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Consider the following statements : St...

Consider the following statements :
Statement I :
`xgtsinx" for all "xgt0`
Statement II : `f(x)=xsinx` is an increasing function for all `xgt0`
Which one of the following is correct in respect of the above statements?

A

Both Statement I and Statement II are true and Statemenet II is the correct explanation of Statement II.

B

Both Statement I and Statement II are true and Statement II is not the correct explanation of Statement I.

C

Statement I is true but Statement II is false

D

Statement I is false but Statement II is true

Text Solution

Verified by Experts

The correct Answer is:
A
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NDA PREVIOUS YEARS-FUNCTIONS, LIMIT, CONTINUITY AND DIFFERENTIABILITY-MCQs
  1. Which one the following graph represents the function f(x)=(x)/(x),x...

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  2. Let g be the greatest integer function. Then the function f(x)=(g(x))^...

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  3. Consider the following statements : Statement I : xgtsinx" for all...

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  4. If f(x)=(4x+x^(4))/(1+4x^(3))andg(x)=In ((1+x)/(1-x)), then what is th...

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  5. Which one of the following is correct in respect of the function f:RRt...

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  6. Suppose f:RRtoRR^(+) is defined by f(x)=(x^(2))/(1+x^(2)). What is the...

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  7. If f(x)=|x|+|x-1|, then which one of the following is correct?

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  8. Conisder the function f(x)={{:(x^(2)ln|x|,xne0),(0,x=0):}. "What is" f...

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  9. If f(x)=(x^(2)-9)/(x^(2)-2x-3),xne3 is continuous at x=3, then which o...

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  10. If f:RRtoS defined by f(x)=4sinxx-3cosx+1 is onto, then what is S equa...

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  11. For f to be a function, what is the domain of f, if f(x)=(1)/(sqrt(|x|...

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  12. What is lim(x to 0) (tanx)/(sin2x) equal to?

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  13. What is lim(h to 0) (sqrt(2x+3h)-sqrt2x)/(2h) equal to?

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  14. If f(x) is an even function, then write whether f^(prime)(x) is eve...

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  15. Let A=(X"inR:-1lexle1)andS be the subset of AxxB, defined by S=[(x,y)i...

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  16. If f(x)=sqrt(x-1)/(x-4) defines a function of R, then what is its doma...

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  17. Consider the function f(x)={{:((sin2x)/(5x),if ,xne0),((2)/(15),if,x...

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  18. For the function f(x)=|x-3|, which of the following is not correct?

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  19. If the function f9x)=(2x-sin^(-1)x)/(2x+tan^(-1)x) is continuous at ea...

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  20. If f(x )=sqrt(25-x^(2)), then what is lim(x to 1) (f(x)-f(1))/(x-1) eq...

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