Home
Class 12
MATHS
Consider the following statements Stat...

Consider the following statements
Statement 1: The range of `log_(1)(1/(1+x^(2)))` is `(-oo,oo)`
Statement 2: If `0ltxle1`, then `log_(1)=xepsilon(-oo,0]`
Which of the following is correct

A

Statement 1: is True, Statement 2 is True , Statement 2 is a correct explanation for statement 1

B

Statement 1 is True, Statement 2 is True Statement 2 is NOT a correct explanation for Statement 1

C

Statement 1 is True, Statement 2 is False

D

Statement 1 is False, Statement 2 is True

Text Solution

Verified by Experts

The correct Answer is:
D
Range of `1/(1+x^(2))` is `(0,1]` is domain `R`.
`:. log(1/(1+x^(2)))epsilon(-oo,0]`
Promotional Banner

Topper's Solved these Questions

  • TEST PAPERS

    RESONANCE ENGLISH|Exercise Math|105 Videos

  • TEST PAPER

    RESONANCE ENGLISH|Exercise MATHEMATICS|48 Videos

  • TEST SERIES

    RESONANCE ENGLISH|Exercise MATHEMATICS|132 Videos

Similar Questions

Explore conceptually related problems

bb"Statement I" The range of log(1/(1+x^(2))) " is " (-infty,infty) . bb"Statement II" " when " 0 lt x le 1, log x in (-infty,0].

Statement 1: The range of f(x)=sin^(2)x-sinx+1 is [3/4,oo) . Statemen 2: The range of f(x)=x^(2)-x+1 is [3/4,oo)AAxepsilonR .

Statement - 1 : If x gt 1 then log_(10)x lt log_(3)x lt log_(e )x lt log_(2)x . Statement - 2 : If 0 lt x lt 1 , then log_(x)a gt log_(x)b implies a lt b .

log(1+x+x^(2)+...oo)=

Statement-1 : f(x) = log_(10)(log_(1/x)x) will not be defined for any value of x. and Statement -2 : log_(1//x)x = -1, AA x gt 0, x != 1

If e^x+e^(f(x))=e , then the range of f(x) is (-oo,1] (b) (-oo,1) (1, oo) (d) [1,oo)

Statement-1: lim_(xrarr oo) (cos (pi)/(x))^x=1 Statement-2: lim_(xrarr oo) -pi tan. (pi)/(x)=0

Consider the function f:(-oo, oo) -> (-oo ,oo) defined by f(x) =(x^2 - ax + 1)/(x^2+ax+1) ;0 lt a lt 2 . Which of the following is true ?

Consider the function f:(-oo,oo)rarr(-oo,oo) defined by f(x)=(x^2-ax+1)/(x^2+ax+1), 0ltalt2 , and let g(x)=int_0^(e^x) (f\'(t)dt)/(1+t^2) . Which of the following is true? (A) g\'(x) is positive on (-oo,0) and negative on (0,oo) (B) g\'(x) is negative on (-oo,0) and positive on (0,oo) (C) g\'(x) changes sign on both (-oo,0) and (0,oo) (D) g\'(x) does not change sign on (-oo,oo)

Statement-1 e^(pi) gt pi^( e) Statement -2 The function x^(1//x)( x gt 0) is strictly decreasing in [e ,oo)

RESONANCE ENGLISH-TEST PAPERS-MATHEMATICS
  1. The distance between the origin and the tangent to the curve y=e^(2x)+...

    Text Solution

    |

  2. The function f(x)=1+x(sinx)[cosx], 0ltxlepi//2, where [.] denotes grea...

    Text Solution

    |

  3. Consider the following statements Statement 1: The range of log(1)(1...

    Text Solution

    |

  4. System of equations x+2y+z=0, 2x+3y-z=0 and (tantheta)x+y-3z=0 has non...

    Text Solution

    |

  5. If x ,y in R , satisfies the equation ((x-4)^2)/4+(y^2)/9=1 , then th...

    Text Solution

    |

  6. If the sum of the coefficients in the expansion of (2x+3cx+c^(2)x^(2))...

    Text Solution

    |

  7. The maximum slope of curve y =-x^(3)+3x^(2)+9x-27 is

    Text Solution

    |

  8. If in the expansion of (1/x+xtanx)^5 the ratio of 4^(th) term to the ...

    Text Solution

    |

  9. If n(1)+n(2)+n(3)+n(4)=20 such that n(i)gei+1AAiin{1,2,3,4} and n(i)"n...

    Text Solution

    |

  10. The number of 4 digit numbers that can be made using exactly two digit...

    Text Solution

    |

  11. There are n urns each containing (n+1) balls such that ith urn contain...

    Text Solution

    |

  12. Let N=3^(n(1))+5^(n(2))+9^(n(3)) where n(1),n(2),n(3)epsilon[1,9]. The...

    Text Solution

    |

  13. If ax+b/x >= c for all positive x, where a, b, c > 0, then-

    Text Solution

    |

  14. If f''(x) gt forall in R, f(3)=0 and g(x) =f(tan^(2)x-2tanx+4y)0ltxlt(...

    Text Solution

    |

  15. If y=f((2x-1)/(x^2+1))andf^'(x)=sinx^2, then find (dy)/(dx)

    Text Solution

    |

  16. Let veca=veci-veck,vecb=xveci+vecj+(1-x)veck and vecc=yveci+xvecj+(1+x...

    Text Solution

    |

  17. The projection of hati+hatj+hatk on the whole equation is vecr=(3+lamd...

    Text Solution

    |

  18. A plane meets the coordinate axes at A ,Ba n dC respectively such that...

    Text Solution

    |

  19. For N=50400 the number of divisor of N, which are divisible by 6, divi...

    Text Solution

    |

  20. The correct statements of the following

    Text Solution

    |