Home
Class 12
MATHS
For r= 0, 1,.....,10, let Ar,Br, and C...

For `r= 0, 1,.....,10`, let `A_r,B_r, and C_r`denote, respectively, the coefficient of `x^r` in the expansions of `(1 +x)^10,(+x)^20 and (1+ x)^30`.Then `sum_(r=1)^10 A_r(B_10B_r-C_10A_r)` is equal to

A

`B_10- C_10`

B

`a_10 (B_10^2 - C_10 A_10)`

C

0

D

`C_10 - B_10`

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • Miscellaneous Exercises

    A DAS GUPTA|Exercise Exercise|77 Videos

  • Pair of Straight Lines and Transformation of Axes

    A DAS GUPTA|Exercise EXERCISE|22 Videos

Similar Questions

Explore conceptually related problems

For r=0,1,.....,10, let A_(r),B_(r),quad and C_(r) denote,respectively,the coefficient of x^(r) in the expansions of (1+x)^(10),(+x)^(20) and (1+x)^(30). Then sum A_(r)(B_(10)B_(r)-C_(10)A_(r)) is equal to

If C_(r)=10C_(r), then sum_(r=1)^(10)C_(r-1)C_(r) is equal to

Let a_r denote the coefficient of y^(r-1) in the expansion of (1 + 2y)^(10) . If (a_(r+2))/(a_(r)) = 4 , then r is equal to

If the coefficients of (2r +1)th and (4r + 5) th terms is the expansion of (1+x)^(10) are equal then r=?

The value sum_(r=1)^(10)r.(n_(C_(r)))/(n_(C_(r-1))) is equal to

The value of sum int_(r=1)^(r=10)rC(10,r) is

Find sum_(r=1)^(10) (r+2)(3r+1).

If A and B are coefficients of x^(r) and x^(n-r) respectively in the expansion of (1+x)^(n), then

A DAS GUPTA-Objective Tests-Exercise
  1. An ellipse intersects the hyperbola 2x^(2)-2y^(2)=1 orthogonally. The ...

    Text Solution

    |

  2. Let L = lim(x rarr 0) ( a - sqrt( a^2 - x^2) - x^2/4)/x^4, a>0.If L is...

    Text Solution

    |

  3. For the function f(x)=x "cos" 1/x, x ge1

    Text Solution

    |

  4. If In=int(-pi)^(pi) \ (sinnx)/((1+pi^x) \ sinx) \ dx, n=0,1,2,...... t...

    Text Solution

    |

  5. The area of the region bounded by the curve y=e^(x) and lines x=0 and ...

    Text Solution

    |

  6. Q. Let p and q real number such that p!= 0,p^2!=q and p^2!=-q. if alph...

    Text Solution

    |

  7. Let S={1,,2,34} . The total number of unordered pairs of disjoint s...

    Text Solution

    |

  8. For r= 0, 1,.....,10, let Ar,Br, and Crdenote, respectively, the coe...

    Text Solution

    |

  9. The number of 3xx3 matrices A whose entries are either 0or1 and for wh...

    Text Solution

    |

  10. If the angle A , B and C of a triangle are in arithmetic progession an...

    Text Solution

    |

  11. Two adjacent sides of a parallelogram A B C D are given by vec A B...

    Text Solution

    |

  12. The equation of the plane containing the straight line x/2=y/3=z/4 and...

    Text Solution

    |

  13. If the distance of the point P(1,-2,1) from the plane x+2y-2z=alpha...

    Text Solution

    |

  14. Let f,g and h be real-valued functions defined on the interval [0,1] b...

    Text Solution

    |

  15. Let f be a real-valued function defined on the inverval (-1,1) such th...

    Text Solution

    |

  16. Let omega be a complex cube root unity with omega!=1. A fair die is th...

    Text Solution

    |

  17. A signal which can be green or red with probability 4/5 and 1/5 respec...

    Text Solution

    |

  18. Let z(1) and z(2) be two distinct complex numbers and z=(1-t)z(1)+iz(2...

    Text Solution

    |

  19. Let ABC be a triangle such that angleACB=pi/6 and let a , b and c deno...

    Text Solution

    |

  20. Let A and B be two distinct points on the parabola y^2 = 4x. If the ax...

    Text Solution

    |