(D) Given that,${ }^{12} C_{2 k-1}={ }^{12} C_{k+1}$.We know that if ${ }^n C_x={ }^n C_y$,then either $x=y$ or $x+y=n$.Case $1$: $2k-1 = k+1$$k = 2$.

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(D) Given that,${ }^{12} C_{2 k-1}={ }^{12} C_{k+1}$.We know that if ${ }^n C_x={ }^n C_y$,then either $x=y$ or $x+y=n$.Case $1$: $2k-1 = k+1$$k = 2$.Case $2$: $(2k-1) + (k+1) = 12$$3k = 12$$k = 4$.Since $k=4$ is one of the given options,the correct value is $4$.

Class 11 Mathematics Permutation and Combination Definition of combinations, Condition combinations

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If ${ }^{12} C_{2 k-1}={ }^{12} C_{k+1}$,then find $k$.

AP EAMCET 2020 All AP EAMCET

A
$3$
B
$6$
C
$9$
D
$4$

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Permutation and Combination

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Definition of combinations, Condition combinations

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If ${ }^{12} C_{2 k-1}={ }^{12} C_{k+1}$,then find $k$.

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In how many ways can $6$ '$+$' signs and $4$ '$$' signs be arranged in a row such that no two '$$' signs occur together?