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### Mathmetics

ISBT Mathmetics for all banking PO,Clerk,IBPS PO,Railway,SSC,IAS,OAS Exams

##### Out of 7 consonants and 4 vowels, how many words of 3  consonants and 2 vowels can be formed ?
 1) 2100 2) 24400 3) 21300 4) 25200 5) None of these
Explanation :
Number of ways of selecting 3 consonants out of 7 = 7C3

Number of ways of selecting 2 vowels out of 4 = 4C2

Number of ways of selecting 3 consonants out of 7 and 2

vowels out of 4 = 7C3 x 4C2

=(7×6×5/3×2×1)×(4×3/2×1)=210

It means that we can have 210 groups where each group

contains total 5 letters(3 consonants and 2 vowels).

Number of ways of arranging 5 letters among themselves = 5! = 5 x 4 x 3 x 2 x 1 = 120

Hence, Required number of ways = 210 x 120 = 25200

##### In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together ?
 1) 100800 2) 120960 3) 240150 4) 4989600 5) None of thesae
Explanation :
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.
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.
So, required number of words = (10080 x 12) = 120960.

##### In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women ?
 1) 42 2) 48 3) 63 4) 90 5) None of these
Explanation : The required number of ways = (7C5 x 3C2) = (7C2 x 3C1) = (7 x 6 )/(2 x 1) x 3 =  63.
##### In how many different ways can the letters of the word 'DETAIL' be arranged in such a way that the vowels occupy only the odd positions ?
 1) 24 2) 32 3) 36 4) 48 5) None of these
Explanation :
There are 6 letters in the given word, out of which there are 3 vowels and 3 consonants.

Let us mark these positions as under:

(1) (2) (3) (4) (5) (6)

Now, 3 vowels can be placed at any of the three places out 4, marked 1, 3, 5.

Number of ways of arranging the vowels = 3P3 = 3! = 6.

Also, the 3 consonants can be arranged at the remaining 3 positions.

Number of ways of these arrangements = 3P3 = 3! = 6.

Total number of ways = (6 x 6) = 36.

##### How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated ?
 1) 6 2) 10 3) 12 4) 20 5) None of thse
Explanation :
Since each desired number is divisible by 5, so we must have 5 at the unit place. So, there is 1 way of doing it.
The tens place can now be filled by any of the remaining 5 digits (2, 3, 6, 7, 9). So, there are 5 ways of filling the tens place.
The hundreds place can now be filled by any of the remaining 4 digits. So, there are 4 ways of filling it.
So, required number of numbers = (1 x 5 x 4) = 20.
##### In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together ?
 1) 810 2) 1440 3) 2880 4) 50400 5) 57600
Explanation :
In the word  'CORPORATION', we consider the vowels OOAIO as one letter.
Thus, we have CRPRTN (OOAIO).
This has 7 (6 + 1) letters of which R occurs 2 times and the rest are different.
Number of ways arranging these letters =7!/2! = 2520.
Now, 5 vowels in which O occurs 3 times and the rest are different, can be arranged in 5!/3!= 20 ways.
So, required number of ways = (2520 x 20) = 50400.
##### In how many different ways can the letters of the word 'LEADING' be arranged in such a way that the vowels always come together ?
 1) 360 2) 480 3) 720 4) 1280 5) None of these
Explanation :
The word 'LEADING'' has 7 different letters.

When the vowels EAI are always together, they can be supposed to form one letter.

Then, we have to arrange the letters LNDG (EAI).

Now, 5 (4 + 1 = 5) letters can be arranged in 5! = 120 ways.

The vowels (EAI) can be arranged among themselves in 3! = 6 ways.

So, required number of ways = (120 x 6) = 720.
##### From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done ?
 1) 565 2) 664 3) 742 4) 756 5) None of these
Explanation :

##### A sum fetched a total simple interest of Rs. 4016.25 at the rate of 9 p.c.p.a. in 5 years. What is the sum ?
 1) Rs. 4462.50 2) Rs. 8032.50 3) Rs. 8900 4) Rs. 8925 5) None of these