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NIMCET 2021 — Mathematics PYQ

NIMCET | Mathematics | 2021

There are 50 questions in a paper. Find the number of way in which a student can attempt one or more questions

Choose the correct answer:

D.
$2^{50} + 2$

Explanation

1. Analyzing the Choices for Each Question

For every single question in the paper, a student has 2 options:

Attempt the question.

Do not attempt the question.

2. Calculating Total Possible Outcomes

Since there are 50 questions and each question has 2 options, the total number of ways to deal with the entire paper is:

$\text{Total ways} = 2 \times 2 \times 2 \times \dots \text{ (50 times)}$

$\text{Total ways} = 2^{50}$

3. Understanding the "One or More" Constraint

The $2^{50}$ total ways include every possible combination, including the single case where the student attempts zero questions (leaves all 50 questions blank).

The problem specifically asks for the number of ways to attempt one or more questions. This means we must subtract the "all blank" case from the total.

Total ways to leave all questions blank = 1 way.

4. Final Calculation

$\text{Ways to attempt at least one question} = (\text{Total ways}) - (\text{Ways to attempt zero questions})$

$\text{Number of ways} = 2^{50} - 1$

Conclusion

This follows the formula for finding the number of non-empty subsets of a set with $n$ elements, which is $2^n - 1$ .

Correct Answer: $2^{50} - 1$

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