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Find the number of different words that can be formed from the letters of the word ‘TRIANGLE’ so that no vowels are together
Concept: undefined >> undefined
There are 10 persons named P1, P2, P3, ... P10. Out of 10 persons, 5 persons are to be arranged in a line such that in each arrangement P1 must occur whereas P4 and P5 do not occur. Find the number of such possible arrangements.
Concept: undefined >> undefined
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In a certain city, all telephone numbers have six digits, the first two digits always being 41 or 42 or 46 or 62 or 64. How many telephone numbers have all six digits distinct?
Concept: undefined >> undefined
A five-digit number divisible by 3 is to be formed using the numbers 0, 1, 2, 3, 4 and 5 without repetitions. The total number of ways this can be done is ______.
Concept: undefined >> undefined
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
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
