Home
Class 12
MATHS
If ^n-1Cr=(k^2-3)^n C(r+1),t h e nk in ...

If `^n-1C_r=(k^2-3)^n C_(r+1),t h e nk in ` `(-oo,-2]` b. `[2,oo)` c. `[-sqrt(3),sqrt(3)]` d. `(sqrt(3),2]`

A

`(- oo, - 2)`

B

`[2 oo]`

C

`[- sqrt(3), sqrt(3)]`

D

`(sqrt(3), 2]`

Text Solution

Verified by Experts

Given, `.^(n-1)C_r=(k^2-3).^Nc_(r+1)`
`rArr .^(n-1)C_(r)=(k^2-3)(n)/(r+1).^(n-1)C_(r)`
`rArr k^2 -3 =(r+1)/(n)`
`[" since ", n ge r rArr (r+1)/(n) le 1 and n r gt 0]`
`rArr 0lt k^2-3 le 1 rArr 3lt k^2 le 4`.
`rArr k in [ -2, -sqrt(3))cup (sqrt(3),2]`.
Promotional Banner

Similar Questions

Explore conceptually related problems

If n-1C_r=(k^2-3)^nC_(r+1), then (a) (-oo,-2] (b) [2,oo) (c) [-sqrt3, sqrt3] (d) (sqrt3,2]

If tan^(-1)(a+x)/a+tan^(-1)(a-x)/a=pi/6,t h e nx^2= (a) 2sqrt(3)a (b) sqrt(3)a (c) 2sqrt(3)a^2 (d) none of these

Values (s)(-i)^(1/3) is/are (sqrt(3)-i)/2 b. (sqrt(3)+i)/2 c. (-sqrt(3)-i)/2 d. (-sqrt(3)+i)/2

If one root x^2-x-k=0 is square of the other, then k= a. 2+-sqrt(5) b. 2+-sqrt(3) c. 3+-sqrt(2) d. 5+-sqrt(2)

If a_n and b_n are positive integers and a_n+sqrt(2)b_n=(2+sqrt(2))^n ,t h e n(lim)_(x->oo)((a_n)/(b_n))= a. 2 b. sqrt(2) c. e^(sqrt(2)) d. e^2

The domain of f(x)=sin^(-1)[2x^2-3],w h e r e[dot] denotes the greatest integer function, is (a) (-sqrt(3/2),sqrt(3/2)) (b) (-sqrt(3/2),-1)uu(-sqrt(5/2),sqrt(5/2)) (c) (-sqrt(5/2),sqrt(5/2)) (d) (-sqrt(5/2),-1)uu(1,sqrt(5/2))

If cos^-1((x^2 -1)/(x^2+1))+ tan^-1 ((2x)/(x^2-1)) = (2pi)/3 , then x equal to (A) sqrt(3) (B) 2+sqrt(3) (C) 2-sqrt(3) (D) -sqrt(3)

The set of all real numbers x for which x^2-|x+2|+x >0 is (-oo,-2) b. (-oo,-sqrt(2))uu(sqrt(2),oo) c. (-oo,-1)uu(1,oo) d. (sqrt(2),oo)

If tan^(-1)x+2cot^(-1)x=(2pi)/3, then x , is equal to (a) (sqrt(3)-1)/(sqrt(3)+1) (b) 3 (c) sqrt(3) (d) sqrt(2)

If 3sin^(-1)((2x)/(1+x^2))-4cos^(-1)((1-x^2)/(1+x^2))+2tan^(-1)((2x)/(1-x^2))=pi/3, w h e r e|x|<1, then x is equal to (a) 1/(sqrt(3)) (b) -1/(sqrt(3)) (c) sqrt(3) (d) -(sqrt(3))/4