Let be the sum of the numbers appeared when two fair dice are rolled and let the probability that are in geometric progression be Then the value of is [2023]

STUDY MATERIALS
COURSES
MORE
SUCCESS STORY
ADMISSION
STORE

Back

JEE ADVANCE

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

JEE MAIN

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

NEET

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

BITSAT

CLASS XI - XII

CLASS XI - XII

CBSE BOARD

CLASS IX

CLASS X

CLASS XI

CLASS XII

CLASS VI

CLASS VII

CLASS VIII

UP BOARD

CLASS IX
CLASS X
CLASS XI
CLASS XII

CLASS IX

CLASS X

CLASS XI

CLASS XII

CUET

CRASH COURSE

CRASH COURSE

Courses

CLASSROOM COURSES
ONLINE COURSES

ONLINE COURSES

More

Solution

Q.
Let $N$ be the sum of the numbers appeared when two fair dice are rolled and let the probability that $N - 2,$ $\sqrt{3 N},$ $N + 2$ are in geometric progression be $\frac{k}{48} .$ Then the value of $k$ is [2023]

1 16

2 2

3 8

4 4

Ans.
(4)

$Here, n (S) = 36$

$N denotes the sum of numbers when two fair dice are rolled.$

$N - 2, \sqrt{3 N}, N + 2 are in G.P.$

$3 N = (N - 2) (N + 2)$

$\Rightarrow 3 N = N^{2} - 4 \Rightarrow N^{2} - 3 N - 4 = 0$

$\Rightarrow (N - 4) (N + 1) = 0$

$\Rightarrow N = 4$ $(since N = - 1 rejected)$

$Favorable cases: (1, 3), (3, 1), (2, 2)$

$Required probability = \frac{3}{36} = \frac{k}{48} (given) \Rightarrow k = 4$

Want Us to Email you About Special Offers & Updates?