Home
Class 12
MATHS
Let Sn=1+q+q^2 +?+q^n and Tn =1+((q+1)/2...

Let `S_n=1+q+q^2 +?+q^n` and `T_n =1+((q+1)/2)+((q+1)/2)^2+?+((q+1)/2)^n` If `alpha T_100=^101C_1 +^101C_2 xS_1 +^101C_101 xS_100,` then the value of `alpha` is equal to (A) `2^99` (B) `2^101` (C) `2^100` (D) `-2^100`

A

`2^99`

B

`2^101`

C

`2^100`

D

`-2^100`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • PROGRESSIONS

    MCGROW HILL PUBLICATION|Exercise Questions from Previous Years. B-Architecture Entrance Examination Papers|25 Videos

  • PROGRESSIONS

    MCGROW HILL PUBLICATION|Exercise EXERCISES (Numerical Answer Type Questions)|19 Videos

  • PROBABILITY

    MCGROW HILL PUBLICATION|Exercise Previous Years B-Architecture Entrance Examination Papers|21 Videos

  • QUADRATIC EQUATIONS

    MCGROW HILL PUBLICATION|Exercise Questions from previous Years. B - architecture entrance examination papers|16 Videos

Similar Questions

Explore conceptually related problems

Let S_(n)=1+q+q^(2)+?+q^(n) and T_(n)=1+((q+1)/(2))+((q+1)/(2))^(2)+?+((q+1)/(2)) If alpha T_(100)=^(101)C_(1)+^(101)C_(2)xS_(1)+^(101)C_(101)xS_(100), then the value of alpha is equal to (A) 2^(99)(B)2^(101)(C)2^(100) (D) -2^(100)

Let S_k=1+q+q^2+...+q^k and T_k=1+(q+1)/2+((q+1)/2)^2+...+((q+1)/2)^k q!=1 then prove that sum_(r=1)^(n+1) ^(n+1)C_rS_(r-1)=2^ nT_n

If P = (101)^(100) and Q = (100)^(101) , then the correct relation is:

If the number of terms in the expansion of (1+x)^(101)(1+x^(2)-x)^(100) is n, then the value of (n)/(25) is euqal to

(C_(0))/(1)+(C_(1))/(2)+(C_(2))/(3)+ . . . .+(C_(100))/(101) equals

If sin^(-1)x+sin^(-1)y+sin^(-1)z=(3 pi)/(2) ,then the value of x^(100)+y^(100)+z^(100)+(12)/(x^(101)+y^(101)+z^(101)) is equal to

If .^nC_0+3.^nC_1+5^nC_2+7^nC_3+ . . .till (n+1) term=2^100*101 then the value of 2[(n-1)/2] where [.] is G.I.F)

MCGROW HILL PUBLICATION-PROGRESSIONS-Questions from Previous Years. AIEEE/JEE Main Papers
  1. The sum of all two digit positive numbers which when divided by 7 yiel...

    Text Solution

    |

  2. The sum of an infinite geometric series with positive terms is 3 and t...

    Text Solution

    |

  3. Let a1,a2," ..."a10 be a G.P. If a3/a1=25," then "a9/a5 equals

    Text Solution

    |

  4. Let S(k) = (1+2+3+...+k)/(k). If S(1)^(2) + s(2)^(2) +...+S(10)^(2) = ...

    Text Solution

    |

  5. The product of three consecutive terms of a G.P. is 512. If 4 is added...

    Text Solution

    |

  6. Let Sn=1+q+q^2 +?+q^n and Tn =1+((q+1)/2)+((q+1)/2)^2+?+((q+1)/2)^n If...

    Text Solution

    |

  7. If 19^(th) term of a non-zero A.P. is zero, then (49^(th) term) : (29^...

    Text Solution

    |

  8. The sum of all natural numbers 'n' such that 100 lt n lt 200 and HCF (...

    Text Solution

    |

  9. The sum underset(k=1)overset(20)sum k (1)/(2^(k)) is equal to

    Text Solution

    |

  10. Let sum(k=1)^(10)f(a+k)=16(2^(10)-1), where the function f satisfies ...

    Text Solution

    |

  11. Let the sum of the first n terms of a non-constant A.P., a(1), a(2), a...

    Text Solution

    |

  12. Some identical balls are arranged in rows to form an equilateral tria...

    Text Solution

    |

  13. The sum of the the series 1+2x3+3x5+4x7+…. Upto 11^(th) term is

    Text Solution

    |

  14. If the sum and product of the first three terms in an AP are 33 and 11...

    Text Solution

    |

  15. Let S=3+(5(a^(3)+2^(3)))/(1^(2)+2^(2))+(7(1^(3)+2^(3)+3^(3)))/(1^(2)+2...

    Text Solution

    |

  16. Let a1,a2,a3,... be in A.P. With a6=2. Then the common difference of t...

    Text Solution

    |

  17. Let a, b and c be in GP with common ratio, r where a !=0 and 0 lt r le...

    Text Solution

    |

  18. value of 1+(1^(3)+2^(3))/(1+2)+(1^(3)+2^(3)+3^(3))/(1+2+3)+……+(1^(3)+2...

    Text Solution

    |

  19. Let S(n) denote the sum of the first n terms of an AP. If S(4) = 16 an...

    Text Solution

    |

  20. If a(1), a(2), a(3),... are in AP such that a(1) + a(7) + a(16) = 40, ...

    Text Solution

    |