Commerce (English Medium) Class 11 - CBSE Question Bank Solutions

How many words, with or without meaning can be made from the letters of the word MONDAY, assuming that no letter is repeated, if

(i) 4 letters are used at a time,

(ii) all letters are used at a time,

(iii) all letters are used but first letter is a vowel?

In how many of the distinct permutations of the letters in MISSISSIPPI do the four I’s not come together?

In how many ways can the letters of the word PERMUTATIONS be arranged if the words start with P and end with S.

In how many ways can the letters of the word PERMUTATIONS be arranged if the vowels are all together.

In how many ways can the letters of the word PERMUTATIONS be arranged if the there are always 4 letters between P and S?

In how many ways can the letters of the word ASSASSINATION be arranged so that all the S’s are together?

Expand the expression: `(2/x - x/2)^5`

Expand the expression: (2x – 3)⁶

Expand the expression: `(x/3 + 1/x)^5`

Expand the expression: `(x + 1/x)^6`

Using Binomial Theorem, evaluate the following:

(96)³

Using binomial theorem, evaluate f the following:

(101)⁴

Using binomial theorem, evaluate the following:

(99)⁵

Using Binomial Theorem, indicate which number is larger (1.1)¹⁰⁰⁰⁰ or 1000.

Find (a + b)⁴ – (a – b)⁴. Hence, evaluate `(sqrt3 + sqrt2)^4 - (sqrt3 - sqrt2)^4`

Find (x + 1)⁶ + (x – 1)⁶. Hence or otherwise evaluate `(sqrt2 + 1)^6 + (sqrt2 -1)^6`

Show that 9ⁿ⁺¹ – 8n – 9 is divisible by 64, whenever n is a positive integer.