If \(\frac{1}{6!}+\frac{1}{7!}=\frac{x}{8!}\), find x.
Solution and Explanation
Given, \(\frac{1}{6!}+\frac{1}{7!}=\frac{x}{8!}\)
\(⇒\frac{1}{6!}+\frac{1}{7\times6!}=\frac{x}{8\times7\times6!}\)
\(⇒\frac{1}{6!}(1+\frac{1}{7})=\frac{x}{8\times7\times6!}\)
\(⇒1+\frac{1}{7}=\frac{x}{8\times7}\)
\(⇒\frac{8}{7}=\frac{x}{8\times7}\)
\(⇒x=\frac{8\times8\times7}{7}\)
\(∴x=64\)
Top CBSE Class XI Mathematics Questions
- A coin is tossed twice, what is the probability that atleast one tail occurs?
- The relation f is defined by
\(f(x) = \begin{cases} x^2, & \quad 0≤x≤3\\ 3x, & \quad 3≤x≤10 \end{cases}\)
The relation g is defined by
\(g(x) = \begin{cases} x^2, & \quad 0≤x≤2\\ 3x, & \quad 2≤x≤10 \end{cases}\)
Show that f is a function and g is not a function. - Let \(f={(x,\frac {x^2}{1+x^2}):x∈R}\) be a function from R into R. Determine the range of f.
- How many 4-letter code can be formed using the first 10 letters of the English alphabet, if no letter can be repeated?
- In how many of the distinct permutations of the letters in MISSISSIPPI do the four I's not come together?
Top CBSE Class XI Questions
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Concepts Used:
Permutations and Combinations
Permutation:
Permutation is the method or the act of arranging members of a set into an order or a sequence.
- In the process of rearranging the numbers, subsets of sets are created to determine all possible arrangement sequences of a single data point.
- A permutation is used in many events of daily life. It is used for a list of data where the data order matters.
Combination:
Combination is the method of forming subsets by selecting data from a larger set in a way that the selection order does not matter.
- Combination refers to the combination of about n things taken k at a time without any repetition.
- The combination is used for a group of data where the order of data does not matter.