Home
Class 12
MATHS
if x , 2y and 3z are in AP where the d...

if x , 2y and 3z are in AP where the distinct numbers x, yand z are in gp. Then the common ratio of the GP is

A

3

B

`1/3`

C

2

D

`1/2`

Text Solution

Verified by Experts

The correct Answer is:
B
x,y and z are in G.P. Hence,
`y=xr,=xr^(2)`
Also,x,2y, and 3z are in A.P. Hnce,
4y=x+3z
`rArr4xr=x+3xr^(2)`
`rArr3r^(2)-4r+1=0`
`rArr(3r-1)(r-1)=0`
`rArrr=1//3` (rne1 is not possible as x,y,z are distinct)
Promotional Banner

Topper's Solved these Questions

  • PROGRESSION AND SERIES

    CENGAGE|Exercise Exercise (Multiple & Comprehension)|66 Videos

  • PROGRESSION AND SERIES

    CENGAGE|Exercise EXERCIESE ( MULTIPLE CORRECT ANSWER TYPE )|2 Videos

  • PROGRESSION AND SERIES

    CENGAGE|Exercise Exercise 5.9|9 Videos

  • PROBABILITY II

    CENGAGE|Exercise JEE Advanced Previous Year|25 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE|Exercise JEE Advanced Previous Year|11 Videos

Similar Questions

Explore conceptually related problems

If the pth ,qth and rth terms of an AP are in G.P then the common ration of the GP is

Three positive numbers form an increasing GP. If the middle term in this GP is doubled, then new numbers are in AP. Then, the common ratio of the GP is

If the 2nd, 5th and 19th terms of a non-constant AP are in GP, then the common ratio of this GP is

Three numbers form an increasing G.P. If the middle number is doubled, then the new numbers are in A.P. The common ratio of the G.P. is

Three numbers are in G.P. if we double the middle term, we get an A.P. Then the common ratio of G.P equals

Find the x, y, and z, given that the number x, 10, y, 24, z are in A.P.

Three numbers from an increasing G.P. If the middle term is doubled the new number are in A.P. The common ratio of G.P will be

The sum of an infinite G.P. is 57 and the sum of their cubes is 9747, then the common ratio of the G.P. is

If 3^(rd) , 7^(th) and 12^(th) terms of A.P. are three consecutive terms of a G.P., then the common ratio of G.P is

CENGAGE-PROGRESSION AND SERIES-Exercise (Single)
  1. If a ,b, c ,d are in G.P, then (b-c)^2+(c-a)^2+(d-b)^2 is equal to

    Text Solution

    |

  2. Let {tn} be a sequence of integers in G.P. in which t4: t6=1:4a n dt2+...

    Text Solution

    |

  3. if x , 2y and 3z are in AP where the distinct numbers x, yand z ar...

    Text Solution

    |

  4. If a,b, and c are in A.P and b-a,c-b and a are in G.P then a:b:c is

    Text Solution

    |

  5. If the sides of a triangle are in G.P., and its largest angle is twice...

    Text Solution

    |

  6. If x,y,z are in G.P and a^x=b^y=c^z,then

    Text Solution

    |

  7. The number of terms common between the series 1+ 2 + 4 + 8..... to 100...

    Text Solution

    |

  8. If a^2+b^2,a b+b c ,a n db^2+c^2 are in G.P., then a ,b ,c are in a. A...

    Text Solution

    |

  9. In a G.P. the first, third, and fifth terms may be considered as the ...

    Text Solution

    |

  10. If the pth ,qth and rth terms of an AP are in G.P then the common rati...

    Text Solution

    |

  11. If p^(th), q^(th), r^(th) and s^(th) terms of an A.P. are in G.P, the...

    Text Solution

    |

  12. If a ,b , a n dc are in G.P. and x ,y , respectively, are the arithmet...

    Text Solution

    |

  13. If a ,ba n dc are in A.P., and pa n dp ' are respectively, A.M. and G....

    Text Solution

    |

  14. If (1+x)(1+x^2)(1+x^4)….(1+x^(128))=Sigma(r=0)^(n) x^r, then n is equa...

    Text Solution

    |

  15. If (1-p)(1+3x+9x^2+27 x^3+81 x^4+243 x^5)=1-p^6p!=1 , then the value o...

    Text Solution

    |

  16. Consider the ten numbers a r ,a r^2, a r^3, ,a r^(10)dot If their sum...

    Text Solution

    |

  17. If x ,y ,a n dz are distinct prime numbers, then x , y , a n dz may be...

    Text Solution

    |

  18. Let a=111 1(55d igi t s),b=1+10+1=^2++10^4,c=1+10^5+10^(10)+10^(15)++1...

    Text Solution

    |

  19. Let a(n) be the n^(th) term of a G.P of positive integers. Let sum(n =...

    Text Solution

    |

  20. The sum of 20 terms of a series of which every term is 2 times the ter...

    Text Solution

    |