1

### JEE Main 2017 (Online) 8th April Morning Slot

If all the words, with or without meaning, are written using the letters of the word QUEEN and are arranged as in English dictionary, then the position of the word QUEEN is :
A
44th
B
45th
C
46th
D
47th
2

### JEE Main 2017 (Online) 9th April Morning Slot

The number of ways in which 5 boys and 3 girls can be seated on a round table if a particular boy B1 and a particular girl G1 never sit adjacent to each other, is :
A
5 $\times$ 6!
B
6 $\times$ 6!
C
7!
D
5 $\times$ 7!

## Explanation

Number of ways = Total - when B1 and G1 sit together

Total ways to seat 8 people on round table = (8 - 1)! = 7!

When B1 and G1 sit together then assume B1 and G1 are one people, so total 7 people are there and among B1 and G1 they can sit 2! ways.

So total no of ways when B1 and G1 sit together
= (7 - 1)! $\times$ 2! = 6! $\times$ 2!

Number of ways = 7! - 6! $\times$ 2! = 6!$\times$(7 - 2) = 5 $\times$ 6!
3

### JEE Main 2018 (Offline)

From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. The number of such arrangements is :
A
at least 750 but less than 1000
B
at least 1000
C
less than 500
D
at least 500 but less than 750

## Explanation

From 6 different novels 4 novels can be chosen = ${}^6{C_4}$ ways

And from 3 different dictionaries 1 can be chosen = ${}^3{C_1}$ ways

$\therefore$ From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary can be chosen = ${}^6{C_4} \times {}^3{C_1}$ ways

Let 4 novels are N1, N2, N3, N4 and 1 dictionary is D1.

Dictionary should be in the middle. So the arrangement will be like this

_ _ D1 _ _

On those 4 blank places 4 novels N1, N2, N3, N4 can be placed. And 4 novels can be arrange $4!$ ways.

$\therefore$ Total no of ways = ${}^6{C_4} \times {}^3{C_1}$$\times 4!$ = 1080
4

### JEE Main 2018 (Online) 15th April Morning Slot

n$-$digit numbers are formed using only three digits 2, 5 and 7. The smallest value of n for which 900 such distinct numbers can be formed, is :
A
6
B
7
C
8
D
9

## Explanation

In n digit number first place can be filled with any one of 2, 5, 7. So no of ways first digit can be filled = 3

Similarly,
no of ways 2nd digit can be filled = 3 ways
.
.
.
.
- - - - - - nth - - - - - - - = 3 ways

$\therefore$ Total numbers = 3 $\times$ 3 $\times$ 3 .... n times
= 3n
$\therefore$ According to question, for smallest value of n,

3n > 900

36 = 729 < 900

37 = 2187 > 900

$\therefore$ n = 7

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