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 General Aptitude
 Permutation and Combination
1.
There are 5 red, 4 white and 3 blue marbles in a bag. They are taken out one by one and arranged in a row. Assuming that all the 12 marbles are drawn, find the number of different arrangements?
 A.27207
 C.27270
 B.27720
 D.22077
 Answer & Explanation
 Report
Answer : [B]
Explanation :
Explanation :
Total number of balls = 12  
Of these 5 balls are of 1^{st} type (red color), 4 balls are of 2^{nd} type and 3 balls are of 3^{rd} type.  


2.
There are 5 different shades of green dye, 4 different shades of blue dye and 3 different shades of red dye. If at least one green and one blue has to be included, how many combinations of dye are possible?
 A.7320
 C.3270
 B.3720
 D.3702
 Answer & Explanation
 Report
Answer : [B]
Explanation :
Explanation :
From the 5 different shades of green, one or more shades can be chosen in  
5C_{1} + 5C_{2} + 5C_{3} + 5C_{4} + 5C_{5} = 31 ways  
From 4 different shades of blue, one or more can be chosen in  
4C_{1} + 4C_{2} + 4C_{3} + 4C_{4} = 15 ways  
Similarly, from 3 different shades of red one or more or none can be taken in  
3C_{3} + 3C_{2} + 3C_{1} + 3C_{0} = 8  


3.
A set of seven parallel lines is interested by another set of five parallel lines. How many parallelograms are formed by this process?
 A.280
 C.210
 B.140
 D.60
 Answer & Explanation
 Report
Answer : [C]
Explanation :
Explanation :
Any two parallel lines from the first set and any two from the second set will form a parallelogram. 
The number of parallelograms that are formed = 7C_{2} x 5C_{2} = 21 x 10 = 210 
4.
In how many ways can the word, ‘RESHMA’ be arranged, so that each word begins with R and ends with M?
 A.6!
 C.24
 B.25
 D.20
 Answer & Explanation
 Report
Answer : [C]
Explanation :
Explanation :
Here the word is to begin with R and to end with M. So, the two places of the word is fixed. 
Hence, remaining 4 places can be filled with 4 words in 4! Ways. 
Required number of ways = 4! = 24 ways 
5.
In an examination, a candidate has to pass in each of the 6 subjects. In how many ways can he fail?
 A.63
 C.6!
 B.2^{6}
 D.6
 Answer & Explanation
 Report
Answer : [A]
Explanation :
Explanation :
The student can fail in the 6 subjects in any of the following ways.  



