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7 votes
2 answers
22
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...
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3 votes
4 answers
23
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$$20 \% \text{ of } xy$
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17 votes
12 answers
25
TIFR CSE 2018 | Part B | Question: 1
What is the remainder when $4444^{4444}$ is divided by $9?$ $1$ $2$ $5$ $7$ $8$
What is the remainder when $4444^{4444}$ is divided by $9?$$1$$2$$5$$7$$8$
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12 votes
2 answers
26
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$
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7 votes
2 answers
27
TIFR CSE 2011 | Part A | Question: 20
Let $n>1$ be an odd integer. The number of zeros at the end of the number $99^{n}+1$ is $1$ $2$ $3$ $4$ None of the above
Let $n>1$ be an odd integer. The number of zeros at the end of the number $99^{n}+1$ is$1$$2$$3$$4$None of the above
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0 votes
2 answers
29
Test of Mathematics at 10+2 Level
The remainder when 3^37 is divided by 79 is A. 78 B. 1 C. 2 D. 35
The remainder when 3^37 is divided by 79 isA. 78B. 1C. 2D. 35
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5 votes
2 answers
31
TIFR CSE 2019 | Part A | Question: 2
How many proper divisors (that is, divisors other than $1$ or $7200$) does $7200$ have ? $18$ $20$ $52$ $54$ $60$
How many proper divisors (that is, divisors other than $1$ or $7200$) does $7200$ have ?$18$$20$$52$$54$$60$
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2 votes
0 answers
32
Modular arithmetic. Solve for x : (103*x) mod 360 = 1.
Solve for x : (103*x) mod 360 = 1. Please explain how to solve this step by step. The answer is 7.
Solve for x :(103*x) mod 360 = 1.Please explain how to solve this step by step.The answer is 7.
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12 votes
2 answers
34
GATE2012 CY: GA-1
If $(1.001)$^{1259}$= $3.52$ and $(1.001)$^{2062}$= $7.85$, then $(1.001)$^{3321}$= $2.23$ $4.33$ $11.37$ $27.64$
If $(1.001)$$^{1259}$= $3.52$ and $(1.001)$$^{2062}$= $7.85$, then $(1.001)$$^{3321}$=$2.23$$4.33$$11.37$$27.64$
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1 votes
2 answers
36
Modulo
What will be the remainder when $\large 6457^{76^{57}}$ is divided by $\large 23$ ?
What will be the remainder when $\large 6457^{76^{57}}$ is divided by $\large 23$ ?
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5 votes
2 answers
37
TIFR2010-Maths-B-12
If $n$ and $m$ are positive integers and $n^{9}=19m+r$, then the possible values for $r$ modulo 19 are. Only 0 Only 0, $\pm$ 1 Only $\pm$ 1 None of the above
If $n$ and $m$ are positive integers and $n^{9}=19m+r$, then the possible values for $r$ modulo 19 are.Only 0Only 0, $\pm$ 1Only $\pm$ 1None of the above
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4 votes
1 answer
38
TIFR-2011-Maths-A-7
The equation $x^{22}\equiv 2$ $\mod 23$ has No solutions $23$ solutions Exactly one solution $22$ solutions
The equation $x^{22}\equiv 2$ $\mod 23$ hasNo solutions$23$ solutionsExactly one solution$22$ solutions
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3 votes
1 answer
39
What will be the in the units place of?
Q1) What is the units digit of $\left (39^{11} – 32^{11} \right)$?     (a) 1  (b) 5     (c) 7  (d) 8 Q2) What will be in the unit place of $45^8 + 19^{11} – 62^{18}$?     (a) 0  (b) 2     (c) 3  (d) 7
Q1) What is the units digit of $\left (39^{11} – 32^{11} \right)$?    (a) 1  (b) 5    (c) 7  (d) 8Q2) What will be in the unit place of $45^8 + 19^{11} – 62...
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2 votes
2 answers
40
Probability
Let $X$ be uniformly distributed on $\{0, 1, 2 \ldots 32\}$. What is probability of choosing $x \in X$ such that $3x + 12 \;\cong\; 0 \pmod{33}$?
Let $X$ be uniformly distributed on $\{0, 1, 2 \ldots 32\}$. What is probability of choosing $x \in X$ such that $3x + 12 \;\cong\; 0 \pmod{33}$?
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