Class 11

Math

Algebra

Permutations and Combinations

How many words can be formed with the letters of FAILURE when all the vowels should come together?

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Using permutation or otherwise, prove that \displaystyle{\left({n}^{{2}}\right)}\frac{!}{{\left({n}!\right)}^{{n}}}{i}{s}{a}{n}\int{e}\ge{r},{w}{h}{e}{r}{e}{n}{i}{s}{a}{p}{o}{s}{i}{t}{i}{v}{e}\int{e}\ge{r}.{\left({J}\exists-{2004}\right]}

In a room there are 12 bulbs of the same wattage, each having separate switch. The number of ways to light the room with different amounts of illumination is (a)$12_{2}−1$ (b) $2_{12}$ (c) $2_{12}−1$ (d) none of these

How many 2 digit even numbers can be formed from the digits 1, 2, 3, 4; 5 if the digits can be repeated?

If a seven-digit number made up of all distinct digits 8, 7, 6, 4, 2, $x$ and $y$ divisible by 3, then $(A)$ Maximum value of $x−y$ is $9$ $(B)$ Maximum value of $x+y$ is $12$ $(C)$ Minimum value of $xy$ is 0 $(D)$ Minimum value of $x+y$ is $3$

If p, q, r are any real numbers, then (A) $max(p,q)<max(p,q,r)$ (B) $min(p,q)=21 (p+q−∣p−q∣)$(C) $max(p,q)<min(p,q,r)$ (D) None of these

The total number of ways of selecting two numbers from the set ${1,2,3,4,……..3n}$ so that their sum is divisible by 3 is equal to a. $22n_{2}−n $ b. $23n_{2}−n $ c. $2n_{2}−n$ d. $3n_{2}−n$

Find the number of ways in which $5A_{prime}sand6B_{′}s$ can be arranged in a row which reads the same backwards and forwards.

How many 3 -digit even numbers can be formed from the digits 1, 2, 3, 4, 5, 6 if the digits can be repeated?