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`(3x-(2)/(x^(2)))^(15)` के विस्तार में कौन-सा पद x से स्वतंत्र है ?

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`(3x-(2)/x^(2))^(15)` में प्रसार का `T_(r + 1)` वां पद
`=.^(15)C_(r)(-(2)/(x^(2)))^(r).(3x)^(15-r)`
`=.^(15)C_(r)(-2)^(r).x^(-2r).(3)^(15-r).x^(15-r)`
`=.^(15)C_(r)(-2)^(r).(3)^(15-r).x^(15-3r)`
यह पद x से स्वतंत्र तब होगा, जब x की घात का मान शून्य होगा |
`therefore` अत: 5 + 1 = 6 वां पद x से स्वतंत्र होगा ।

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