Home
Class 11
MATHS
Let n be a positive integer with f(n)=1!...

Let n be a positive integer with `f(n)=1!+2!+3!+….+n!` and P(x) and Q(x) be polynomials in x such that `f(n+2) = Q(n)f(n) + P(n)f(n+1)`. Find P(2).

A

P(x)=x+3

B

Q(x)=-1+2

C

P(X)=-1-2

D

Q(x)=x+3

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • DERIVATIVES

    PATHFINDER|Exercise QUESTION BANK|81 Videos
  • FUNCTIONS

    PATHFINDER|Exercise QUESTION BANK|66 Videos

Similar Questions

Explore conceptually related problems

f(x)=e^(-1/x),w h e r ex >0, Let for each positive integer n ,P_n be the polynomial such that (d^nf(x))/(dx^n)=P_n(1/x)e^(-1/x) for all x > 0. Show that P_(n+1)(x)=x^2[P_n(x)-d/(dx)P_n(x)]

Let f be a function from the set of positive integers to the set of real number i.e f : N rarr R , such that f(1) + 2f{2} + 3f{3} + ….. + nf{n} = n(n + 1) f(n) for n ge 2 Then the of 1/f(4) must be

Let f be a function from the set of positive integers to the set of real number i.e f : N rarr R , such that f(1) = 1 and r=1 to n ∑ ​ rf(r)=n(n+1)f(n),∀n≥2' then the value of 2126f(1063)

If n be a positive interger and p_(n) denotes the product of the binomial coefficients in the expansion of (1+x)^(n)," Prove that, "(P_(n+1))/(P_(n))=(n+1)^(n)/(n!) .

Let f(x) be the polynomial of degree n, then Delta^(n-1) f(x) is a polynomial of degree.

Let f:N->N be defined by f(x)=x^2+x+1,x in N . Then f(x) is

Let f(n)=1+1/2+1/3++1/ndot Then f(1)+f(2)+f(3)++f(n) is equal to (a) nf(n)-1 (b) (n+1)f(n)-n (c) (n+1)f(n)+n (d) nf(n)+n

Let f(n)=2cosn xAAn in N , then f(1)f(n+1)-f(n) is equal to

Let N be the set of natural numbers and two functions f and g be defined as f, g : N to N such that : f(n)={((n+1)/(2),"if n is odd"),((n)/(2),"if n is even"):}and g(n)=n-(-1)^(n) . The fog is :

Let p be a prime number and n be a positive integer then exponent of p in n! is denoted by E_p(n!) and is given by E_p(n!)=[n/p]+[n/(p)^2]+[n/(p)^3]+....[n/(p^k)] where p^kltnltp^(k+1) and [x] denotes the greatest integral part of x if we isolate the power of each prime contained in any number N then N can be written as N=2^(alpha_1).3^(alpha_2).5^(alpha_3).7^(alpha_4) ....where alpha_i are whole numbers the exponent of 7 in ,^100c_50 is

PATHFINDER-FUNCTION-QUESTION BANK
  1. The domain of y=cos^-1((1-2|x|)/3)+log|x-1|x is

    Text Solution

    |

  2. Let f:[-pi/3, 2pi/3] rarr [0,4] be a function defined as f(x)=sqrt3 si...

    Text Solution

    |

  3. Let n be a positive integer with f(n)=1!+2!+3!+….+n! and P(x) and Q(x)...

    Text Solution

    |

  4. A function f:R rarr R is defined by f(x+y)-kxy=f(x)+2y^2, AA xy in R a...

    Text Solution

    |

  5. If f(x)=1+x^2 and [g(x)]=1+x^2-2x^3+x^4, g(2)=2, then

    Text Solution

    |

  6. pi is the FUNDAMENTAL period of

    Text Solution

    |

  7. If the range of the function y=(x-1)/(a-x^2+1) does not contain any va...

    Text Solution

    |

  8. Let f: d rarr R be defined by f(X)=In (In(In(In x))) then

    Text Solution

    |

  9. Let f(x)=max{1+sinx,1,1-cosx}, xin[0,2pi] and g(x)=max{1,|x-1|} x in R...

    Text Solution

    |

  10. Let f(x)=(e^-x)/(1+[x]), then

    Text Solution

    |

  11. The value(s) of a, for which (x^3-6x^2+11x-6)/(x^3+x^2-10x+8) + a/30 =...

    Text Solution

    |

  12. f(x) is real valued function, satisfying f(x+y)+f(x-y)=2f(X),f(y) for ...

    Text Solution

    |

  13. If S is the set of all real numbers x for which (2x-1)/(2x^3+3x^2+x) g...

    Text Solution

    |

  14. If f'(x)=(1-2sin^2x)/f(x), (f(x) ge 0, AA x in R and f(0)=1) then f(x...

    Text Solution

    |

  15. If f(x)=sin^2x+sin^2(x+pi/3)+cos x.cos(x+pi/3) and g(5/4)=1, then

    Text Solution

    |

  16. Let f:[-pi/3, 2pi/3] rarr [0,4] be a function defined as f(x)=sqrt3 si...

    Text Solution

    |

  17. If f(x)=x/(x^2+1) and f(A)={y:-1/2 le y lt 0}, then set A is

    Text Solution

    |

  18. If f(x)=cos([pi^2|x)+cos([-pi^2|x), where [x] stands for the greatest ...

    Text Solution

    |

  19. Domain of f(x)=sin^-1[2-4x^2] is ([.] denotes the greatest integer fun...

    Text Solution

    |

  20. f(x)=cos^2x+cos^2(pi/3 +x)-cosxcos(pi/3 +x) is

    Text Solution

    |