MCQOPTIONS
Saved Bookmarks
MCQOPTIONS
This section includes 8666 Mcqs, each offering curated multiple-choice questions to sharpen your Joint Entrance Exam - Main (JEE Main) knowledge and support exam preparation. Choose a topic below to get started.
| 2001. |
If in the equation \[a{{x}^{2}}+bx+c=0,\] the sum of roots is equal to sum of square of their reciprocals, then \[\frac{c}{a},\frac{a}{b},\frac{b}{c}\] are in [RPET 2000] |
| A. | A.P. |
| B. | G.P. |
| C. | H.P. |
| D. | None of these |
| Answer» B. G.P. | |
| 2002. |
Let the positive numbers a, b, c, d be in A.P., then abc, abd acd, bcd are [IIT Screening 2001] |
| A. | Not in A.P./G.P./H.P. |
| B. | In A.P. |
| C. | In G.P. |
| D. | In H.P. |
| Answer» E. | |
| 2003. |
If \[{{A}_{1}},\ {{A}_{2}};{{G}_{1}},\ {{G}_{2}}\] and \[{{H}_{1}},\ {{H}_{2}}\] be two A.M.s, G.M.s and H.M.s between two numbers respectively, then\[\frac{{{G}_{1}}{{G}_{2}}}{{{H}_{1}}{{H}_{2}}}\times \frac{{{H}_{1}}+{{H}_{2}}}{{{A}_{1}}+{{A}_{2}}}\] = [RPET 1997] |
| A. | 1 |
| B. | 0 |
| C. | 2 |
| D. | 3 |
| Answer» B. 0 | |
| 2004. |
Given \[a+d>b+c\] where \[a,\ b,\ c,\ d\] are real numbers, then [Kurukshetra CEE 1998] |
| A. | \[a,\ b,\ c,\ d\] are in A.P. |
| B. | \[\frac{1}{a},\ \frac{1}{b},\ \frac{1}{c},\ \frac{1}{d}\] are in A.P. |
| C. | \[(a+b),\ (b+c),\ (c+d),\ (a+d)\]are in A.P. |
| D. | \[\frac{1}{a+b},\ \frac{1}{b+c},\ \frac{1}{c+d},\ \frac{1}{a+d}\] are in A.P. |
| Answer» C. \[(a+b),\ (b+c),\ (c+d),\ (a+d)\]are in A.P. | |
| 2005. |
If first three terms of sequence \[\frac{1}{16},a,b,\frac{1}{6}\] are in geometric series and last three terms are in harmonic series, then the value of \[a\] and \[b\] will be [UPSEAT 1999] |
| A. | \[a=-\frac{1}{4},b=1\] |
| B. | \[a=\frac{1}{12},b=\frac{1}{9}\] |
| C. | (a) and (b) both are true |
| D. | None of these |
| Answer» D. None of these | |
| 2006. |
If \[p,\ q,\ r\] are in one geometric progression and \[a,\ b,\ c\] in another geometric progression, then \[cp,\ bq,\ ar\] are in [Roorkee 1998] |
| A. | A.P. |
| B. | H.P. |
| C. | G.P. |
| D. | None of these |
| Answer» D. None of these | |
| 2007. |
If a ,b, c are in A.P., then \[\frac{1}{\sqrt{a}+\sqrt{b}},\,\frac{1}{\sqrt{a}+\sqrt{c}},\] \[\frac{1}{\sqrt{b}+\sqrt{c}}\] are in [Roorkee 1999; Kerala (Engg.) 2005] |
| A. | A.P. |
| B. | G.P. |
| C. | H.P. |
| D. | None of these |
| Answer» B. G.P. | |
| 2008. |
If three numbers be in G.P., then their logarithms will be in [BIT 1992] |
| A. | A.P. |
| B. | G.P. |
| C. | H.P. |
| D. | None of these |
| Answer» B. G.P. | |
| 2009. |
If \[\frac{a}{b+c},\frac{b}{c+a},\frac{c}{a+b}\]are in H.P., then \[a,b,c\] are in [RPET 1999] |
| A. | A.P. |
| B. | G.P. |
| C. | H.P. |
| D. | None of these |
| Answer» D. None of these | |
| 2010. |
If \[{{G}_{1}}\] and \[{{G}_{2}}\] are two geometric means and A the arithmetic mean inserted between two numbers, then the value of \[\frac{G_{1}^{2}}{{{G}_{2}}}+\frac{G_{2}^{2}}{{{G}_{1}}}\]is [DCE 1999] |
| A. | \[\frac{A}{2}\] |
| B. | A |
| C. | 0.0833333333333333 |
| D. | None of these |
| Answer» D. None of these | |
| 2011. |
