Home
Class 12
MATHS
Let J=int0^1x/(1+x^8)dx. Consider the fo...

Let `J=int_0^1x/(1+x^8)dx`. Consider the following assertions: `I.`J>1/4` II.`J

A

only I is true

B

only II is true

C

both I and II are true

D

neither I nor II is true

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • SOLVED PAPER 2018

    KVPY PREVIOUS YEAR|Exercise EXAMPLE|27 Videos

Similar Questions

Explore conceptually related problems

The function f is continuous and has the property f(f(x))=1-x for all x in [0,1] and J=int_0^1 f(x)dx . Then which of the following is/are true? (A) f(1/4)+f(3/4)=1 (B) the value of J equals to 1/2 (C) f(1/3).f(2/3)=1 (D) int_0^(pi/2) (sinxdx)/(sinx+cosx)^3 has the same value as J

The function f is continuous and has the property f(f(x))=1-x for all x in [0,1] and J=int_0^1 f(x)dx . Then which of the following is/are true? (A) f(1/4)+f(3/4)=1 (B) f(1/3).f(2/3)=1 (C) the value of J equals to 1/2 (D) int_0^(pi/2) (sinxdx)/(sinx+cosx)^3 has the same value as J

Let I=int_(0)^(1)(sin)/(sqrt(x))dx and J=int_(0)^(1)(cos x)/(sqrt(x))dx Then which one of the following is true? (1) I>(2)/(3) and j>2(2)I 2(4)I>(2)/(3) and j<2

Let I=int_0^1 (sinx)/sqrtx dx and J=int_0^1 (cos x)/sqrtx dx . Then which of the following is true?

Let J=int _(-1) ^(2) (cot ^(-1) ""(1)/(x )+ cot ^(-1) x ) dx, K =int _(-2pi) ^(7pi) (sin x)/(|sin x|)dx. Then which of the following alternative (s) is/are correct ?

Let I=int_(1)^(oo)((x-1)^(4))/((x^(8)+x^(10)))dx then :

Let I=int_(kpi)^((k+1)pi)(|sin2x|)/(|sinx|+|cosx|)dx,(kepsilonN) and J=int_(0)^((pi)/(4))(dx)/(sinx+cosx) which of the following holds good?

Let J_(n,m) = int_0^(1//2) x^n/(x^m-1), AA ngt mand n, m in N . Consider a matrix A= [a_(ij)]_(3xx3) where a_(ij)={{:(J_(6 + i,3) - J_(i + 3, 3)",", ile j),(0",",igtj):} . Then abs(adj A^(-1)) is :

KVPY PREVIOUS YEAR-SOLVED PAPER 2019-EXAMPLE
  1. Let f(x)={(xsin(1/x), whenx!=0),(1, when x=0):} and A={x inR:f(x)=1}. ...

    Text Solution

    |

  2. Let S be a subset of the plane defined by:S={(x,y):|x|+2|y|=1} Then th...

    Text Solution

    |

  3. The number of solutions of the equation sin(9x)+sin(3x)=0 in the close...

    Text Solution

    |

  4. Among all the parallelograms whose diagonals are 10 and 4, the one hav...

    Text Solution

    |

  5. The number of ordered pairs (a,b) of positive integers such that(2a-1)...

    Text Solution

    |

  6. Let z=x+iy and w=u+iv be two complex numbers, such that |z|=|w|=1 and ...

    Text Solution

    |

  7. Let sigma1,sigma2,sigma3 be planes passing through the origin. Assume ...

    Text Solution

    |

  8. Ravi and Rashmi are each holding 2 red cards and 2 black cards (all fo...

    Text Solution

    |

  9. Let A1,A2 and A3 be the region on R^2 defined by A1={(x,y):xge0,yge0,2...

    Text Solution

    |

  10. Let f:RrarrR be a continuous function such that f(x^2)=f(x^3) for all ...

    Text Solution

    |

  11. Suppose a continuous function f:[0,infty)rarrR satisfies f(x)=2int0^xt...

    Text Solution

    |

  12. Let a>0, a!=0. Then the set S of all positive real numbers b satisfyin...

    Text Solution

    |

  13. Let f:RrarrR be function defined by f(x)={(sin(x^2)/2, ifx!=0),(0,if x...

    Text Solution

    |

  14. The points C and D on a semicircle with AB as diameter are such that A...

    Text Solution

    |

  15. Let f(x)=x^6-2x^5+x^3+x^2-x-1 and g(x)=x^4-x^3-x^2-1 be two polynomial...

    Text Solution

    |

  16. The number of solutions to sin(pisin^2(theta))+sin(picos^2(theta))=2co...

    Text Solution

    |

  17. Let J=int0^1x/(1+x^8)dx. Consider the following assertions: I.J>1/4 II...

    Text Solution

    |

  18. Let f:(-1,1)rarrR be a differentiable function satisfying (f'(x))^4=16...

    Text Solution

    |

  19. Let A be the set of vectors veca=(a1,a2,a3) satisfying (sum(i=1)^3ai/2...

    Text Solution

    |

  20. Let f:[0,1]rarr[0,1] be a continuous function such that x^2+(f(x))^2le...

    Text Solution

    |