Python Week 4

Multiple Choice Questions 🧠

2. Python Code – Size of the List rolls

(From Image 2)

Question: What is the size of the list rolls in the given code?

import random

rolls = []
for i in range(100000):
    roll = random.randint(1, 6)
    rolls.append(roll)

Step-by-step Solution:

• The loop runs from 0 to 99,999 (that’s 100,000 iterations).
• In each iteration, one value is appended to rolls.

Final Answer: The size of the list rolls is 100,000. 🔢

3. Python Code – What Does some_var Represent?

(From Image 2)

Question: Given:

some_var = count / len(rolls)

What does the variable some_var represent?

Step-by-step Solution:

• count counts how many elements in rolls are in the list primes = [^1][^2].
• len(rolls) is the total number of elements (100,000).
• So, some_var is the fraction of numbers in rolls that are prime numbers (2, 3, or 5).

Final Answer: It represents the probability that a number chosen at random from the list rolls is a prime. 🎲✅

4. Python Code – List L and flag Logic

(From Image 3)

Question: If flag is True at the end of the code, which statements are always true?

s = 0
for x in L:
    s += x

flag = False
y = -1
for x in L:
    if x * len(L) == s:
        flag = True
        y = x
        break

Step-by-step Solution:

• $ s $ is the sum of all elements in $ L $.
• For each $ x $ in $ L $, if $ x \times len(L) = s $, then $ x = \frac{s}{len(L)} $.
• So, $ x $ is the average (mean) of the list, and since all elements are distinct and positive integers, the mean is an element of the list only if the mean is an integer and present in $ L $.

Final Answers:

• $ y $ is an element in the list $ L $. ✅
• $ y $ is the average (arithmetic mean) of the numbers in the list. ✅

5. Python Code – When is flag True?

(From Image 3)

Question: Assume $ L $ is the list of the first $ n $ positive integers ($ n > 0 $). Under what condition will flag be True at the end?

Step-by-step Solution:

• $ s = 1 + 2 + … + n = \frac{n(n+1)}{2} $
• For some $ x $ in $ L $, $ x \times n = s \implies x = \frac{s}{n} = \frac{n+1}{2} $
• $ x $ must be an integer in $ L $, so $ n+1 $ must be even $ \implies n $ is odd.

Final Answer: flag will be True if and only if $ n $ is an odd integer. 🟢

6. Python Code – What is the Output of the Code?

(From Image 4)

Question: Given the code and $ L = $, what is the output after execution?

Step-by-step Solution:

1. Initially, $ S = $.
2. The outer loop runs $ j $ from 1 to 5.
3. For each $ j $, check if $ L[j] < S $. The first time this is true is at $ j = 2 $ ($ L[^1] = 8 < S = 90 $).
4. At this point:
   • $ before_j = S[:2] = $
   • $ new_j = [L[^1]] = $
   • $ after_j = S[2:] = [] $
   • So, $ S = + + [] = $
   • Set flag to False and break.
5. Since flag is False, append $ L[^3] = 47 $ to $ S $: $ S = $.

Final Output: **** is the output. 🖨️

Q6: Grid of Integer Points – Python Representation

Question: You are given a grid of integer points in the plane: $ P_{ij} = (i, j) $, $ 0 \leq i, j \leq 4 $. You want to represent this grid as a list of tuples called points, where each tuple is of the form (x, y). Which code snippets correctly implement this? (MSQ)

Options: 1. python points = [] for x in range(0, 5): for y in range(0, 5): points.append(x, y) 2. python points = [] for x in range(0, 5): for y in range(0, 5): points.append([x, y]) 3. python points = () for x in range(0, 5): for y in range(0, 5): points.append((x, y)) 4. python points = [] for x in range(0, 5): for y in range(0, 5): points.append((x, y))

Answer & Explanation:

• Option 1: ❌ Incorrect. append(x, y) is not valid; append takes only one argument.
• Option 2: ❌ Incorrect. Appends a list [x, y] instead of a tuple (x, y).
• Option 3: ❌ Incorrect. points is initialized as a tuple, which does not have an append method.
• Option 4: ✅ Correct! Appends a tuple to a list, as required.

