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|Exercise MATHEMATICS|263 Videos

Similar Questions

Explore conceptually related problems

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

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 .

Consider the following statements 1 f(x)=In x is an increasing funciton on (0,oo) 2 f(x) =e^(x)-x(In x) is an increasing function on (1,oo) Which of the above statement is / are correct ?

Consider the following statements 1 y=e^(x)+e^(-x)./(2) is an increasing funciton on [0,oo) 2 y=(e^(x)-e^(-x))/(2) is an increasing function on (-oo,oo) Which of the above statement is / are are correct ?

Evaluate int(log(1+x))/(1+x)dx on (-1,oo)

Consider the following statements : 1. The function f(x)=x^(2)+2cosx is increasing in the interval (0,pi) 2. The function f(x)=1n(sqrt(1+x^(2)-x)) is decreasing in the interval (-oo,oo) Which of the above statements is/ are correct ?

for 0

Which of the following statement(s) is/are correct? 1+(2)/(2)+(3)/(2^(2))+(4)/(2^(3))+.........+oo=4

Consider the following statements I.The function f(x)=x^(2)+2cos x is increasing in the interval (0,pi). II.The function f(x)=ln(sqrt(1+x^(2))-x) is decreasing in the interval (-oo,oo). Which of the above statement(s) is/are correct?

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

    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 slope of the tangent to the curve y=-x^(3)+3x^(2)+9x-27 is maximum...

    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+1AAiepsilon{1,2,3,4} and 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 numbered 1 to n. The ith urn contains i white 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)) and f^'(x)=sinx^(2), then (dy)/(dx) is equal ...

    Text Solution

    |

  16. Let veca=hati-hatk, vecb=xhati+hatj+(1-x)hatk and vecc=yhati+xhatj+(1+...

    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

    |