Home
Class 12
MATHS
Number of values of r satisfying the equ...

Number of values of r satisfying the equation
` ""^(69)C_(3r-1)- ""^(69)C_(r^(2)) = ""^(69)C_(r^(2)-1) - ""^(69)C_(3r) ` is

A

1

B

2

C

3

D

7

Text Solution

Verified by Experts

The correct Answer is:
c,d
`""^(69)C_(3r) + ""^(69)C_(3r) = ""^(69)C_(r^(2)-1) + ""^(69)C_(r^(2))`
` rArr ""^(70)C_(3r) = ""^(70)C_(r^(2))`
` rArr r^(2) = 3r or 70 - 3r = r^(3)`
`rArr r = 0 , 3 or r^(3( + 3r - 70 = 0 `
` rArr r = 0 , 3 or (r + 10 ) (r - 7) = 0 `
` rArr r = 0, 3, 7, - 10 `
But r = 0 , - 10 do not satisfiles the given equation .
Hence , two values of r satisfies ,
i.e. r = 3,7
Promotional Banner

Topper's Solved these Questions

  • BIONOMIAL THEOREM

    ARIHANT MATHS|Exercise Exercise (Passage Based Questions)|21 Videos

  • BIONOMIAL THEOREM

    ARIHANT MATHS|Exercise Exercise (Single Integer Answer Type Questions)|9 Videos

  • BIONOMIAL THEOREM

    ARIHANT MATHS|Exercise Exercise (Single Option Correct Type Questions)|30 Videos

  • AREA OF BOUNDED REGIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|23 Videos

  • CIRCLE

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|16 Videos

Similar Questions

Explore conceptually related problems

The number of values of 'r' satisfying the equation ""^(39)C_(3r-1)- ""^(39)C_(r^(2) )= ""^(39)C_(r^(2)-1) - ""^(39)C_(3r) is

The number of values of r satisfying the equation ""^(39)C_(3r-1) -""^(39)C_(r^2) = ""^(39)C_(r^2-1) -""^(39)C_(3r) is

Find the value (s) of r satisfying the equation ^69C_(3r-1)-^(69)C_(r^(2))=^(69)C_(r^(2)-1)-^(69)C_(3r)

The number of values of r satisfying the equation 69C_(3r-1)-69C_(r^(2))=^(69)C_(r^(2)-1)-6 is a.1 b.2 c.3d.7

The number of values of r satisfying the equation,39C_(3r-1)-39C_(r^(2))=39C_(r^(2)-1)-39C_(3r) is :

The number of values of r satisfying the equation C(69,3r-1)-C(69,r^(2))=C(69,r^(2)-1)-C(69,3r) is (A)1(B)2(C) 3( textrmD ) 7