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    Python Functions and Recursion PYQs for GATE DA

    Solve 3+ Python Functions and Recursion previous year questions for GATE DA with answers and detailed solutions. Free sample questions below.

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    Question 1
    2026 PYQ
    Level 3: Exam Standard
    A recursive function in Python is given.

    def mystery(n):
        if n <= 0:
            return 1
        else:
            return mystery(n-1) + mystery(n-2)

    Now, consider the following function call:

    mystery(4)

    Assume that a typical runtime stack is used to manage function calls. Each function call is pushed onto the stack and removed only after it finishes execution.

    Which of the following options denotes the total number of function calls (i.e., the total number of stack activations), including the initial call, to compute mystery(4)?
    Question 2
    2025 PYQ
    Level 3: Exam Standard
    Consider the following Python code snippet.

    def f(a,b):
if (a==0):
return b
if (a%2==1):
return 2*f((a-1)/2,b)
return b+f(a-1,b)
print(f(15,10))

    The value printed by the code snippet is (Answer in integer)
    Question 3
    2024 PYQ
    Level 3: Exam Standard
    Consider the following Python code:
    def count(child_dict, i):
    if i not in child_dict.keys():
    return 1
    ans = 1
    for j in child_dict[i]:
    ans += count(child_dict, j)
    return ans
    child_dict = dict()
    child_dict[0] = [1,2]
    child_dict[1] = [3,4,5]
    child_dict[2] = [6,7,8]
    print(count(child_dict,0))
    Which ONE of the following is the output of this code?
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    Python Functions and Recursion PYQs for GATE DA

    Solve 3+ Python Functions and Recursion previous year questions for GATE DA with answers and detailed solutions. Free sample questions below.

    Chapter Roadmap: Python Functions and Recursion

    Chapter Roadmap: Python Functions and Recursion

    1
    Recursive Function Tracing and Return Values
    Core Focus. Execution flow, stack frames, return propagation.
    2
    Chapter Mastery Achieved

    The Mental Model: Stack Frames as Isolated Worlds

    The Mental Model: Stack Frames as Isolated Worlds

    Recursion is not a loop that reuses memory. It is a chain of independent function invocations.

    Frame 3: ans = 1
    Frame 2: ans = 1
    Frame 1: ans = 1
    • Each call New Stack Frame (new local namespace)
    • Parent state is frozen at the call site
    • Execution resumes only after child returns a value
    • Variables like n, ans, or i are distinct copies per frame
    Key Insight: When tracing, never update a variable "globally" across recursive calls unless explicitly passed by reference (which Python primitives do not support). Each ans = 1 in a new call starts fresh.

    Python Functions and Recursion: Solved Questions with Step-by-Step Explanations (3 Problems)

    Question 1 · Programming, Data Structures and Algorithms · 2026 MCQ
    A recursive function in Python is given.

    def mystery(n):
        if n <= 0:
            return 1
        else:
            return mystery(n-1) + mystery(n-2)

    Now, consider the following function call:

    mystery(4)

    Assume that a typical runtime stack is used to manage function calls. Each function call is pushed onto the stack and removed only after it finishes execution.

    Which of the following options denotes the total number of function calls (i.e., the total number of stack activations), including the initial call, to compute mystery(4)?
    1. A.

      5

    2. B.

      9

    3. C.

      15

    4. D.

      17

    Correct Answer:

    C

    Step-by-Step Solution

    Insight: The total number of function calls follows a recurrence relation , where the accounts for the current function call itself.

    Exam route: Compute iteratively from base cases. . Then , , , .

    Learning route: Draw the recursion tree for mystery(4). The root is 1 call. It branches to mystery(3) and mystery(2). Count all nodes in this call tree. Total nodes = 15. Note that mystery(0) and mystery(-1) are base cases that make 1 call each and return immediately without further branching.

    Question 2 · Programming, Data Structures and Algorithms · 2025 NAT
    Consider the following Python code snippet.

    def f(a,b):
if (a==0):
return b
if (a%2==1):
return 2*f((a-1)/2,b)
return b+f(a-1,b)
print(f(15,10))

    The value printed by the code snippet is (Answer in integer)
    Correct Answer:

    160.00

    Step-by-Step Solution

    Insight: The function evaluates conditions sequentially. Since is always odd in the recursive steps, it always takes the a%2==1 branch, multiplying the result by 2 at each step until .

    Exam route: .

    Learning route: Trace frame by frame. Note that (a-1)/2 in Python 3 produces a float (e.g., 7.0). However, a%2==1 still evaluates to True for 7.0 % 2 == 1.0. The base case a==0 catches 0.0. The return value is multiplied by 2 exactly 4 times.

    Question 3 · Programming, Data Structures and Algorithms · 2024 MCQ
    Consider the following Python code:
    def count(child_dict, i):
    if i not in child_dict.keys():
    return 1
    ans = 1
    for j in child_dict[i]:
    ans += count(child_dict, j)
    return ans
    child_dict = dict()
    child_dict[0] = [1,2]
    child_dict[1] = [3,4,5]
    child_dict[2] = [6,7,8]
    print(count(child_dict,0))
    Which ONE of the following is the output of this code?
    1. A.

      6

    2. B.

      1

    3. C.

      8

    4. D.

      9

    Correct Answer:

    D

    Step-by-Step Solution

    Insight: The function computes the total number of nodes in a tree represented by an adjacency list, where each node counts itself (ans = 1) and adds the counts of its children via return values.

    Exam route: Draw the tree. Root 0 has children 1, 2. Node 1 has 3, 4, 5. Node 2 has 6, 7, 8. Total nodes = 1 (root) + 1 (node 1) + 3 (leaves of 1) + 1 (node 2) + 3 (leaves of 2) = 9.

    Learning route: Trace using stack frames. Frame 0 calls Frame 1 and Frame 2. Frame 1 calls 3, 4, 5 which return 1 each. Frame 1 returns . Frame 2 similarly returns 4. Frame 0 returns . The key is that ans = 1 resets in every frame, so it is return-value aggregation, not a shared global counter.

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