 2016
by
makhdoom ghaya
598
views
ugcnetcse-june2010-paper2
digital-logic
number-theory
6
votes
3
answers
19
ISI2016
Find the number of positive integers n for which $n^{2}+96$ is a perfect square.
abhi18459
asked
in
Set Theory & Algebra
May 9, 2016
by
abhi18459
902
views
isi2016
set-theory&algebra
number-theory
numerical-answers
3
votes
3
answers
20
GATE2012 AE: GA-8
If a prime number on division by $4$ gives a remainder of $1,$ then that number can be expressed as sum of squares of two natural numbers sum of cubes of two natural numbers sum of square roots of two natural numbers sum of cube roots of two natural numbers
Akash Kanase
asked
in
Quantitative Aptitude
Feb 16, 2016
by
Akash Kanase
1.1k
views
gate2012-ae
number-theory
quantitative-aptitude
3
votes
1
answer
21
TIFR CSE 2014 | Part A | Question: 20
Consider the equation $x^{2}+y^{2}-3z^{2}-3t^{2}=0$. The total number of integral solutions of this equation in the range of the first $10000$ numbers, i.e., $1 \leq x, y, z, t \leq 10000$, is $200$ $55$ $100$ $1$ None of the above
makhdoom ghaya
asked
in
Quantitative Aptitude
Nov 19, 2015
by
makhdoom ghaya
682
views
tifr2014
number-theory
quantitative-aptitude
10
votes
2
answers
22
GATE1991-01,xiii
The number of integer-triples $(i,j,k)$ with $1 \leq i,j,k \leq 300$ such that $i+j+k$ is divisible by 3 is________
ibia
asked
in
Combinatory
Nov 13, 2015
by
ibia
1.3k
views
number-theory
18
votes
2
answers
23
GATE CSE 2015 Set 2 | Question: 9
The number of divisors of $2100$ is ____.
go_editor
asked
in
Set Theory & Algebra
Feb 12, 2015
by
go_editor
7.4k
views
gatecse-2015-set2
set-theory&algebra
number-theory
easy
numerical-answers
29
votes
7
answers
24
GATE IT 2005 | Question: 34
Let $n =$ $p^{2}q$, where $p$ and $q$ are distinct prime numbers. How many numbers m satisfy $1 ≤ m ≤ n$ and $gcd$ $(m, n) = 1?$ Note that $gcd$ $(m, n)$ is the greatest common divisor of $m$ and $n$. $p(q - 1)$ $pq$ $\left ( p^{2}-1 \right ) (q - 1)$ $p(p - 1) (q - 1)$
Ishrat Jahan
asked
in
Set Theory & Algebra
Nov 3, 2014
by
Ishrat Jahan
5.8k
views
gateit-2005
set-theory&algebra
normal
number-theory
21
votes
3
answers
25
GATE IT 2007 | Question: 16
The minimum positive integer $p$ such that $3^{p} \pmod {17} = 1$ is $5$ $8$ $12$ $16$
Ishrat Jahan
asked
in
Set Theory & Algebra
Oct 30, 2014
by
Ishrat Jahan
5.7k
views
gateit-2007
set-theory&algebra
normal
number-theory
13
votes
3
answers
26
GATE IT 2008 | Question: 24
The exponent of $11$ in the prime factorization of $300!$ is $27$ $28$ $29$ $30$
Ishrat Jahan
asked
in
Set Theory & Algebra
Oct 28, 2014
by
Ishrat Jahan
6.4k
views
gateit-2008
set-theory&algebra
normal
number-theory
6
votes
2
answers
27
GATE CSE 1995 | Question: 7(A)
Determine the number of divisors of $600.$
Kathleen
asked
in
Set Theory & Algebra
Oct 8, 2014
by
Kathleen
1.3k
views
gate1995
set-theory&algebra
number-theory
numerical-answers
23
votes
2
answers
28
GATE CSE 2014 Set 3 | Question: GA-10
Consider the equation: $(7526)_8 − (Y)_8 = (4364)_8$, where $(X)_N$ stands for $X$ to the base $N$. Find $Y$. $1634$ $1737$ $3142$ $3162$
go_editor
asked
in
Quantitative Aptitude
Sep 28, 2014
by
go_editor
4.1k
views
gatecse-2014-set3
quantitative-aptitude
number-theory
normal
digital-logic
24
votes
3
answers
29
GATE CSE 2014 Set 2 | Question: 49
The number of distinct positive integral factors of $2014$ is _____________
go_editor
asked
in
Set Theory & Algebra
Sep 28, 2014
by
go_editor
7.7k
views
gatecse-2014-set2
set-theory&algebra
easy
numerical-answers
number-theory
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