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STD 11 - 7. binomial theoram — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsSTD 11 - 7. binomial theoram1 Mark
MCQ
Value $\sum\limits_{r = 0}^{15} {\left( {{}^{15}{C_r}{}^{40}{C_{15}}{}^{20}{C_r} - {}^{35}{C_{15}}{}^{15}{C_r}{}^{25}{C_r}} \right)} $ is-
  • ✓
    $0$
  • B
    ${{}^{40}{C_{15}} - {}^{35}{C_{15}}}$
  • C
    ${{}^{35}{C_{15}} - {}^{40}{C_{15}}}$
  • D
    $^{40}C_{15}$
✓

Answer

Correct option: A.
$0$
a
$^{40}{C_{15}}\sum\limits_{r = 0}^{15} {{\,^{15}}{C_r}} {\,^{20}}{C_{20 - r}} - {\,^{35}}{C_{15}}\sum\limits_{r = 0}^{15} {{\,^{15}}{C_r}} {\,^{25}}{C_{25 - r}}$

$^{40}{C_{15}}{\,^{35}}{C_{20}} - {\,^{35}}{C_{15}}{\,^{40}}{C_{25}} = 0$

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