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Recent questions tagged number-theory

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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

4 votes

2 answers

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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

3 votes

2 answers

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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

3 votes

2 answers

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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

2 votes

1 answer

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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

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

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

1 vote

2 answers

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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

465 views

1 vote

0 answers

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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

0 votes

0 answers

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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

2 votes

1 answer

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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

3 votes

1 answer

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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

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

0 votes

1 answer

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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

7 votes

1 answer

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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

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

3 votes

2 answers

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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

0 votes

1 answer

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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

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

902 views

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

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

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

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

7.4k views

29 votes

7 answers

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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

21 votes

3 answers

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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

13 votes

3 answers

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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

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

1.3k views

23 votes

2 answers

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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

4.1k views

24 votes

3 answers

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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

7.7k views

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Recent questions tagged number-theory