Home
Class 11
MATHS
If a ,ba n dc are in A.P., and pa n dp ...

If `a ,ba n dc` are in A.P., and `pa n dp '` are respectively, A.M. and G.M. between `aa n dbw h i l eq , q '` are , respectively, the A.M. and G.M. between `ba n dc ,` then `p^2+q^2=p^('2)+q^('2)` b. `p q=p ' q '` c. `p^2-q^2=p^('2)-q^('2)` d. none of these

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    CENGAGE ENGLISH|Exercise All Questions|9 Videos
  • STRAIGHT LINES

    CENGAGE ENGLISH|Exercise All Questions|491 Videos

Similar Questions

Explore conceptually related problems

If p ,q be two A.M. ' s and G be one G.M. between two numbers, then G^2= a) (2p-q)(p-2q) (b) (2p-q)(2q-p) c) (2p-q)(p+2q) (d) none of these

If a ,b ,a n dc are in A.P. p ,q ,a n dr are in H.P., and a p ,b q ,a n dc r are in G.P., then p/r+r/p is equal to a/c+c/a

If a ,b ,a n dc are in A.P. p ,q ,a n dr are in H.P., and a p ,b q ,a n dc r are in G.P., then p/r+r/p is equal to a/c-c/a b. a/c+c/a c. b/q+q/b d. b/q-q/b

If a ,b ,a n dc are in A.P. p ,q ,a n dr are in H.P., and a p ,b q ,a n dc r are in G.P., then p/r+r/p is equal to a/c-c/a b. a/c+c/a c. b/q+q/b d. b/q-q/b

Let a,b,c be in A.P. If p is the A.M. between a and b and q is the A.M between b and c, then b is equal to

If a,b,c are in AP and p is the AM between a and b and q is the AM between b and c, then show that b is the AM between p and q.

If (p+q)^(t h)a n d\ (p-q)^(t h) terms of a G.P. re m\ a n d\ n respectively, then write it p t h term.

If sec alpha and alpha are the roots of x^2-p x+q=0, then (a) p^2=q(q-2) (b) p^2=q(q+2) (c) p^2q^2=2q (d) none of these

In Delta P Q R , if P Q=Q R and L ,M and N are the mid-points of the sides P Q ,Q R and R P respectively. Prove that L N=M Ndot

if the A.M. between pth and qth terms of an A.P. be equal to the A.M. between rth and sth terms of the A.P., then show that p+q=r+s

CENGAGE ENGLISH-SEQUENCES AND SERIES-All Questions
  1. The sum of the series a-(a+d)+(a+2d)-(a+3d)+... up to (2n+1) terms is:...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  4. Find the sum 3/(1xx2)xx1/2+4/(2xx3)xx(1/2)^2+5/(3xx4)xx(1/2)^2+ ton te...

    Text Solution

    |

  5. If the sum of n terms of the series (2n+1)/(2n-1)+3((2n+1)/(2n-1))^...

    Text Solution

    |

  6. Let x=1+3a+6a^2+10 a^3+ ,|a|<1. y=1+4b+10 b^2+20 b^3+ ,|b|<1. Find S...

    Text Solution

    |

  7. If the first and the nth terms of a G.P are a and b , respectively, an...

    Text Solution

    |

  8. Along a road lie an odd number of stones placed at intervals of 10 met...

    Text Solution

    |

  9. Find a three – digit number such that its digits are in increasing G.P...

    Text Solution

    |

  10. If the terms of the A.P, sqrt(a-x),sqrt(x),sqrt(a+x) are all in integ...

    Text Solution

    |

  11. For a ,x ,>0 prove tht at most one term of the G.P. sqrt(a-x),sqrt(x),...

    Text Solution

    |

  12. If 1/(1^2)+1/(2^2)+1/(3^2)+ .......=(pi^2)/6,t h e n1/(1^2)+1/(3^2)+1/...

    Text Solution

    |

  13. Coefficient of x^(18) in (1+x+2x^2+3x^3++18 x^(18))^2 equal to 995 b. ...

    Text Solution

    |

  14. Let alphaa n dbeta be the roots of x^2-x+p=0a n dgammaa n ddelta be th...

    Text Solution

    |

  15. If the sum of the first 2n terms of the A.P. 2, 5, 8, ..., is equal to...

    Text Solution

    |

  16. Statement 1: If the arithmetic mean of two numbers is 5/2 geometric ...

    Text Solution

    |

  17. Let the positive numbers a ,b ,ca d nd be in the A.P. Then a b c ,a b ...

    Text Solution

    |

  18. If three positive real numbers a,b ,c are in A.P such that a b c=4 , t...

    Text Solution

    |

  19. Consider an infinite geometric series with first term a and common rat...

    Text Solution

    |

  20. The maximum sum of the series 20+19 1/3+18 2/3+...... is (A) 310 (...

    Text Solution

    |