A regular dodecagon (12-sided regular polygon) is inscribed in a circle of radius r cm as shown in the figure. The side of the dodecagon is d cm. All the triangles (numbered 1 to 12 in the figure) are used to form squares of side r cm, and each numbered triangle is used only once to form a square. The number of squares that can be formed and the number of triangles required to form each square, respectively, are

Questions Asked in GATE DA exam

Create empty stack S
Set x = 0, flag = 0, sum = 0
Push x onto S
while (S is not empty){
    if (flag equals 0){
        Set x = x + 1
        Push x onto S
    }
    if (x equals 8):
        Set flag = 1
    if (flag equals 1){
        x = Pop(S)
        if (x is odd):
            Pop(S)
        Set sum = sum + x
    }
}
Output sum

The value of \( sum \) output by a program executing the above pseudocode is:

GATE DA - 2025
Data Structures

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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 160 (Answer in integer).

GATE DA - 2025
Recursion

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Consider the following tables, Loan and Borrower, of a bank.

Query: \[ \pi_{\text{branch\_name}, \text{customer\_name}} (\text{Loan} \bowtie \text{Borrower}) \div \pi_{\text{branch\_name}}(\text{Loan}) \] where \( \bowtie \) denotes natural join. The number of tuples returned by the above relational algebra query is 1 (Answer in integer).
- GATE DA - 2025
- Relational Algebra
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The Correct Option is A

Solution and Explanation

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Questions Asked in GATE DA exam

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