Final Answer: Only Option 4 is correct. ✅

Q7: List Comprehension Equivalence

Question: Given:

L = [y - x for x in [1, 2, 3] for y in [3, 4, 5] if y > x]

Which of the following codes are equivalent? (MSQ)

Options: 1. python L = [] for x in [1, 2, 3]: for y in [3, 4, 5]: if y > x: L.append(y - x) 2. python L = [] for y in [3, 4, 5]: for x in [1, 2, 3]: if y > x: L.append(y - x) 3. python L = [] for x in [1, 2, 3]: for y in [3, 4, 5]: if y > x: L += [y - x] 4. python L = [] for y in [3, 4, 5]: for x in [1, 2, 3]: if y > x: L += [y - x]

Answer & Explanation:

• The order of for x in ... for y in ... matters for list comprehensions.
• The original comprehension is: for each x in [^1][^2][^3], then for each y in [^3][^4][^5], if y > x, add y-x.
• Options 1 and 3 match the order and logic.
• Options 2 and 4 reverse the order, so the output list will be in a different order.

Final Answer: Options 1 and 3 are equivalent to the given comprehension. ✅✅

Q8: Find All Integer Triplets (x, y, z)

Question: Find all integer triplets $(x, y, z)$ such that $x^2 + y^2 = z^2$ and $0 < x < y < z < 100$. Which code snippets correctly create such a list called triplets? (MSQ)

Options: 1. python triplets = [(x, y, z) for x in range(1, 100) for y in range(x + 1, 100) for z in range(y + 1, 100) if x ** 2 + y ** 2 == z ** 2] 2. python triplets = [] for x in range(1, 100): for y in range(x + 1, 100): for z in range(y + 1, 100): if x ** 2 + y ** 2 == z ** 2: triplets.append((x, y, z)) 3. python triplets = [(x, y, z) for x in range(1, 100) for y in range(1, 100) for z in range(1, 100) if x ** 2 + y ** 2 == z ** 2 and x < y < z]

Answer & Explanation:

• Option 1: ✅ Correct. List comprehension, correct ranges.
• Option 2: ✅ Correct. Nested loops, correct logic.
• Option 3: ✅ Correct. Uses all ranges from 1 to 99, but the condition x < y < z ensures only valid triplets are included.

Final Answer: All three options are correct. ✅✅✅

Q9: Filter Names Starting with a Capital Letter

Question: Given a list L of names, create a list P that contains only those names in L that begin with a capital letter. Which implementations are correct? (MSQ)

Options: 1. python P = [name for name in L if 'a' <= name[^0] <= 'z'] 2. python P = [name for name in L if 'A' <= name[^0] <= 'Z'] 3. python P = [] for name in L: if 'A' <= name[^0] <= 'Z': P.append(name)

Answer & Explanation:

• Option 1: ❌ Incorrect. This checks for lowercase letters.
• Option 2: ✅ Correct. This checks for uppercase letters.
• Option 3: ✅ Correct. This also checks for uppercase letters.

Final Answer: Options 2 and 3 are correct. ✅✅

Q10. Filter strings without the letter ’e’ from input (MSQ)

Question: Accept a sequence of comma-separated strings as input from the user and populate a list of strings that do not have the letter ’e’ in them. Print this list as output to the console. Select all code snippets that achieve this.

Options: 1. python P = input().split(',') L = [] for word in P: if 'e' not in word: L.append(word) print(L) 2. python L = [word for word in input().split(',') if 'e' not in word] print(L) 3. python print([word for word in input().split(',') if 'e' not in word])

Answer: ✅ All three code snippets (1, 2, and 3) correctly achieve the required task.

• Option 1 uses a loop and conditional append.
• Option 2 uses a list comprehension and then prints.
• Option 3 prints the list comprehension directly.

Q11. Which return statement is executed in minmax(x, x)?

