If 5 C r - r -5 C r -1- then the number of values of r isA- 2B- 1C- 3D- 0

The correct option is B 1Given : nbsp;^5C_r=r· ^5C_r 1 ⇒ ^5C_r ^5C_r 1=r ⇒ 5 r+1r=r (since ^nC_r ^nC_r 1=n r+1r) ∴ r^2+r 6=0 ⇒ (r+3)(r 2)=0 r= 3,2 rejecti ...

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Standard XII

Mathematics

Permutations and Combinations

If 5 C r = r ...

Question

If $^{5} C_{r} = r \cdot^{5} C_{r - 1}$ , then the number of value(s) of $r$ is

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Solution

The correct option is B $1$
Given : $^{5} C_{r} = r \cdot^{5} C_{r - 1}$
$\Rightarrow \frac{^{5} C_{r}}{^{5} C_{r - 1}} = r$
$\Rightarrow \frac{5 - r + 1}{r} = r$ $(since \frac{^{n} C_{r}}{^{n} C_{r - 1}} = \frac{n - r + 1}{r})$

$∴ r^{2} + r - 6 = 0$
$\Rightarrow (r + 3) (r - 2) = 0$
$r = - 3, 2$
rejecting $r = - 3$ as $r \in W$
$∴$ Number of solution $= 1$

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Permutations and Combinations

Standard XII Mathematics

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If 5Cr=r⋅ 5Cr−1, then the number of value(s) of r is

The correct option is B 1Given : 5Cr=r⋅ 5Cr−1 ⇒ 5Cr 5Cr−1=r ⇒ 5−r+1r=r (since nCr nCr−1=n−r+1r) ∴ r2+r−6=0 ⇒ (r+3)(r−2)=0 r=−3,2 rejecting r=−3 as r∈W ∴ Number of solution =1

If $^{5} C_{r} = r \cdot^{5} C_{r - 1}$ , then the number of value(s) of $r$ is