Home
Class 12
MATHS
let f(x)=2+cosx for all real x Statemen...

let `f(x)=2+cosx` for all real x Statement 1: For each real t, there exists a pointc in `[t,t+pi]` such that `f'(c)=0` Because statement 2: `f(t)=f(t+2pi)` for each real t

A

Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1

B

Statement-1 is True, Statemcnt-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

Promotional Banner

Topper's Solved these Questions

  • Some New Pattern Problems

    A DAS GUPTA|Exercise Exercise|137 Videos
  • Screening Tests

    A DAS GUPTA|Exercise Exercise|38 Videos
  • Total Conditional Probability and Bayes' Theorem

    A DAS GUPTA|Exercise Exercise|29 Videos

Similar Questions

Explore conceptually related problems

let f(x)=2+cos x for all real x Statement 1: For each real t,there exists a pointc in [t,t+pi] such that f'(c)=0 Because statement 2:f(t)=f(t+2 pi) for each real t

Statement I For each eal, there exists a pooint c in [t,t+pi] such that f('c) Because Statement II f(t)=f(t+2pi) for each real t .

Let F(x) be an indefinite integral of sin^(2)x Statement-1: The function F(x) satisfies F(x+pi)=F(x) for all real x. because Statement-2: sin^(3)(x+pi)=sin^(2)x for all real x. A) Statement-1: 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.

Let f(x)=(1-x)^(2)sin^(2)x+x^(2) for all x in IR, and let g(x)=int_(1)^(x)((2(t-1))/(t-1)-ln t)f(t) dt for all x,in(1,oo). Consider the statements: P: There exists some x in IR such that f(x)+2x=2(1+x^(2)) Q: There exists some x in IR such that 2f(x)+1=2x(1+x) Then

If f(x)=x^(2)+bx+c and f(2+t)=f(2-t) for all real number t, then which of the following is true?

Let f(x) be differentiable on the interval (0,oo) such that f(1)=1 and lim_(t rarr x)(t^(2)f(x)-x^(2)f(t))/(t-x)=1 for each x>0 Then f(x)=

If f(x) is an integrable function over every interval on the real line such that f(t+x)=f(x) for every x and real t, then int_(a)^(a+1) f(x)dx is equal to

A DAS GUPTA-Some New Pattern Problems-Exercise
  1. Let C be the locus of a point the sum of whose distances from the poi...

    Text Solution

    |

  2. Let F(x) be an indefinite integral of sin^(2)x Statement I The funct...

    Text Solution

    |

  3. let f(x)=2+cosx for all real x Statement 1: For each real t, there ex...

    Text Solution

    |

  4. Assertion- Reason Type Question: STATEMENT -1: 1*3*5* ….*(2n-1) gt n^...

    Text Solution

    |

  5. Let (1 + x)^(36) = a(0) +a(1) x + a(2) x^(2) +...+ a(36)x^(36). Then ...

    Text Solution

    |

  6. The vlaue of ((5050)underset(0)overset(1)int(1-x^(50))^(100)dx)/(under...

    Text Solution

    |

  7. In !ABC it is given that a:b:c = cos A:cos B:cos C Statement-1: !ABC...

    Text Solution

    |

  8. Let H1, H2,..., Hn be mutually exclusive events with P (Hi) > 0, i = ...

    Text Solution

    |

  9. Let Aa n dB b e two independent events. Statement 1: If (A)=0. 3a n dP...

    Text Solution

    |

  10. The equations of two straight lines are (x-1)/2=(y+3)/1=(z-2)/(-3) a...

    Text Solution

    |

  11. Assertion- Reason Type Question:

    Text Solution

    |

  12. Statement-1: The cubic equation 4x^(3) - 15x^(2)+14x-5 = 0 has a root ...

    Text Solution

    |

  13. Consider, L(1) : 2x + 3y + p – 3 = 0 , L(2) : 2x + 3y + p + 3 = 0, whe...

    Text Solution

    |

  14. Let a,b,c,p,q be the real numbers. Suppose alpha,beta are the roots of...

    Text Solution

    |

  15. For the following question, choose the correct answer from the codes (...

    Text Solution

    |

  16. Consider three planes P1:x-y+z=1, P2:x+y-z=-1,P3,x-3y+3z=2 Let L1,L2,L...

    Text Solution

    |

  17. Consider the system of equations x-2y+3z=-1 -x+y-2z=k x-3y+4z=1 ...

    Text Solution

    |

  18. Consider the system of equations ax + by = 0; cx + dy = 0, where a, b,...

    Text Solution

    |

  19. Let f and g be real valued functions defined on interval (-1,\ 1) such...

    Text Solution

    |

  20. Match the integrals in Column I with the values in Column II and indi...

    Text Solution

    |