Q47 / 77 · NTA Abhyas (JEE Main) 2020 · Mathematics · Statistics

If the mean and the variance of the numbers a, b, 8, 5 and 10 are 6 and 6.8 respectively, then the value of a3+b3 is equal to

  • A
    58
  • B
    61
  • Correct answer
    C
    91
  • D
    89

Solution

Mean =6=a+b+8+5+105⇒a+b=7
Variance =6.8=a2+b2+64+25+1005-36
⇒a2+b2=25
2ab=a+b2-a2+b2⇒ab=12
Now, a3+b3=a+b3-3aba+b
=343-3×12×7
=91

Hence, the correct answer is option: 'C'.

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