Home
Class 12
MATHS
The number of values of 'r' satisfying t...

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

A

1

B

2

C

3

D

4

Text Solution

Verified by Experts

The correct Answer is:
b
We have , `""^(39)C_(3r-1) + ""^(39)C_(3r) = ""^(39)C_(r^(2)) + ""^(39)C_(r^(2) - 1)`
` rArr ""^(40)C_(3r) + ""^(40)C_(r^(2))`
`rArr 3r = r^(2) or 40 - 3r = r^(2)`
` rArr r= 0,3 or r^(2) + 3r - 40 = 0 `
`rArr (r + 8)(r-5) = 0 rArr r= 0 , 3,5-8`
But r = 0 , - 8 do not satisfy the given equation
` therefore r = 3,5 `
Promotional Banner

Similar Questions

Explore conceptually related problems

""^(n)C_(n-r)+3.""^(n)C_(n-r+1)+3.""^(n)C_(n-r+2)+""^(n)C_(n-r+3)=""^(x)C_(r)

If .^(15)C_(3r)=.^(15)C_(r+3), find .^(r)C_(2) .

f(n)=sum_(r=1)^(n) [r^(2)(""^(n)C_(r)-""^(n)C_(r-1))+(2r+1)(""^(n)C_(r ))] , then

if .^(2n)C_(2):^(n)C_(2)=9:2 and .^(n)C_(r)=10 , then r is equal to

Number of solutions of the equation cosectheta=k in [0,pi] where k=lim_(n->oo)pi_(r=2)^n((r^3-1)/(r^3+1)) is

The differintial eauation of all circle of radius r, is given by (a) {1+(y_(1))^(2)}^(2)=r^(2)y_(2)^(3) (b) {1+(y_(1))^(2)}^(3)=r^(2)y_(2)^(3) ( c ) {1+(y_(1))^(2)}^(3)=r^(2)y_(2)^(2) (d) None of these

The sum of the series sum_(r=0)^(10) .^(20)C_(r) , is 2^(19)+{(.^(20)C_(10))/2} .

sum_(r=0)^(n).^(n)C_(r)4^(r)=..........

If r be the ratio ofthe roots of the equation ax^2 +bx + c = 0 , show that (r+1)^2/r =(b^2)/(ac)

Write ‘True’ or ‘False’ and justify your answer: The volume of the frustum of a cone (1)/(3)pi h(r_(1)^(2)+r_(2)^(2)-r_(1)r_(2)) where h is the vertical height of the frustum and r_(1),r_(2) are the radii of the ends.