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JEE Main 20204 SeptemberMorning Shift
Exam
JEE Main
Year
2020
Date
4 September
Shift
Morning Shift
Subject
Mathematics
Chapter
Binomial Theorem

JEE Main 2020 · 4 September · Morning Shift · Mathematics · Binomial Theorem

The value of ∑ _ r = 0 ^ 20 C6 50 - r is equal to:

The value of ∑r=020C650−r\mathop{∑}_{r = 0}^{20} C6 50 - r is equal to:

Options

  1. AC751−C730C7 51 - C7 30
  2. BC750−C730C7 50 - C7 30
  3. CC650−C630C6 50 - C6 30
  4. DC751+C730C7 51 + C7 30

Correct answer

A. C751−C730C7 51 - C7 30

Step-by-step solution

∑r=020C650−r=\mathop{∑}_{r = 0}^{20} C6 50 - r =

=50C6+49C6+48C6+....+30C6{=}^{50}{C}_{6}{+}^{49}{C}_{6}{+}^{48}{C}_{6} + . .. . {+}^{30}{C}_{6}

=−30C7+30C7+30C6+31C6+32C6+....+50C6= {-}^{30}{C}_{7}{+}^{30}{C}_{7}{+}^{30}{C}_{6}{+}^{31}{C}_{6}{+}^{32}{C}_{6} + . ... {+}^{50}{C}_{6}

=−30C7+31C7+31C6+32C6+....+50C6= {-}^{30}{C}_{7}{+}^{31}{C}_{7}{+}^{31}{C}_{6}{+}^{32}{C}_{6} + . ... {+}^{50}{C}_{6}

=−30C7+32C7+32C6+....+50C6= {-}^{30}{C}_{7}{+}^{32}{C}_{7}{+}^{32}{C}_{6} + . ... {+}^{50}{C}_{6}

=−30C7+51C7= {-}^{30}{C}_{7}{+}^{51}{C}_{7}.

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