Class 11

Math

Algebra

Permutations and Combinations

The number of ways the letters of the word 'SIGNAL' can be arranged such that the vowels occupy only odd position is

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In an examination, a question paper consists of 12 questions divided into two parts i.e., Part I and Part II, containing 5 and 7 questions, respectively. A student is required to attempt 8 questions in all, selecting at least 3 from each part. In how many ways can a student select the questions?

If $N$ denotes the number of ways of selecting $r$ objects of out of $n$ distinct objects $(r≥n)$ with unlimited repetition but with each object included at least once in selection, then $N$ is equal is a. $._{r−1}C_{r−n}$ b. $._{r−1}C_{n}$ c. $._{r−1}C_{n−1}$ d. none of these

The streets of a city are arranged like the like the lines of a chess board. There are $m$ streets running from north to south and $n$ streets from east to west. Find the number of ways in which a man can travel from north-west to south-east corner, covering shortest possible distance.

The value of $r=0∑n−1 _{n}C_{r}/(_{n}C_{r}+_{n}C_{r+1})$ equals a. $n+1$ b. $n/2$ c. $n+2$ d. none of these

In how many ways can 5 girls and 3 boys be seated in a row so that no two boys are together?

Total number of six-digit numbers that can be formed having the property that every succeeding digit is greater than the preceding digit is equal to a. $_{9}C_{3}$ b. $_{10}C_{3}$ c. $_{9}p_{3}$ d. $_{10}p_{3}$

If $6!1 +7!1 =8!x ,$find x

d. minimum value on number of necklaces which can be formed using 17 identical pearls and two identical diamonds and similarly 8 m is number of necklaces which can be formed using 17 identical pearls and different diamonds, then m 18 15