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Let f ={(x ,(x^2)/(1+x^2)):x in R}be a f...

Let `f ={(x ,(x^2)/(1+x^2)):x in R}`be a function from R into R. Determine the rage of f.

A

[0, 1)

B

[0, 1]

C

[0,2)

D

None of these

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The correct Answer is:
A
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MTG-WBJEE-SETS , RELATIONS AND FUNCTIONS-WB JEE PREVIOUS YEARS QUESTIONS (SINGLE OPTION CORRECT TYPE)
  1. Let f ={(x ,(x^2)/(1+x^2)):x in R}be a function from R into R. Determi...

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  2. Let f : R rarr R be such that f is injective and f(x) f(y ) = f(x+ y...

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  3. We define a binary relationon ~ on the set of all 3 xx 3 real matrices...

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  4. The number of onto functions from the set {1,2,...., 11} to the set {1...

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  5. LEt f(x)=2^(100)x+1 and g(x)=3^(100)x+1 Then the set of real numbers x...

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  6. For any two real numbers a and b, we define a R b if and only if sin^2...

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  7. The minimum value of the function f(x) = 2|x - 1| + |x - 2| is

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  8. Let the number of elements of the sets A and B be p and q respectively...

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  9. Let R be the set of all real numbers and f : Rrarr R be given by f(x) ...

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  10. The function f(x)=x^(2)+bx+c, where b and c are real constants, descri...

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  11. Find the range of the function f(x)=3 sin (sqrt((pi^(2))/(16)-x^(2))).

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  12. There is a group of 265 persons who like either singing or dancing or ...

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  13. The number of real roots of equation log(e )x + ex = 0 is

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  14. If f:[0,pi/2)->R is defined as f(theta)=|(1,tantheta,1),(-tantheta,1,...

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  15. Let f:R-> R be defined as f(x)=(x^2-x+4)/(x^2+x+4). Then the range of ...

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  16. Let S={a,b,c}epsilonNxxNxxN:a+b+c=21,a<=b<=c} and T={(a,b,c)epsilon Nx...

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  17. Let R be a relation defined on the set Z of all integers and x Ry whe...

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  18. if A={5^(n)-4n-1: n in N} and B={16(n-1):n in N} then

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  19. If the function R to R is defined by f(x)=(x^2+1)^(35)AA in R then f ...

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  20. Let P be the set of all non-singular matrices of order 3 over ú and Q ...

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  21. On the set R of real numbers we defined xPy i and only if xylt 0. T...

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