Question: Given:

def minmax(a, b):
    if a <= b:
        return a, b
    return b, a

If $ x $ is a real number, when minmax(x, x) is called, which return statement is executed?

Options:

• The return statement in line-3 which is inside the if-block.
• The return statement in line-4 which is outside the if-block.
• Both return statements are executed.
• Neither return statement is executed.

Answer: ✅ The return statement in line-3 which is inside the if-block is executed.

• Because $ x \leq x $ is always true, so the function returns from inside the if-block.

Q12. Select all correct implementations of unique(L) (MSQ)

Question: Select all correct implementations of a function unique that accepts a non-empty list L of integers and returns a list with only the first occurrence of each distinct element (removing duplicates, order preserved).

Options: 1. python def unique(L): L_uniq = [] for elem in L: if elem not in L_uniq: L_uniq.append(elem) return L_uniq 2. python def unique(L): L_uniq = [] for elem in L: if elem in L_uniq: L_uniq.append(elem) return L_uniq 3. python def unique(L): L_uniq = [L[^0]] for i in range(1, len(L)): if not (L[i] in L[:i]): L_uniq.append(L[i]) return L_uniq 4. python def unique(L): L_uniq = [] for i in range(len(L)): if not (L[i] in L[:i]): L_uniq.append(L[i]) return L_uniq 5. python def unique(L): L_uniq = [] for i in range(len(L)): if not (L[i] in L[i+1:]): L_uniq.append(L[i]) return L_uniq

Answer: ✅ Options 1, 3, and 4 are correct.

• Option 1: Standard method, keeps first occurrence.
• Option 3: Starts with first element, then checks if not in previous.
• Option 4: Similar to 3, works for all indices.
• Option 2: Incorrect logic (appends duplicates).
• Option 5: Checks future elements, so it keeps last occurrence, not first.

Q13. Correct implementation of poly(L, x_0) (polynomial evaluation)

Question: Given a Python list of the coefficients of a polynomial $ L = [a_0, a_1, a_2, …, a_n] $, write a function poly that accepts the list and a real number $ x_0 $ and returns the polynomial evaluated at $ x_0 $.

Options: 1. python def poly(L, x_0): n = len(L) psum = 0 for i in range(n): psum = psum + L[i] * (x_0 ** i) return psum 2. python def poly(L, x_0): psum = 0 n = len(L) for i in range(1, n): psum = psum + L[i] * (x_0 ** i) return psum 3. python def poly(L, x_0): psum = 0 n = len(L) for i in range(n): psum = psum + L[i] * (x_0 ** i) return psum 4. python def poly(L, x_0): psum = 0 n = len(L) for i in range(n): psum = psum + x_0 * (L[i] ** i) return psum

Answer: ✅ Options 1 and 3 are correct.

• Both correctly compute $ a_0 + a_1 x_0 + a_2 x_0^2 + … $
• Option 2 skips $ a_0 $ (constant term), so it’s incorrect.
• Option 4 uses the wrong formula.

Q14. Correct implementation of poly_zeros(L, a, b)

Question: Write a function poly_zeros that accepts the list of coefficients L and two integers a and b. It should return a list of all integer zeros of the polynomial in the range $[a, b]$, inclusive, in ascending order (no repeats).

Options: 1. python def poly_zeros(L, a, b): zeros = [] for x in range(a, b+1): if poly(L, x) == 0: zeros.append(x) return zeros 2. python def poly_zeros(L, a, b): zeros = [] for x in range(a, b+1): if poly(L, x) == 0: zeros.append(x) return zeros 3. python def poly_zeros(L, a, b): zeros = [] for x in range(a, b+1): if poly(L, x) == 0: zeros.append(x) return zeros 4. python def poly_zeros(L, a, b): zeros = [] for x in range(a, b+1): if poly(L, x) == 0: zeros.append(x) return zeros

Answer: ✅ All four options are identical and correct.

• They all check each integer $ x $ in $[a, b]$, and append $ x $ if it is a root.