The image presents multiple-choice questions. We will solve questions 34, 35, 36, and 37. Question 34: Find the result of the modulo operation $19 \pmod{20}$. Question 35: Determine the output of the Pascal program segment: `Write ('saman'): Write (75): Writeln ('Amal'): Wtire (79)`. Question 36: Identify which of the given options is not a valid identifier in Pascal. Question 37: Find the output of the following segment of a Pascal Programme? i. 012345 ii.0123456 iii. 12345 iv. cannot compile because of an error

Number TheoryModular ArithmeticModulo Operation
2025/3/31

1. Problem Description

The image presents multiple-choice questions. We will solve questions 34, 35, 36, and
3
7.
Question 34: Find the result of the modulo operation 19(mod20)19 \pmod{20}.
Question 35: Determine the output of the Pascal program segment: `Write ('saman'): Write (75): Writeln ('Amal'): Wtire (79)`.
Question 36: Identify which of the given options is not a valid identifier in Pascal.
Question 37: Find the output of the following segment of a Pascal Programme?
i. 012345
ii.0123456
iii. 12345
iv. cannot compile because of an error

2. Solution Steps

Question 34:
The modulo operation a(modb)a \pmod{b} finds the remainder when aa is divided by bb. Since 19<2019 < 20, the remainder when 19 is divided by 20 is simply
1

9. $19 \pmod{20} = 19$

Question 35:
The Pascal code does the following:
- `Write ('saman')`: Prints "saman" to the console without a newline.
- `Write (75)`: Prints "75" to the console without a newline, after "saman".
- `Writeln ('Amal')`: Prints "Amal" to the console, followed by a newline.
- `Wtire (79)`: Is likely a typo and intended to be `Write(79)` which prints "79" after "Amal".
So the output will be "saman75Amal" on the first line, followed by "79" on the next. Considering given answers, the corrected `Write(79)` command will give "saman 75 Amal 79" as a single line output.
Question 36:
In Pascal, identifiers (names for variables, procedures, etc.) must start with a letter or underscore, and can consist of letters, digits, and underscores. The '#' character is not allowed in Pascal identifiers.
Therefore, `Num#` is not a valid identifier.
Question 37:
Assuming the intent is to output a numeric value, the options are:
i. 012345
ii. 0123456
iii. 12345
iv. cannot compile because of an error
Pascal will implicitly discard leading zeros if it recognizes the value as numeric, thus it would output a value as a number. If it's a string, the leading zeros would remain.
Since Pascal is case-insensitive, `Programme` might or might not work based on context. More information needed. For a general case, leading zeros would likely be stripped.

3. Final Answer

Question 34: i. 19
Question 35: iii. Saman 75 Amal 79
Question 36: iv. Num#
Question 37: Either iii. 12345 or iv. cannot compile because of an error, depending on what's meant by `segment of pascal programme.`

Related problems in "Number Theory"

Question 9: Find the binary, hexadecimal, or octal number that is equivalent to the decimal value 16...

Number Base ConversionsBinaryHexadecimalOctalDecimal
2025/4/8

The problem asks us to fill in a 2x2 table with numbers less than 100. The rows are "a square number...

Number PropertiesSquare NumbersEven and Odd Numbers
2025/4/4

We have four digit cards: 7, 5, 2, and 1. We need to choose two cards each time to make two-digit nu...

DivisibilityFactorsMultiplesSquare Numbers
2025/4/4

We are given that a positive integer $N$ is represented as $abc$ in base 5 and $cba$ in base 9. We w...

Number BasesBase ConversionDiophantine Equations
2025/3/31

The problem asks to find the hexadecimal equivalent of $X+Y$, where $X = 10010_2$ and $Y = 1111_2$ a...

Number SystemsBinaryHexadecimalBase ConversionArithmetic Operations
2025/3/31

We are asked to find which of the given numbers cannot be the base of the number $12012$.

Number BasesBase Conversion
2025/3/31

The problem asks us to classify given numbers into different sets of numbers: - N: Natural numbers -...

Number SetsReal NumbersRational NumbersIrrational NumbersIntegersNatural Numbers
2025/3/30

We are given the number 243, which is not a perfect square. We need to find the smallest natural num...

Perfect SquaresPrime FactorizationInteger Properties
2025/3/30

The problem asks us to find the smallest natural number that we need to divide 675 by to obtain a pe...

Prime FactorizationPerfect SquaresDivisibility
2025/3/30

Determine whether the number $\frac{\pi}{5}$ is rational or irrational.

Rational NumbersIrrational NumbersReal NumbersPi
2025/3/21