Home
Class 12
MATHS
Let In=int0^1(1 – x^k)^n dx, n in N. If ...

Let `I_n=int_0^1(1 – x^k)^n dx, n in N`. If 147 `I_(2) = 148 I_(21)` then the value of k is equal to

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • JEE MAIN 2024

    JEE MAINS PREVIOUS YEAR|Exercise Questions|18 Videos

  • JEE MAIN 2023

    JEE MAINS PREVIOUS YEAR|Exercise Question|435 Videos

  • JEE MAIN 2024 ACTUAL PAPER

    JEE MAINS PREVIOUS YEAR|Exercise Question|598 Videos

Similar Questions

Explore conceptually related problems

Let I_(n) = int_(0)^(1)(1-x^(3))^(n)dx, (nin N) then

Let I_(n)=int_(0)^(pi//2) sin^(n)x dx, nin N . Then

Let I_(n)= int_(0)^(1)(x ln x)^(n)dx, if I_(4)=k int_(0)^(1)x^(4)(ln x)^(3)dx, then |[k]| is equal to ([.] denotes greatest integer function).

If I_(n)=int_(0)^(1)x^(n)e^(-x)dx for n in N, then I_(7)-I_(6)=

If I _(n)=int _(0)^(pi) (sin (2nx))/(sin 2x)dx, then the value of I _( n +(1)/(2)) is equal to (n in I) :

For each positive interger n, define f_(n)(x)= minimum (x^(n)/(n!), ((1-x)^(n))/(n!)) , for 0 le x le 1 . Let I_(n)= int_(0)^(1) f_(n) (x) dx, n ge 1 . Then I_(n)=sum_(n=1)^(oo) I_(n) is equal to -

JEE MAINS PREVIOUS YEAR-JEE MAIN 2024-Questions
  1. Let In=int0^1(1 – x^k)^n dx, n in N. If 147 I(2) = 148 I(21) then the ...

    Text Solution

    |

  2. If f(x)={(-2,,,-2,le,x, <,0),(x-2,,,0,le,x, le,2):} and h(x) = f(|x|) ...

    Text Solution

    |

  3. Let ABC be a triangle. If P1, P2, P3, P4, P5 are five points on side A...

    Text Solution

    |

  4. Let y(x) be a curve given by differential equation (dy)/(dx) - y = 1 +...

    Text Solution

    |

  5. Let there are 3 bags A, B and C. Bag contain 5 black balls and 7 red b...

    Text Solution

    |

  6. The number of rational terms in the expansion of (2^(1/2) + 3^(1/3))^(...

    Text Solution

    |

  7. 2 and 6 are roots of the equation ax^2 + bx + 1 = 0 then the quaratic ...

    Text Solution

    |

  8. Let f(x)={(frac{1-cos2x}{x^2},x, <,0),(alpha,x,=,0),(beta (frac{sqrt(1...

    Text Solution

    |

  9. One point of intersection of curve y = 1 + 3x - 2x^2 and y = 1/x is (...

    Text Solution

    |

  10. If alpha and beta are sum and product of non zero solution of the equa...

    Text Solution

    |

  11. If domain of the function f(x) = sin^(-1) (frac{3x - 22}{2x - 19}) + l...

    Text Solution

    |

  12. The value of lim(xrarr 4) frac{(5 + x)^(1/3) - (1 + 2x)^(1/3)}{(5 + x)...

    Text Solution

    |

  13. If the function f(x) ={(1/|x|,|x|,ge,2),(zx^2+2b,|x|,<,2):} differenti...

    Text Solution

    |

  14. Let alpha, beta in R. If the mean and the variable of 6 observation, -...

    Text Solution

    |

  15. A square is inclined in the circle x^2 + y^2 - 10 x - 6y + 30 = 0 such...

    Text Solution

    |

  16. Let f(x) = x^5 + 2e^(x/4) AA x in R. Consider a function of (gof) (x) ...

    Text Solution

    |

  17. Let f(x) =frac{2x^2 - 3x + 9} {2x^2 +3x + 4}, x in R, if maximum and m...

    Text Solution

    |

  18. int0^(pi/4) frac{sin^2 x}{1 + sin x. cos x}, dx = 0

    Text Solution

    |

  19. 2, p, q are in G.P. (where p ne q) and in A.P., 2 is third term, p is ...

    Text Solution

    |