JEE Main & Advanced Mathematics Sequence & Series Question Bank

done Harmonic Progression Total Questions - 23

• question_answer1)
  If the \[{{m}^{th}}\] term of a H.P. be \[n\] and \[{{n}^{th}}\] be \[m\], then the \[{{r}^{th}}\] term will be
  A)
  \[\frac{r}{mn}\] done clear
  B)
  \[\frac{mn}{r+1}\] done clear
  C)
  \[\frac{mn}{r}\] done clear
  D)
  \[\frac{mn}{r-1}\] done clear
  View Solution play_arrow

• question_answer2)
  Which number should be added to the numbers 13, 15, 19 so that the resulting numbers be the consecutive terms of a H.P.
  A)
  7 done clear
  B)
  6 done clear
  C)
  \[-6\] done clear
  D)
  \[-7\] done clear
  View Solution play_arrow

• question_answer3)
  The fifth term of the H.P., \[2,\ 2\frac{1}{2},\ 3\frac{1}{3},.............\] will be  [MP PET 1984]
  A)
  \[5\frac{1}{5}\] done clear
  B)
  \[3\frac{1}{5}\] done clear
  C)
  1/10 done clear
  D)
  10 done clear
  View Solution play_arrow

• question_answer4)
  If \[{{a}_{1}},\ {{a}_{2}},\ {{a}_{3}},...............,\ {{a}_{n}}\] are in H.P., then \[{{a}_{1}}{{a}_{2}}+{{a}_{2}}{{a}_{3}}+\] \[..........+{{a}_{n-1}}{{a}_{n}}\] will be equal to [IIT 1975]
  A)
  \[{{a}_{1}}{{a}_{n}}\] done clear
  B)
  \[n{{a}_{1}}{{a}_{n}}\] done clear
  C)
  \[(n-1){{a}_{1}}{{a}_{n}}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer5)
  If \[x,\ y,\ z\] are in H.P., then the value of expression \[\log (x+z)+\log (x-2y+z)\] will be  [RPET 1985, 2000]
  A)
  \[\log (x-z)\] done clear
  B)
  \[2\log (x-z)\] done clear
  C)
  \[3\log (x-z)\] done clear
  D)
  \[4\log (x-z)\] done clear
  View Solution play_arrow

• question_answer6)
  If \[{{5}^{th}}\] term of a H.P. is \[\frac{1}{45}\]and \[{{11}^{th}}\] term is \[\frac{1}{69}\], then its \[{{16}^{th}}\]  term will be [RPET 1987,  97]
  A)
  1/89 done clear
  B)
  1/85 done clear
  C)
  1/80 done clear
  D)
  1/79 done clear
  View Solution play_arrow

• question_answer7)
  The first term of a harmonic progression is 1/7 and the second term is 1/9. The \[{{12}^{th}}\] term is [MP PET 1994]
  A)
  1/19 done clear
  B)
  1/29 done clear
  C)
  1/17 done clear
  D)
  1/27 done clear
  View Solution play_arrow

• question_answer8)
  If \[a,\ b,\ c\] are three distinct positive real numbers which are in H.P., then \[\frac{3a+2b}{2a-b}+\frac{3c+2b}{2c-b}\] is
  A)
  Greater than or equal to 10 done clear
  B)
  Less than or equal to 10 done clear
  C)
  Only equal to 10 done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer9)
  If \[a,\ b,\ c,\ d\] are in H.P., then \[ab+bc+cd\] is equal to
  A)
  \[3ad\] done clear
  B)
  \[(a+b)(c+d)\] done clear
  C)
  \[3ac\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer10)
  If the \[{{7}^{th}}\] term of a harmonic progression is 8 and the \[{{8}^{th}}\]term is 7, then its \[{{15}^{th}}\] term is [MP PET 1996]
  A)
  16 done clear
  B)
  14 done clear
  C)
  \[\frac{27}{14}\] done clear
  D)
    \[\frac{56}{15}\] done clear
  View Solution play_arrow

• question_answer11)
  If the \[{{7}^{th}}\] term of a H.P. is \[\frac{1}{10}\] and the \[{{12}^{th}}\] term is \[\frac{1}{25}\], then the \[{{20}^{th}}\] term is [MP PET 1997]
  A)
  \[\frac{1}{37}\] done clear
  B)
    \[\frac{1}{41}\] done clear
  C)
    \[\frac{1}{45}\] done clear
  D)
    \[\frac{1}{49}\] done clear
  View Solution play_arrow

• question_answer12)
  If sixth term of a H.P. is \[\frac{1}{61}\] and its tenth term is \[\frac{1}{105},\] then first term of that H.P. is [Karnataka CET 2001]
  A)
  \[\frac{1}{28}\] done clear
  B)
  \[\frac{1}{39}\] done clear
  C)
  \[\frac{1}{6}\] done clear
  D)
  \[\frac{1}{17}\] done clear
  View Solution play_arrow

