If - r -044 49- r 5-50 C X- then the values of x is-areB- 5C- 44D- 45

The correct options are A 6 C 44Given : nbsp;∑_r=0^44 ^49 rC_5= ^50C_x Now, nbsp; ∑_r=0^44 ^49 rC_5 nbsp;= nbsp; nbsp; ^49C_5+ ^48C_5+ ^47C_5+⋯+ ^5C_ ...

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Standard XII

Mathematics

Binomial Expression

If ∑ r =044 4...

Question

If $44 \sum r = 0^{49 - r} C_{5} =^{50} C_{x}$ , then the value(s) of $x$ is/are

6

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5

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44

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45

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Solution

The correct options are
A $6$
C $44$
Given : $44 \sum r = 0^{49 - r} C_{5} =^{50} C_{x}$
Now,
$44 \sum r = 0^{49 - r} C_{5} =^{49} C_{5} +^{48} C_{5} +^{47} C_{5} + \dots +^{5} C_{5} =^{5} C_{5} +^{6} C_{5} +^{7} C_{5} + \dots +^{49} C_{5} =^{6} C_{6} +^{6} C_{5} +^{7} C_{5} + \dots +^{49} C_{5} (∵^{6} C_{6} =^{5} C_{5}) =^{49 + 1} C_{6} =^{50} C_{6}$
Now,
$^{50} C_{x} =^{50} C_{6} \Rightarrow x = 6, (50 - 6) ∴ x = 6, 44$

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Binomial Expression

Standard XII Mathematics

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If 44∑r=0 49−rC5= 50Cx, then the value(s) of x is/are

The correct options are A 6 C 44Given : 44∑r=0 49−rC5= 50Cx Now, 44∑r=0 49−rC5= 49C5+ 48C5+ 47C5+⋯+ 5C5= 5C5+ 6C5+ 7C5+⋯+ 49C5= 6C6+ 6C5+ 7C5+⋯+ 49C5 (∵ 6C6= 5C5)= 49+1C6= 50C6 Now, 50Cx= 50C6⇒x=6,(50−6)∴x=6,44

If $44 \sum r = 0^{49 - r} C_{5} =^{50} C_{x}$ , then the value(s) of $x$ is/are