Home
Class 12
MATHS
Let I(n) = int(0)^(1) x^(n) tan^(-1) x d...

Let `I_(n) = int_(0)^(1) x^(n) tan^(-1) x dx`. If `a_(n) I_(n+2) + b_(n)I_(n) = c_(n)` for all `n ge 1`, then

A

`a_(1), a_(2), a_(3)` are in G.P.

B

`b_(1), b_(2), b_(3)` are in A.P

C

`c_(1), c_(2), c_(3)` are in H.P

D

`a_(1), a_(2), a_(3)` are in A.P

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • QUESTION PAPER 2018

    WB JEE PREVIOUS YEAR PAPER|Exercise MULTIPLE CHOICE QUESTIONS|75 Videos

  • QUESTION PAPER 2021

    WB JEE PREVIOUS YEAR PAPER|Exercise MULTIPLE CHOICE QUESTION|75 Videos

Similar Questions

Explore conceptually related problems

Let I_(n)=int_(0)^(1)x^(n)sqrt(1-x^(2))dx. Then lim_(nrarroo)(I_(n))/(I_(n-2))=

Let I_n=int_0^1x^ntan^(-1)xdx." Then prove that "(n+1)I_(n)+(n-1)I_(n-2)=pi/2-1/n"

If I_(n)=int_(0)^((pi)/(4)) tan^(n)x dx , then the value of (I_(8)+I_(6)) is -

If I_(n)=int_(0)^(pi)x^(n)sinxdx , then find the value of I_(5)+20I_(3) .

int dx/(x^n(1+x^n)^(1/n)) is

If I_(n)=int_(0)^((pi)/(4)) tan^(n)x dx , then the value of lim_(n to oo) n(I_(n)+I_(n-2)) is -

IfI_n=int_0^1x^n(tan^(-1)x)dx ,t h e np rov et h a t (n+1)I_n+(n-1)I_(n-2)=-1/n+pi/2

Q. int_0^pie^(cos^2x)( cos^3(2n+1) x dx, n in I

If I_(n)=int (logx)^(n)dx , then the value of (I_(n)+nI_(n-1)) is -

Prove that: I_n=int_0^oox^(2n+1) e^ (-x^2) dx=(n !)/2,n in N .

WB JEE PREVIOUS YEAR PAPER-QUESTION PAPER 2019-MULTIPLE CHOICE QUESTIONS
  1. The length of conjugate axis of a hyperbola is greater than the length...

    Text Solution

    |

  2. Let f(x) = x^(4) - 4x^(3) + 4x^(2) + c, c in R. Then

    Text Solution

    |

  3. The graphs of the polynomial x^(2)-1 and cos x intersect

    Text Solution

    |

  4. A point is in motion along a hyperbola y = (10)/(x) so that its abscis...

    Text Solution

    |

  5. Let a = min {x^(2) + 2x + 3 : x in R} and b = lim(theta rarr 0)(1-cos...

    Text Solution

    |

  6. Let a gt b gt 0 and I(n) = a^(1//n) - b^(1//n), J(n) = (a-b)^(1//n) fo...

    Text Solution

    |

  7. Let hat(alpha), hat(beta), hat(gamma)be three unit vectors such that h...

    Text Solution

    |

  8. The position vectors of the points A, B, C and D are 3hat(i) - 2hat(j)...

    Text Solution

    |

  9. A particle starts at the origin and moves 1 unit horizontally to the r...

    Text Solution

    |

  10. For any non-zero complex number z, the minimum value of |z| + |z-1| is

    Text Solution

    |

  11. Let A = ((3, 0, 3), (0, 3, 0), (3,0,3)). Then the roots of the equatio...

    Text Solution

    |

  12. If A and B are (-2, -2) and (2, -4) respectively, find the coordinates...

    Text Solution

    |

  13. Equation of a tangent to the hyperbola 5x^(2) - y^(2) = 5 and which pa...

    Text Solution

    |

  14. Let f and g be differentiable on the interval I and let a, b in I, a l...

    Text Solution

    |

  15. Consider the function f(x) = (x^(3))/(4) - sin pi x + 3

    Text Solution

    |

  16. Let I(n) = int(0)^(1) x^(n) tan^(-1) x dx. If a(n) I(n+2) + b(n)I(n) =...

    Text Solution

    |

  17. Two particles A and B move from rest along a straight line with consta...

    Text Solution

    |

  18. The area bounded by y = x + 1 and y = cos x and the x-axis, is

    Text Solution

    |

  19. Let x(1), x(2) be the roots of x^(2) - 3x + a = 0 and x(3), x(4) be th...

    Text Solution

    |

  20. If theta in RR and (1 +i cos theta)/(1-2 i cos theta) is real number,...

    Text Solution

    |