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Let alpha(a) and beta(a) be the roots of...

Let `alpha(a)` and `beta(a)` be the roots of the equation `((1+a)^(1/3)-1)x^2 +((1+a)^(1/2)-1)x+((1+a)^(1/6)-1)=0` where `agt-1` then `lim_(a->0^+)alpha(a)` and `lim_(a->0^+)beta(a)`

A

`-5/2` and 1

B

`-1/2` and -1

C

`-7/2` and 2

D

`-9/2` and 3

Text Solution

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The correct Answer is:
C
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ARIHANT MATHS ENGLISH-LIMITS-Exercise (Questions Asked In Previous 13 Years Exam)
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  5. Let L=("lim")(xvec0)(a-sqrt(a^2-x^2)-(x^2)/4)/(x^4),a > 0. IfLi sfin i...

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  6. underset(xto(pi)/(2))lim(cotx-cosx)/((pi-2x)^(3)) equals

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  7. Let p=underset(xto0^(+))lim(1+tan^(2)sqrt(x))^((1)/(2x)). Then log(e)p...

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  8. lim(n -> oo) (((n+1)(n+2)(n+3).......2n) / n^(2n))^(1/n)is equal to

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  9. underset(xto0)lim(sin(picos^(2)x))/(x^(2)) is equal to

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  10. lim(xto0)((1-cosx)(3+cosx))/(x tan 4x) is equal to

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  11. If underset(xtooo)lim((x^(2)+x+1)/(x+1)-ax-b)=4, then

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  12. Let alpha(a) and beta(a) be the roots of the equation ((1+a)^(1/3)-1)x...

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  13. If ("lim")(xvec0)[1+x1n(1+b^2)]^(1/x)=2bsin^2theta,b >0,s mftheta in ...

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  14. The value of lim(x->0)((sinx)^(1/x)+(1/x)^(sinx)) , where x >0, is (a)...

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  15. lim(h->0) (f(2h+2+h^2)-f(2))/(f(h-h^2+1)-f(1)) given that f'(2)=6 and ...

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  16. lim(x->0) (sin(nx)((a-n)nx – tanx))/x^2= 0, when n is a non-zero posit...

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  17. The integer n for which ("lim")(xvec0)((cosx-1)(cosx-ehatx)/(x^n) is f...

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  18. Let f: R->R be such that f(1)=3 and f^(prime)(1)=6. Then lim(x->0)((f...

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  19. lim(x to oo) ((x-3)/(x+2)) is equal to :

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