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]`

If n-1C_(r)=(k^(2)-3)^(n)C_(r+1), then (a) (-oo,-2](2,oo)(c)[-sqrt(3),sqrt(3)](d)(sqrt(3),2]

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

lim_(n to oo)[(sqrt(n+1)+sqrt(n+2)+....+sqrt(2n))/(n sqrt((n)))]

If 3^(49)(x+iy)=((3)/(2)+(sqrt(3))/(2)i)^(100) and x=ky then k is: a.-1/3 b.sqrt(3)c.-sqrt(3)d-(1)/(sqrt(3))

If A >0,\ B >0\ a n d\ A+B=\ pi/6 , then the minimum value of t a n A+t a n B is: 2-sqrt(3) b. 4-2sqrt(3) c. sqrt(3)-sqrt(2) d. 2/(sqrt(3))

The set of value of a for which both the roots of the equation x^2-(2a-1)x+a=0 are positie is (A) {(2-sqrt(3))/2} (B) {(2-sqrt(3))/2,(2+sqrt(3))/2} (C) [(2+sqrt(3)/2,oo) (D) none of these

lim_(n rarr oo)((sqrt(n+3)-sqrt(n+2))/(sqrt(n+2)-sqrt(n+1)))

lim_(n rarr oo)[(sqrt(1)+2sqrt(2)+3sqrt(3)+ .......... +nsqrt(n))/(n^(5/2))]

The value of lim_(n rarr oo)(sqrt(3n^(2)-1)-sqrt(2n^(2)-1))/(4n+3) is

If |x-2| (A) x in R , (B) x in[0,oo)] , (C) x in(-oo,(4-sqrt(2))/(2)]uu[(5)/(2),oo), (D) x in(-oo,(4-sqrt(2))/(2)]uu[(5+sqrt(3))/(2),oo]