If \[{{a}^{x}}={{b}^{y}}={{c}^{z}}\,\text{and}\,\,a,b,c\] are in G.P. then \[x,y,z\] are in [Pb. CET 1993; DCE 1999; AMU 1999] |
| A. | A. P. |
| B. | G. P. |
| C. | H. P. |
| D. | None of these |
| Answer» D. None of these | |
| 2012. |
Three non-zero real numbers form an A.P. and the squares of these numbers taken in the same order form a G.P. Then the number of all possible common ratios of the G.P. is |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | None of these |
| Answer» D. None of these | |
| 2013. |
\[{{\log }_{3}}2,\ {{\log }_{6}}2,\ {{\log }_{12}}2\]are in [RPET 1993, 2001] |
| A. | A.P. |
| B. | G.P. |
| C. | H.P. |
| D. | None of the above |
| Answer» D. None of the above | |
| 2014. |
If \[a,\ b,\ c\] are in A.P., then \[{{10}^{ax+10}},\ {{10}^{bx+10}},\ {{10}^{cx+10}}\] will be in [Pb. CET 1989] |
| A. | A.P. |
| B. | G.P. only when \[x>0\] |
| C. | G.P. for all values of \[x\] |
| D. | G.P. for \[x<0\] |
| Answer» D. G.P. for \[x<0\] | |
| 2015. |
If the A.M., G.M. and H.M. between two positive numbers \[a\] and \[b\] are equal, then [RPET 2003] |
| A. | \[a=b\] |
| B. | \[ab=1\] |
| C. | \[a>b\] |
| D. | \[a<b\] |
| Answer» B. \[ab=1\] | |
| 2016. |
If the ratio of H.M. and G.M. between two numbers \[a\] and \[b\] is \[4:5\], then the ratio of the two numbers will be [IIT 1992; MP PET 2000] |
| A. | \[1:2\] |
| B. | \[2:1\] |
| C. | \[4:1\] |
| D. | \[1:4\] |
| Answer» E. | |
| 2017. |
If \[{{\log }_{a}}x,\ {{\log }_{b}}x,\ {{\log }_{c}}x\] be in H.P., then \[a,\ b,\ c\] are in |
| A. | A.P. |
| B. | H.P. |
| C. | G.P. |
| D. | None of these |
| Answer» D. None of these | |
| 2018. |
If the product of three terms of G.P. is 512. If 8 added to first and 6 added to second term, so that number may be in A.P., then the numbers are [Roorkee 1964] |
| A. | 2, 4, 8 |
| B. | 4, 8, 16 |
| C. | 3, 6, 12 |
| D. | None of these |
| Answer» C. 3, 6, 12 | |
| 2019. |
If \[{{x}^{a}}={{x}^{b/2}}{{z}^{b/2}}={{z}^{c}}\], then \[a,b,c\] are in |
| A. | A.P. |
| B. | G.P. |
| C. | H.P. |
| D. | None of these |
| Answer» D. None of these | |
| 2020. |
If A.M. of two terms is 9 and H.M. is 36, then G.M. will be [RPET 1995] |
| A. | 18 |
| B. | 12 |
| C. | 16 |
| D. | None of the above |
| Answer» B. 12 | |
| 2021. |
If \[a,\ b,\ c\] are in H.P., then for all \[n\in N\] the true statement is [RPET 1995] |
| A. | \[{{a}^{n}}+{{c}^{n}}<2{{b}^{n}}\] |
| B. | \[{{a}^{n}}+{{c}^{n}}>2{{b}^{n}}\] |
| C. | \[{{a}^{n}}+{{c}^{n}}=2{{b}^{n}}\] |
| D. | None of the above |
| Answer» C. \[{{a}^{n}}+{{c}^{n}}=2{{b}^{n}}\] | |
| 2022. |
If \[\frac{a+bx}{a-bx}=\frac{b+cx}{b-cx}=\frac{c+dx}{c-dx}(x\ne 0)\], then \[a,\ b,\ c,\ d\] are in [RPET 1986] |
| A. | A.P. |
| B. | G.P. |
| C. | H.P. |
| D. | None of these |
| Answer» C. H.P. | |
| 2023. |
The geometric mean of two numbers is 6 and their arithmetic mean is 6.5 . The numbers are [MP PET 1994] |
| A. | (3, 12) |
| B. | (4, 9) |
| C. | (2, 18) |
| D. | (7, 6) |
| Answer» C. (2, 18) | |
| 2024. |
If \[{{\log }_{x}}y,\ {{\log }_{z}}x,\ {{\log }_{y}}z\] are in G.P. \[xyz=64\] and \[{{x}^{3}},\ {{y}^{3}},\ {{z}^{3}}\] are in A.P., then |
| A. | \[x=y=z\] |
| B. | \[x=4\] |
| C. | \[x,\ y,\,z\] are in G.P. |
