In the word 'MATHEMATICS', we treat the vowels AEAI as one letter.
Thus, we have MTHMTCS (AEAI).
Now, we have to arrange 8 letters, out of which M occurs twice, T occurs twice and the rest are different.
So,Number of ways of arranging these letters = (8!/2!*2!)=10080.
Now, AEAI has 4 letters in which A occurs 2 times and the rest are different.
Number of ways of arranging these letters = (4!/2)=12.
=> Required number of words = (10080 * 12) = 120960.
Workspace
NA
SHSTTON
41
Solv. Corr.
78
Solv. In. Corr.
119
Attempted
1 M:54 S
Avg. Time
12 / 100
Choose the correct option.
Consider the word ROTOR. Whichever way you read it, from left to right or from right to left, you get the same word. Such a word is known as palindrome. Find the maximum possible number of 5-letter palindromes?
The first letter from the right can be chosen in 26 ways because there are 26 alphabets.
Having chosen this, the second letter can be chosen in 26 ways.
=> The first two letters can be chosen in 26*26=676 ways
Having chosen the first two letters, the third letter can be chosen in 26 ways.
=> All the three letters can be chosen in 676*26=17576 ways.
=> maximum possible number of five letter palindromes is 17576 because the fourth letter is the same as the second letter and the fifth letter is the same as the first letter.
Workspace
NA
SHSTTON
64
Solv. Corr.
69
Solv. In. Corr.
133
Attempted
1 M:29 S
Avg. Time
13 / 100
Choose the correct option.
In how many ways can an animal trainer arrange 5 lions and 4 tigers in a row so that no two lions are together
All 9 letters are different so Number of words possible are 9!
Workspace
NA
SHSTTON
14
Solv. Corr.
59
Solv. In. Corr.
73
Attempted
1 M:8 S
Avg. Time
15 / 100
Choose the correct option.
There are 5 Rock songs, 6 Carnatic songs and 3 Indi pop songs. How many different albums can be formed using the above repertoire if the albums should contain at least 1 Rock song and 1 Carnatic song?
Rock can be done in (2^5 - 1) = 32 - 1 = 31 ways.
6 Carnatic songs, choosing at least one, can be selected in 2^6 - 1 = 64 - 1 = 63 ways.
3 Indi pop can be selected in 2^3 = 8 ways
Therefore, the total number of combinations = 31 * 63 * 8 = 15624
Workspace
NA
SHSTTON
48
Solv. Corr.
52
Solv. In. Corr.
100
Attempted
0 M:46 S
Avg. Time
16 / 100
Choose the correct option.
How many 6 digit telephone numbers can be formed if each number starts with 35 and no digit appears more than once?
6 digits telephone number can be formed by 10 digits (0,1,2...9)
As Given, each number start with 35.
So we have 8 digits remaining and 4 place.
So, 4 places can be formed in 8*7*6*5=1680.
Workspace
NA
SHSTTON
22
Solv. Corr.
69
Solv. In. Corr.
91
Attempted
0 M:57 S
Avg. Time
17 / 100
Choose the correct option.
When all words in "MASTER" is sorted in alphabetical order then what is the 49th word ?
Arranged alphabet: A E M R S T
word start with A: A _ _ _ _ _ =120
so,word start with A
next, A E _ _ _ _=24
next, A M _ _ _ _=24
total word is 48
so.word at 49 rank is A R E M S T.
Workspace
NA
SHSTTON
37
Solv. Corr.
41
Solv. In. Corr.
78
Attempted
0 M:0 S
Avg. Time
18 / 100
Choose the correct option.
There are 20 balls which are red,blue,or green.If 7 balls are green and the sum of red balls and green balls is less than 13, at most how may red balls are ?
Given condition 2 vowel should comes together : {_L_D_N_G_)
So, 3 vowels can be placed at 5 positions = 5p3 * 4! = 60*24 = 1440.
So required arrangements : (5040 - 1440) = 3600
Workspace
NA
SHSTTON
47
Solv. Corr.
27
Solv. In. Corr.
74
Attempted
0 M:0 S
Avg. Time
20 / 100
Choose the correct option.
In a meeting between 2 countries each country has 12 delegates. All the delegates of one country shake hands with all delegates of other countries. Find the number of handshakes possible?
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