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An online exam is attempted by 50 candidates out of which 20 are boys. The average marks obtained by boys is 12 with a variance 2. The variance of marks obtained by 30 girls is also 2. The average marks of all 50 candidates is 15 . If is the average marks of girls and is the variance of marks of 50 candidates, then is equal to_________.
All the arrangements, with or without meaning, of the word FARMER are written excluding any word that has two appearing together. The arrangements are listed serially in the alphabetic order as in the English dictionary. Then the serial number of the word FARMER in this list is____________
The number of -digit numbers which are neither multiple of nor multiple of 3 is ____________.
Let be two complex numbers such that arg satisfy the equation . Then the imaginary part of is equal to__________.
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