If $^{15} P_{r - 1} :^{15} P_{r - 2} = 3 : 4$ , then $r =$

10

No worries! We‘ve got your back. Try BYJU‘S free classes today!

14

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

6

No worries! We‘ve got your back. Try BYJU‘S free classes today!

8

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $14$
Given,

$^{15} P_{r - 1} :^{16} P_{r - 2} = 3 : 4$

$\frac{15!}{(16 - r)!} : \frac{16!}{(18 - r)!} = \frac{3}{4}$

$\frac{15!}{(16 - r)!} \times \frac{(18 - r) (17 - r) (16 - r)!}{16 \times 15!} = \frac{3}{4}$

$\frac{(18 - r) (17 - r)}{16} = \frac{3}{4}$

$\frac{(18 - r) (17 - r)}{4} = 3$

$r^{2} - 35 r + 306 = 12$

$r^{2} - 35 r + 294 = 0$

$(r - 21) (r - 14) = 0$

$∴ r = 14$

Suggest Corrections

Similar questions

:

$X$	$2 - 4$	$4 - 6$	$6 - 8$	$8 - 10$	$10 - 12$	$12 - 14$	$14 - 16$
$F$	$1$	$2$	$2$	$3$	$6$	$3$	$2$

A = {2, 3, 4, 8, 10},

B = {3, 4, 5, 10, 12},

C = {4, 5, 6, 12, 14},

(A \cup B) \cap (A \cup C)

If A:B = $\frac{1}{2} : \frac{3}{8}$ , B:C = $\frac{1}{3} : \frac{5}{9}$ and C:D = $\frac{5}{6} : \frac{3}{4}$ , then the ratio A:B:C:D is

X = {1, 2, 3, 4}

Y = {2, 3, 5, 7}, Z = {3, 6, 8, 9}

W = {2, 4, 8, 10}

Join BYJU'S Learning Program