A set S contains (2n + 1) elements. If the number of subsets of S which contain at most n elements is 1024, then what is the value of n ?
- A. 10
- B. 8
- C. 6
- D. 5 ✓
Correct Answer: D. 5
Explanation
The sum of binomial coefficients up to n for 2n+1 is half the total sum, yielding 2^{2n}. Equating 2^{2n} to 1024 gives n = 5.
Related questions on Algebra
- How many four-digit natural numbers are there such that <strong>ALL</strong> of the digits are odd?
- What is \sum_{r=0}^{n}2^{r}C(n,r) equal to ?
- If different permutations of the letters of the word 'MATHEMATICS' are listed as in a dictionary, how many words (with or without meaning) a...
- Consider the following statements : 1. If f is the subset of Z\times Z defined by f=\{(xy,x-y);x,y\in Z\}, then f is a function from...
- For how many quadratic equations, the sum of roots is equal to the product of roots?