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The value of lim(x to 0) (27^(x)-9^(x)-...

The value of `lim_(x to 0) (27^(x)-9^(x)-3^(x)+1)/(log_(e)(1+(x^(2))/(2)))` is equal to -

A

`4(log_(e)3)^(2)`

B

`2(log_(e)3)^(2)`

C

`8(log_(e)3)^(2)`

D

`(log_(e)3)^(2)`

Text Solution

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The correct Answer is:
A
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CHHAYA PUBLICATION-MCQ ZONE -Question Paper 8
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  2. In the mean value theorem f(b)-f(a)=(b-a)f'(c )(a lt c lt b), "if " a=...

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  3. The value of lim(x to 0) (27^(x)-9^(x)-3^(x)+1)/(log(e)(1+(x^(2))/(2)...

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  4. The value of lim(x to 0) (1-3x)^((3)/(x)) is equal to -

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  5. If x sqrt(1-y^(2))+y sqrt(1-x^(2))=k, then the value of (dy)/(dx) at...

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  6. If x=a cot theta and y=(1)/(x^(2)+a^(2)), then the value of (d^(2)...

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  7. If y=(sin^(-1)x)^(2)+(cos^(-1)x)^(2), then which of the following is...

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  8. If y=e^(m sin^(-1)x), then the value of [(d^(2)y)/(dx^(2))](x=0) is ...

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  9. If x sqrt(1+y)+y sqrt(1+x)=0 then the value of (dy)/(dx) is -

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  10. If x^(2)+y^(2)=t+(1)/(t) and x^(4)+y^(4)=t^(2)+(1)/(t^(2)), then the ...

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  11. If siny=x sin(a+y), then the value of (dy)/(dx) is -

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  12. If y="tan"^(-1)(sqrt(1+x^(2))-sqrt(1-x^(2)))/(sqrt(1+x^(2))+sqrt(1-x^(...

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  13. If the equation a(n)x^(n)+a(n-1)x^(n-1)+…+a(1)x=0 (a(1) ne 0, n ge 2)...

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  14. If x sin y+y cos x=pi, then the value of y''(0) is -

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  15. Let f(x) be a function satisfying f'(x)=f(x) with f(0)=1 and g(x) be ...

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  16. The value of int(dx)/(x(x^(7)+1)) is equal to -

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  17. If f(x)=|x-1|, then the value of int(0)^(2)f(x) dx is -

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  18. If I(m)=int(1)^(x)(logx)^(m)dx satisfies the relation I(m)=x(logx)^...

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  19. If int(-(1)/(2))^((1)/(2)) cos x log((1+x)/(1-x))dx=k log2, then the ...

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  20. The value of int cos[2cot^(-1) sqrt((1-x)/(1+x))]dx is equal to -

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