| D. | All the above |
| Answer» E. | |
| 2025. |
If the ratio of A.M. between two positive real numbers \[a\] and \[b\]to their H.M. is \[m:n\], then \[a:b\] is |
| A. | \[\frac{\sqrt{m-n}+\sqrt{n}}{\sqrt{m-n}-\sqrt{n}}\] |
| B. | \[\frac{\sqrt{n}+\sqrt{m-n}}{\sqrt{n}-\sqrt{m-n}}\] |
| C. | \[\frac{\sqrt{m}+\sqrt{m-n}}{\sqrt{m}-\sqrt{m-n}}\] |
| D. | None of these |
| Answer» D. None of these | |
| 2026. |
If the roots of\[a\,(b-c){{x}^{2}}+b\,(c-a)x+c\,(a-b)=0\] be equal, then \[a,\ b,\ c\]are in [RPET 1997] |
| A. | A.P. |
| B. | G.P. |
| C. | H.P. |
| D. | None of these |
| Answer» D. None of these | |
| 2027. |
If all the terms of an A.P. are squared, then new series will be in |
| A. | A.P. |
| B. | G.P. |
| C. | H.P. |
| D. | None of these |
| Answer» E. | |
| 2028. |
If \[,a,\ b,\,c\] be in G.P. and \[a+x,\ b+x,\ c+x\] in H.P., then the value of \[x\] is (\[a,\ b,\ c\] are distinct numbers) |
| A. | \[c\] |
| B. | \[b\] |
| C. | \[a\] |
| D. | None of these |
| Answer» C. \[a\] | |
| 2029. |
An A.P., a G.P. and a H.P. have the same first and last terms and the same odd number of terms. The middle terms of the three series are in |
| A. | A.P. |
| B. | G.P. |
| C. | H.P. |
| D. | None of these |
| Answer» C. H.P. | |
| 2030. |
If \[\frac{x+y}{2},\ y,\ \frac{y+z}{2}\] are in H.P., then \[x,\ y,\ z\]are in [RPET 1989; MP PET 2003] |
| A. | A.P. |
| B. | G.P. |
| C. | H.P. |
| D. | None of these |
| Answer» C. H.P. | |
| 2031. |
If \[a,\ b,\ c\] are in H.P., then \[\frac{a}{b+c},\ \frac{b}{c+a},\ \frac{c}{a+b}\] are in [Roorkee 1980] |
| A. | A.P. |
| B. | G.P. |
| C. | H.P. |
| D. | None of these |
| Answer» D. None of these | |
| 2032. |
If the ratio of two numbers be \[9:1\], then the ratio of geometric and harmonic means between them will be |
| A. | \[1:9\] |
| B. | \[5:3\] |
| C. | \[3:5\] |
| D. | \[2:5\] |
| Answer» C. \[3:5\] | |
| 2033. |
If \[\frac{b+a}{b-a}=\frac{b+c}{b-c}\], then\[a,\ b,\ c\] are in |
| A. | A.P. |
| B. | G.P. |
| C. | H.P. |
| D. | None of these |
| Answer» E. | |
| 2034. |
If the ratio of H.M. and G.M. of two quantities is \[12:13\], then the ratio of the numbers is [RPET 1990] |
| A. | \[1:2\] |
| B. | \[2:3\] |
| C. | \[3:4\] |
| D. | None of these |
| Answer» E. | |
| 2035. |
If \[a,\ b,\ c\] are in A.P., then\[\frac{a}{bc},\ \frac{1}{c},\ \frac{2}{b}\] are in [MNR 1982; MP PET 2002] |
| A. | A.P. |
| B. | G.P. |
| C. | H.P. |
| D. | None of these |
| Answer» E. | |
| 2036. |
The numbers \[(\sqrt{2}+1),\ 1,\ (\sqrt{2}-1)\] will be in [AMU 1983] |
| A. | A.P. |
| B. | G.P. |
| C. | H.P. |
| D. | None of these |
| Answer» C. H.P. | |
| 2037. |
In the four numbers first three are in G.P. and last three are in A.P. whose common difference is 6. If the first and last numbers are same, then first will be [IIT 1974] |
| A. | 2 |
| B. | 4 |
| C. | 6 |
| D. | 8 |
| Answer» E. | |
| 2038. |
If 9 A.M.'s and H.M.'s are inserted between the 2 and 3 and if the harmonic mean \[H\]is corresponding to arithmetic mean \[A\], then \[A+\frac{6}{H}=\] [ISM Dhanbad 1987] |
| A. | 1 |
| B. | 3 |
| C. | 5 |
| D. | 6 |
| Answer» D. 6 | |
| 2039. |
