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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
How many sequences are formed with 2 1s and 2 -1s?
💡 Hint: Think about choosing positions for 1s.
Question 2
Easy
If a sequence has more -1s than 1s, is it valid?
💡 Hint: Recall the definition of valid sequences.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What is the formula for the number of valid sequences with n 1s and n -1s?
- C(2n
- n)
- C(2n
- n + 1)
- Both A and B
💡 Hint: Think of how we derive valid counts.
Question 2
True or False: If a sequence has an initial position with a negative sum, it is invalid.
- True
- False
💡 Hint: Refer back to the definition of valid sequences.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Find the number of valid sequences for n=4 and explain your approach.
💡 Hint: Make sure to outline both sets clearly.
Question 2
Create a sequence of n=5 and justify its validity.
💡 Hint: Visualize how the sum changes as you construct the sequence step-by-step.
Challenge and get performance evaluation