Please select a subject first
Advertisements
Advertisements
The number of 5-digit telephone numbers having atleast one of their digits repeated is ______.
Concept: undefined >> undefined
The total number of 9 digit numbers which have all different digits is ______.
Concept: undefined >> undefined
Advertisements
The number of words which can be formed out of the letters of the word ARTICLE, so that vowels occupy the even place is ______.
Concept: undefined >> undefined
The number of permutations of n different objects, taken r at a line, when repetitions are allowed, is ______.
Concept: undefined >> undefined
The number of different words that can be formed from the letters of the word INTERMEDIATE such that two vowels never come together is ______.
Concept: undefined >> undefined
In the permutations of n things, r taken together, the number of permutations in which m particular things occur together is `""^(n - m)"P"_(r - m) xx ""^r"P"_m`.
Concept: undefined >> undefined
Five boys and five girls form a line. Find the number of ways of making the seating arrangement under the following condition:
| C1 | C2 |
| (a) Boys and girls alternate: | (i) 5! × 6! |
| (b) No two girls sit together : | (ii) 10! – 5! 6! |
| (c) All the girls sit together | (iii) (5!)2 + (5!)2 |
| (d) All the girls are never together : | (iv) 2! 5! 5! |
Concept: undefined >> undefined
Using the digits 1, 2, 3, 4, 5, 6, 7, a number of 4 different digits is formed. Find
| C1 | C2 |
| (a) How many numbers are formed? | (i) 840 |
| (b) How many number are exactly divisible by 2? | (i) 200 |
| (c) How many numbers are exactly divisible by 25? | (iii) 360 |
| (d) How many of these are exactly divisible by 4? | (iv) 40 |
Concept: undefined >> undefined
How many words (with or without dictionary meaning) can be made from the letters of the word MONDAY, assuming that no letter is repeated, if
| C1 | C2 |
| (a) 4 letters are used at a time | (i) 720 |
| (b) All letters are used at a time | (ii) 240 |
| (c) All letters are used but the first is a vowel | (iii) 360 |
Concept: undefined >> undefined
Find the rth term in the expansion of `(x + 1/x)^(2r)`
Concept: undefined >> undefined
Expand the following (1 – x + x2)4
Concept: undefined >> undefined
Find the 4th term from the end in the expansion of `(x^3/2 - 2/x^2)^9`
Concept: undefined >> undefined
Evaluate: `(x^2 - sqrt(1 - x^2))^4 + (x^2 + sqrt(1 - x^2))^4`
Concept: undefined >> undefined
Find the coefficient of x11 in the expansion of `(x^3 - 2/x^2)^12`
Concept: undefined >> undefined
Determine whether the expansion of `(x^2 - 2/x)^18` will contain a term containing x10?
Concept: undefined >> undefined
Find the term independent of x in the expansion of `(sqrt(x)/sqrt(3) + sqrt(3)/(2x^2))^10`.
Concept: undefined >> undefined
Show that `2^(4n + 4) - 15n - 16`, where n ∈ N is divisible by 225.
Concept: undefined >> undefined
If n is a positive integer, find the coefficient of x–1 in the expansion of `(1 + x)^2 (1 + 1/x)^n`
Concept: undefined >> undefined
Which of the following is larger? 9950 + 10050 or 10150
Concept: undefined >> undefined
Find the coefficient of x50 after simplifying and collecting the like terms in the expansion of (1 + x)1000 + x(1 + x)999 + x2(1 + x)998 + ... + x1000 .
Concept: undefined >> undefined
