Question
What is the primary advantage of using a stack in
recursive algorithms?Solution
Stacks are crucial in recursive algorithms because they support backtracking by maintaining a history of function calls. Every recursive call is pushed onto the stack, and when a base condition is met, the stack unwinds (pops) the calls in reverse order. This property is integral for problems like solving mazes, tree traversal (DFS), or evaluating expressions. The Last-In-First-Out (LIFO) nature of stacks ensures that the most recent state is resumed first, making them perfect for backtracking scenarios. Why Other Options Are Incorrect ·        Option 1 (Efficient sorting): Stacks are not inherently used for sorting. Algorithms like Quick Sort and Merge Sort do not directly depend on stacks for sorting efficiency. ·        Option 2 (Memory allocation for variables): This is managed by the program's runtime stack, not the data structure itself. ·        Option 4 (Managing concurrent processes): This is more relevant to queues or process schedulers. ·        Option 5 (Sorting data): Stacks are used in algorithms like stack-based parsing but are not designed for general sorting.
I. 6y2 - 17y + 12 = 0
II. 15x2 - 38x + 24 = 0
I. 8x² + 2x – 3 = 0
II. 6y² + 11y + 4 = 0
Solve the quadratic equations and determine the relation between x and y:
Equation 1: x² - 50x + 600 = 0
Equation 2: y² - 51y + 630 = 0
 If 4x = 40, 3y = 33, what is the value of 6x + 4y?
I. 15y2 + 4y – 4 = 0
II. 15x2 + x – 6 = 0
Equation 1: x² - 120x + 3500 = 0
Equation 2: y² - 110y + 3025 = 0
I. x² + 11x + 24 = 0
II. y² + 17y + 72 = 0
I. 20y² - 13y + 2 = 0
II. 6x² - 25x + 14 = 0
The equation x2 – px – 60 = 0, has two roots ‘a’ and ‘b’ such that (a – b) = 17 and p > 0. If a series starts with ‘p’ such...
Solve the quadratic equations and determine the relation between x and y:
Equation 1: x² - 54x + 704 = 0
Equation 2: y² - 44y + 448 = 0