• question_answer13)
  In a H.P., pth term is q and the qth term is p. Then pqth term is   [Karnataka CET 2002]
  A)
  0 done clear
  B)
  1 done clear
  C)
  pq done clear
  D)
  \[pq(p+q)\] done clear
  View Solution play_arrow

• question_answer14)
  The 4th term of a H.P. is \[\frac{3}{5}\] and 8th term is \[\frac{1}{3},\] then its 6th term is [MP PET 2003]
  A)
  \[\frac{1}{6}\] done clear
  B)
  \[\frac{3}{7}\] done clear
  C)
  \[\frac{1}{7}\] done clear
  D)
  \[\frac{3}{5}\] done clear
  View Solution play_arrow

• question_answer15)
  If \[H\] is the harmonic mean between \[p\] and \[q\], then the value of  \[\frac{H}{p}+\frac{H}{q}\]  is [MNR 1990; UPSEAT 2000,  01]
  A)
  2 done clear
  B)
  \[\frac{pq}{p+q}\] done clear
  C)
  \[\frac{p+q}{pq}\] done clear
  D)
  None of these done clear
  View Solution play_arrow

• question_answer16)
  If the harmonic mean between \[a\] and \[b\] be \[H\], then the value of  \[\frac{1}{H-a}+\frac{1}{H-b}\] is
  A)
  \[a+b\] done clear
  B)
  \[ab\] done clear
  C)
  \[\frac{1}{a}+\frac{1}{b}\] done clear
  D)
  \[\frac{1}{a}-\frac{1}{b}\] done clear
  View Solution play_arrow

• question_answer17)
  H.M. between the roots of the equation \[{{x}^{2}}-10x+11=0\] is [MP PET 1995]
  A)
  \[\frac{1}{5}\] done clear
  B)
  \[\frac{5}{21}\] done clear
  C)
  \[\frac{21}{20}\] done clear
  D)
  \[\frac{11}{5}\] done clear
  View Solution play_arrow

• question_answer18)
  The harmonic mean of \[\frac{a}{1-ab}\] and \[\frac{a}{1+ab}\] is [MP PET 1996; Pb. CET 2001]
  A)
    \[\frac{a}{\sqrt{1-{{a}^{2}}{{b}^{2}}}}\] done clear
  B)
    \[\frac{a}{1-{{a}^{2}}{{b}^{2}}}\] done clear
  C)
  \[a\] done clear
  D)
  \[\frac{1}{1-{{a}^{2}}{{b}^{2}}}\] done clear
  View Solution play_arrow

• question_answer19)
  The sixth H.M. between 3 and \[\frac{6}{13}\] is [RPET 1996]
  A)
    \[\frac{63}{120}\] done clear
  B)
    \[\frac{63}{12}\] done clear
  C)
    \[\frac{126}{105}\] done clear
  D)
    \[\frac{120}{63}\] done clear
  View Solution play_arrow

• question_answer20)
  If \[\frac{{{a}^{n+1}}+{{b}^{n+1}}}{{{a}^{n}}+{{b}^{n}}}\] be the harmonic mean between \[a\] and \[b\], then the value of \[n\] is [Assam  PET 1986]
  A)
  1 done clear
  B)
  \[-1\] done clear
  C)
  0 done clear
  D)
  2 done clear
  View Solution play_arrow

• question_answer21)
  If the harmonic mean between \[a\] and \[b\] be \[H\], then \[\frac{H+a}{H-a}+\frac{H+b}{H-b}=\] [AMU 1998]
  A)
  4 done clear
  B)
  2 done clear
  C)
  1 done clear
  D)
  \[a+b\] done clear
  View Solution play_arrow

• question_answer22)
  If \[a,\ b,\ c\] be in H.P., then
  A)
  \[{{a}^{2}}+{{c}^{2}}>{{b}^{2}}\] done clear
  B)
  \[{{a}^{2}}+{{b}^{2}}>2{{c}^{2}}\] done clear
  C)
  \[{{a}^{2}}+{{c}^{2}}>2{{b}^{2}}\] done clear
  D)
  \[{{a}^{2}}+{{b}^{2}}>{{c}^{2}}\] done clear
  View Solution play_arrow

• question_answer23)
  If \[a,\ b,\ c,\ d\] are in H.P., then [RPET 1991]
  A)
  \[a+d>b+c\] done clear
  B)
  \[ad>bc\] done clear
  C)
  Both (a) and (b) done clear
  D)
  None of these done clear
  View Solution play_arrow