Find r if ^ 12 P_ r-2 : ^ 11 P_ r-1 =3: 14 - Vidyadip

Question

Find $r$ if ${ }^{12} \mathrm{P}_{\mathrm{r}-2}:{ }^{11} \mathrm{P}_{\mathrm{r}-1}=3: 14$

✓

Answer

$
\begin{aligned}
& { }^{12} \mathrm{P}_{\mathrm{r}-2}:{ }^{11} \mathrm{P}_{\mathrm{r}-1}=3: 14 \\
& \therefore \quad \frac{12 !}{(12-r+2) !} \div \frac{11 !}{(11-r+1) !}=\frac{3}{14} \\
& \therefore \quad \frac{12 !}{(14-r) !} \times \frac{(12-r) !}{11 !}=\frac{3}{14} \\
& \therefore \quad \frac{12 \times 11 !}{(14-r)(13-r)(12-r) !} \times \frac{(12-r) !}{11 !}=\frac{3}{14} \\
& \therefore \quad \frac{12}{(14-r)(13-r)}=\frac{3}{14} \text { MaharashtraBoardSolutions.in } \\
& \therefore(14-r)(13-r)=8 \times 7 \\
&
\end{aligned}
$
Comparing on both sides, we get
$
\begin{aligned}
& 14-r=8 \\
& \therefore r=6
\end{aligned}
$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "Solve the Following Question.(2 Marks)" from Permutations and Combinations (p-2)→Permutations and Combinations (p-2) — all question types→Maths (commerce) STD 11 Commerce / Arts question papers→Maharashtra Board STD 11 Commerce / Arts question papers→Maharashtra Board question paper generator→

Similar questions

How many distinct 5 digit numbers can be formed using the digits $3,2,3,2,4,5$.

In a hostel, 25 students take tea, 20 students take coffee, 15 students take milk, 10 students take both tea and coffee, 8 students take both milk and coffee. None of them take tea and milk both and everyone takes atleast one beverage, find the number of students in the hostel.

Differentiate the following functions w.r.t. x. : $\frac{e^x}{e^x+1}$

If $\mathrm{f}(\mathrm{x})=\frac{2 x-1}{5 x-2}, x \neq \frac{2}{5}$, verify whether (fof) $(\mathrm{x})=\mathrm{x}$

How many four-digit numbers will not exceed 7432 if they are formed using the digits 2, 3, 4, 7 without repetition?

Mr. Manish purchased a motorcycle at ₹ 70,000/-. After some years he sold his motorcycle at its exact depreciated value of it that is $₹ 51,030 /-$. The rate of depreciation was taken as $10 \%$. Find out how many years he sold his motorcycle.

Solve the following examples: : The supply $S$ for a commodity at price $P$ is given by $S=P^2+9 P-2$. Find the marginal supply when the price is 7 .

Evaluate the following:

$\lim _{x \rightarrow 0}\left[\frac{5^x+3^x-2^x-1}{x}\right]$

A Signal is generated from 2 flags by putting one flag above the other. If 4 flags of different colours are available, how many different signals can be generated?

Find the value of k, if the area of $\triangle P Q R$ is 4 square units and vertices are $P(k, 0), Q(4,0), R(0,2)$.