If the \[{{p}^{th}},\ {{q}^{th}}\] and \[{{r}^{th}}\]term of a G.P. and H.P. are \[a,\ b,\ c\], then \[a(b-c)\log a+b(c-a)\] \[\log b+c(a-b)\log c=\] [Dhanbad Engg. 1976] |
| A. | \[-1\] |
| B. | 0 |
| C. | 1 |
| D. | Does not exist |
| Answer» C. 1 | |
| 2040. |
\[x+y+z=15\] if \[9,\ x,\ y,\ z,\ a\] are in A.P.; while \[\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=\frac{5}{3}\] if \[9,\ x,\ y,\ z,\ a\] are in H.P., then the value of \[a\] will be [IIT 1978] |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 9 |
| Answer» B. 2 | |
| 2041. |
If the A.M. is twice the G.M. of the numbers \[a\] and \[b\], then \[a:b\]will be [Roorkee 1953] |
| A. | \[\frac{2-\sqrt{3}}{2+\sqrt{3}}\] |
| B. | \[\frac{2+\sqrt{3}}{2-\sqrt{3}}\] |
| C. | \[\frac{\sqrt{3}-2}{\sqrt{3}+2}\] |
| D. | \[\frac{\sqrt{3}+2}{\sqrt{3}-2}\] |
| Answer» C. \[\frac{\sqrt{3}-2}{\sqrt{3}+2}\] | |
| 2042. |
If G.M. = 18 and A.M. = 27, then H.M. is [RPET 1996] |
| A. | \[\frac{1}{18}\] |
| B. | \[\frac{1}{12}\] |
| C. | 12 |
| D. | \[9\sqrt{6}\] |
| Answer» D. \[9\sqrt{6}\] | |
| 2043. |
If the \[{{(m+1)}^{th}},\ {{(n+1)}^{th}}\] and \[{{(r+1)}^{th}}\] terms of an A.P. are in G.P. and \[m,\ n,\ r\] are in H.P., then the value of the ratio of the common difference to the first term of the A.P. is [MNR 1989; Roorkee 1994] |
| A. | \[-\frac{2}{n}\] |
| B. | \[\frac{2}{n}\] |
| C. | \[-\frac{n}{2}\] |
| D. | \[\frac{n}{2}\] |
| Answer» B. \[\frac{2}{n}\] | |
| 2044. |
If \[a,\ b,\ c\] are in A.P., then \[{{3}^{a}},\ {{3}^{b}},\ {{3}^{c}}\] shall be in [Pb. CET 1990] |
| A. | A.P. |
| B. | G.P. |
| C. | H.P. |
| D. | None of these |
| Answer» C. H.P. | |
| 2045. |
If \[{{A}_{1}},\ {{A}_{2}}\] are the two A.M.'s between two numbers \[a\]and \[b\]and \[{{G}_{1}},\ {{G}_{2}}\] be two G.M.'s between same two numbers, then \[\frac{{{A}_{1}}+{{A}_{2}}}{{{G}_{1}}.{{G}_{2}}}=\] [Roorkee 1983; DCE 1998] |
| A. | \[\frac{a+b}{ab}\] |
| B. | \[\frac{a+b}{2ab}\] |
| C. | \[\frac{2ab}{a+b}\] |
| D. | \[\frac{ab}{a+b}\] |
| Answer» B. \[\frac{a+b}{2ab}\] | |
| 2046. |
Given \[{{a}^{x}}={{b}^{y}}={{c}^{z}}={{d}^{u}}\] and \[a,\ b,\ c,\ d\] are in G.P., then \[x,y,z,u\] are in [ISM Dhanbad 1972; Roorkee 1984; RPET 2001] |
| A. | A.P. |
| B. | G.P. |
| C. | H.P. |
| D. | None of these |
| Answer» D. None of these | |
| 2047. |
If \[a,\ b,\ c\] are in G.P., \[a-b,\ c-a,\ b-c\]are in H.P., then \[a+4b+c\]is equal to |
| A. | 0 |
| B. | \[1\] |
| C. | \[-1\] |
| D. | None of these |
| Answer» B. \[1\] | |
| 2048. |
If \[a,\ b,\ c\]are in A.P., \[b,\ c,\ d\] are in G.P. and \[c,\ d,\ e\]are in H.P., then \[a,\ c,\ e\] are in [AMU 1988, 2001; MP PET 1993] |
| A. | No particular order |
| B. | A.P. |
| C. | G.P. |
| D. | H.P. |
| Answer» D. H.P. | |
| 2049. |
If three unequal non-zero real numbers \[a,\ b,\ c\]are in G.P. and \[b-c,\ c-a,\ a-b\]are in H.P., then the value of \[a+b+c\] is independent of |
| A. | \[a\] |
| B. | \[b\] |
| C. | \[c\] |
| D. | None of these |
| Answer» E. | |
| 2050. |
If \[a,\ b,\ c\] are in A.P. and \[|a|,\ |b|,\ |c|\ |
| A. | A.P. |
| B. | G.P. |
| C. | H.P. |
| D. | None of these |
| Answer» D. None of these | |