Home
Class 12
MATHS
Let F(x) be an indefinite integral of si...

Let F(x) be an indefinite integral of `sin^(2)x`
Statement I The function F(x) satisfies `F(x+pi)=F(x)` for all real x.
Because
Statement II `sin^(2)(x+pi)=sin^(2)x,` for all real x.

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) 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) be an indefinite integral of sin2x . Statement- 1: The function F(x) satisfies F(x+pi)=F(x) for all real x . Statement- 2: sin2(x+pi)=sin2x for all real x . (A) Statement I is true, Statement II is also true, Statement II is the correct explanation of Statement I. (B)Statement I is true, Statement II is also true, Statement II is not the correct explanation of Statement I. (C) Statement I is true, Statement II is false. (D) Statement I is false, Statement II is ture.

Let f(x) be an indefinite integral of sin^(2)x . Consider the following statements : Statements 1. The function f(x) satisfies f(x+pi)=f(x) for all real x. 2. Sin^(2)(x+pi)=sin^(2)x for all real x. Which one of the following is correct in respect of the above statements ?

A function f (x) which satisfies, f ' (sin ^(2)x) = cos ^(2) x for all real x & f (1)=1 is

If a real valued function f(x) satisfies the equation f(x+y)=f(x)+f(y) for all x,y in R then f(x) is

If f(x) satisfies the relation 2f(x)+(1-x)=x^(2) for all real x, then find f(x) .

Let f(x)=sin((x)/(3))+cos((3x)/(10)) for all real x.Find the least natural number n such that f(n pi+x)=f(x) for all real x.

Consider function f satisfying f(x+4)+f(x-4)=f(x) for all real x .Then f(x) is periodic with period

f(x) is a real valued function, satisfying f(x+y)+f(x-y)=2f(x).f(y) for all yinR , Then

Domain of definition of the function f(x)=sqrt(sin^(-1)(2x)+pi/6) for real valued of x, is

A DAS GUPTA-Some New Pattern Problems-Exercise
  1. The lines L(1) : y - x = 0 and L(2) : 2x + y = 0 intersect the line ...

    Text Solution

    |

  2. Let C be the locus of a point the sum of whose distances from the poi...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  12. Assertion- Reason Type Question:

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |