Home
Class 12
MATHS
If x=1+(y)/(2)+((y)/(2))^(2)+((y)/(2))^(...

If `x=1+(y)/(2)+((y)/(2))^(2)+((y)/(2))^(3)+……" where "|y|lt2`, what is 1y equal to ?

A

`(x-1)/(x)`

B

`(x-1)/(2x)`

C

`(2x-2)/(x)`

D

`(2x+1)/(2x)`

Text Solution

Verified by Experts

The correct Answer is:
C
`x=1+(y)/(2)+((y)/(2))^(2)+((y)/(2))^(3)+......`
Here, `(y)/(2)lt1` and this a GP. With first term=1 and common ratio`=(y)/(2)` so,
`implies" "x=(1)/(1-(y)/(2))impliesx=(2)/(2-y)`
`implies" "2x-xy=2impliesy=(2x-2)/(x)`
Promotional Banner

Topper's Solved these Questions

  • QUESTION PAPER 2021(I)

    NDA PREVIOUS YEARS|Exercise MULTIPLE CHOICE QUESTION|108 Videos

  • SETS, RELATIONS, FUNCTIONS AND NUMBER SYSTEM

    NDA PREVIOUS YEARS|Exercise MCQ|271 Videos

Similar Questions

Explore conceptually related problems

If (x)/(2)+(y)/(3)=4 "and" (2)/(x)+(3)/(y)=1 then what is x+y equal to ?

If (3)/(x+y)+(2)/(x-y)=2 and (9)/(x+y)-(4)/(x-y)=1 then what is (x)/(y) equal to ?

If (dy)/(dx)=(2^(x+y)-2^(x))/(2^(y)),y(0)=1 then y(1) is equal to

Prove that tan{1/2sin^(-1)((2x)/(1+x^(2)))+1/2cos^(-1)((1-y^(2))/(1+y^(2)))}=(x+y)/(1-xy) , where |x| lt 1,y gt 0 and xy lt 1 .

If x^(2)+y^(2)=1 and P=(3x-4x^(3))^(2)+(3y-4y^(3))^(2) then P is equal to

if y = x + x^(2) + x^(3) + …oo, where |x| lt 1, then for |y| lt 1, (dx)/(dy) is equal to

If sinx=(1)/(sqrt5).siny=(1)/(sqrt(10)) , where 0 lt x lt (pi)/(2),0 lt y lt (pi)/(2) , then what is (x+y) equal to?

int(1)/(3x^(2)y^(2)) where y is constant

If x/2 + y/3 = 4 and 2/x + 3/y = 1, then what is x + y equal to ?

NDA PREVIOUS YEARS-SEQUENCE AND SERIES -MATH
  1. One of the roots of a quadratic equation with real coefficients is (1)...

    Text Solution

    |

  2. What is the sum of the first 50 terms of the series (1xx3)+(3xx5)+(5xx...

    Text Solution

    |

  3. If x=1+(y)/(2)+((y)/(2))^(2)+((y)/(2))^(3)+……" where "|y|lt2, what is ...

    Text Solution

    |

  4. What is the product of first 2n+1 terms of a geometric progression ?

    Text Solution

    |

  5. The following question consist of two statements, one labelled as the ...

    Text Solution

    |

  6. If x+1,4x+1," and "8x+1 are in geometric progrssion, then what is the ...

    Text Solution

    |

  7. The equation (a^(2)+b^(2))x^(2)-2b(a+c)x+(b^(2)+c^(2))=0 has equal roo...

    Text Solution

    |

  8. If p^(th) term of an AP is q, and its q^(th) term is p, then what is t...

    Text Solution

    |

  9. If a,b,c are in geometric progression and a,2b,3c are in arithmetic pr...

    Text Solution

    |

  10. For an AP with first term u and common difference v, the p^(th) term i...

    Text Solution

    |

  11. If a, b and c are three positive numbers in an arithmetic progression,...

    Text Solution

    |

  12. If |x|lt(1)/(2), what is the value of 1+[(x)/(1-x)]+[(n(n+1))/(2!)][...

    Text Solution

    |

  13. The sum of the first (2p+1) terms of an AP is {(p+1).(2p+1)}. Which on...

    Text Solution

    |

  14. a, b, c are in G.P. with 1ltaltbltn," and "ngt1 is an integer. log(a)n...

    Text Solution

    |

  15. What is the sum of the series 1-(1)/(2)+(1)/(4)-(1)/(8)+.... equal to?

    Text Solution

    |

  16. If b(1),b(2),b(3) are three consecutive terms of an arithmetic progres...

    Text Solution

    |

  17. If 1, x, y, z, 16 are in geometric progression, then what is the value...

    Text Solution

    |

  18. If the nth term of an arithmetic progression is 3n+7, then what is the...

    Text Solution

    |

  19. If, for positive real numbers x, y, z, the numbers x+y, 2y and y + z a...

    Text Solution

    |

  20. What is the sum of the series 1+(1)/(8)+(1.3)/(8.16)+(1.3.5)/(8.16.2...

    Text Solution

    |