# If K + 5pk + 1 = 11 ( K − 1 ) 2 . K + 3pk , Then the Values of K Are, 7 and 11 , 6 and 7 , 2 and 11 , 2 and 6 - Mathematics

MCQ

If k + 5Pk + 1 =$\frac{11 (k - 1)}{2}$. k + 3Pk , then the values of k are

• 7 and 11

• 6 and 7

• 2 and 11

• 2 and 6

#### Solution

6 and 7

k + 5Pk + 1 =$\frac{11 (k - 1)}{2}$. k + 3Pk

$\Rightarrow \frac{\left( k + 5 \right)!}{\left( k + 5 - k - 1 \right)!} = \frac{11\left( k - 1 \right)}{2} \times \frac{\left( k + 3 \right)!}{\left( k + 3 - k \right)!}$
$\Rightarrow \frac{\left( k + 5 \right)!}{4!} = \frac{11\left( k - 1 \right)}{2} \times \frac{\left( k + 3 \right)!}{3!}$
$\Rightarrow \frac{\left( k + 5 \right)!}{\left( k + 3 \right)!} = \frac{11\left( k - 1 \right)}{2} \times \frac{4!}{3!}$
$\Rightarrow \left( k + 5 \right)\left( k + 4 \right) = 22\left( k - 1 \right)$
$\Rightarrow k^2 + 9k + 20 = 22k - 22$
$\Rightarrow k^2 - 13k + 42 = 0$
$\Rightarrow k = 6, 7$

Concept: Permutations
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 16 Permutations
Q 17 | Page 47