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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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