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.
| 1951. |
If the product of the roots of the equation \[(a+1){{x}^{2}}+(2a+3)x+(3a+4)=0\] be 2, then the sum of roots is |
| A. | 1 |
| B. | -1 |
| C. | 2 |
| D. | -2 |
| Answer» C. 2 | |
| 1952. |
If the roots of the equation \[a{{x}^{2}}+bx+c=0\] are reciprocal to each other, then [RPET 1985] |
| A. | \[a-c=0\] |
| B. | \[b-c=0\] |
| C. | \[a+c=0\] |
| D. | \[b+c=0\] |
| Answer» B. \[b-c=0\] | |
| 1953. |
If the roots of the equation \[\frac{1}{x+p}+\frac{1}{x+q}=\frac{1}{r}\] are equal in magnitude but opposite in sign, then the product of the roots will be [IIT 1967; RPET 1999] |
| A. | \[\frac{{{p}^{2}}+{{q}^{2}}}{2}\] |
| B. | -\[\frac{({{p}^{2}}+{{q}^{2}})}{2}\] |
| C. | \[\frac{{{p}^{2}}-{{q}^{2}}}{2}\] |
| D. | -\[\frac{({{p}^{2}}-{{q}^{2}})}{2}\] |
| Answer» C. \[\frac{{{p}^{2}}-{{q}^{2}}}{2}\] | |
| 1954. |
The quadratic equation with real coefficients whose one root is\[7+5i\], will be [RPET 1992] |
| A. | \[{{x}^{2}}-14x+74=0\] |
| B. | \[{{x}^{2}}+14x+74=0\] |
| C. | \[{{x}^{2}}-14x-74=0\] |
| D. | \[{{x}^{2}}+14x-74=0\] |
| Answer» B. \[{{x}^{2}}+14x+74=0\] | |
| 1955. |
If the sum of the roots of the quadratic equation \[a{{x}^{2}}+bx+c=0\] is equal to the sum of the squares of their reciprocals, then \[a/c,\,b/a,\,c/b\]are in [AIEEE 2003; DCE 2000] |
| A. | A.P. |
| B. | G.P. |
| C. | H.P. |
| D. | None of these |
| Answer» D. None of these | |
| 1956. |
If the difference of the roots of \[{{x}^{2}}-px+8=0\] be 2, then the value of p is [Roorkee 1992] |
| A. | \[\pm 2\] |
| B. | \[\pm 4\] |
| C. | \[\pm 6\] |
| D. | \[\pm 8\] |
| Answer» D. \[\pm 8\] | |
| 1957. |
The quadratic in \[t\], such that A.M. of its roots is \[A\] and G.M. is G, is [IIT 1968, 1974] |
| A. | \[{{t}^{2}}-2At+{{G}^{2}}=0\] |
| B. | \[{{t}^{2}}-2At-{{G}^{2}}=0\] |
| C. | \[{{t}^{2}}+2At+{{G}^{2}}=0\] |
| D. | None of these |
| Answer» B. \[{{t}^{2}}-2At-{{G}^{2}}=0\] | |
| 1958. |
If \[\alpha ,\beta \] be the roots of \[{{x}^{2}}-px+q=0\]and \[{\alpha }',{\beta }'\] be the roots of \[{{x}^{2}}-{p}'x+{q}'=0\], then the value of \[{{(\alpha -\alpha ')}^{2}}+{{(\beta -{\alpha }')}^{2}}+{{(a-{\beta }')}^{2}}+{{(\beta -{\beta }')}^{2}}\] is |
| A. | \[2\{{{p}^{2}}-2q+{{{p}'}^{2}}-2{q}'-p{p}'\}\] |
| B. | \[2\{{{p}^{2}}-2q+{{{p}'}^{2}}-2{q}'-q{q}'\}\] |
| C. | \[2\{{{p}^{2}}-2q-{{{p}'}^{2}}-2{q}'-p{p}'\}\] |
| D. | \[2\{{{p}^{2}}-2q-{{{p}'}^{2}}-2{q}'-q{q}'\}\] |
| Answer» B. \[2\{{{p}^{2}}-2q+{{{p}'}^{2}}-2{q}'-q{q}'\}\] | |
| 1959. |
If one root of \[a{{x}^{2}}+bx+c=0\] be square of the other, then the value of \[{{b}^{3}}+a{{c}^{2}}+{{a}^{2}}c\]is |
| A. | \[3abc\] |
| B. | \[-3abc\] |
| C. | 0 |
| D. | None of these |
| Answer» B. \[-3abc\] | |
| 1960. |
If \[\alpha ,\beta \] are the roots of \[{{x}^{2}}+px+1=0\] and \[\gamma ,\delta \]are the roots of \[{{x}^{2}}+qx+1=0\],then \[{{q}^{2}}-{{p}^{2}}\]= [IIT 1978; DCE 2000] |
| A. | \[(\alpha -\gamma )(\beta -\gamma )(\alpha +\delta )(\beta +\delta )\] |
| B. | \[(\alpha +\gamma )(\beta +\gamma )(\alpha -\delta )(\beta +\delta )\] |
| C. | \[(\alpha +\gamma )(\beta +\gamma )(\alpha +\delta )(\beta +\delta )\] |
| D. | None of these |
| Answer» B. \[(\alpha +\gamma )(\beta +\gamma )(\alpha -\delta )(\beta +\delta )\] | |
| 1961. |
If the roots of the equation \[\frac{\alpha }{x-\alpha }+\frac{\beta }{x-\beta }=1\] be equal in magnitude but opposite in sign, then \[\alpha +\beta \]= |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | None of these |
| Answer» B. 1 | |
| 1962. |
If the sum of the roots of the equation \[a{{x}^{2}}+bx+c=0\] be equal to the sum of their squares, then |
| A. | \[a(a+b)=2bc\] |
| B. | \[c(a+c)=2ab\] |
| C. | \[b(a+b)=2ac\] |
| D. | \[b(a+b)=ac\] |
| Answer» D. \[b(a+b)=ac\] | |
| 1963. |
If \[\alpha ,\ \beta \] are the roots of the equation \[a{{x}^{2}}+bx+c=0\], then \[\frac{\alpha }{a\beta +b}+\frac{\beta }{a\alpha +b}=\] |
| A. | \[\frac{2}{a}\] |
| B. | \[\frac{2}{b}\] |
| C. | \[\frac{2}{c}\] |
| D. | \[-\frac{2}{a}\] |
| Answer» E. | |
| 1964. |
If the ratio of the roots of the equation \[a{{x}^{2}}+bx+c=0\]be \[p:q\], then [Pb. CET 1994] |
| A. | \[pq{{b}^{2}}+{{(p+q)}^{2}}ac=0\] |
| B. | \[pq{{b}^{2}}-{{(p+q)}^{2}}ac=0\] |
| C. | \[pq{{a}^{2}}-{{(p+q)}^{2}}bc=0\] |
| D. | None of these |
| Answer» C. \[pq{{a}^{2}}-{{(p+q)}^{2}}bc=0\] | |
| 1965. |
If \[\alpha ,\beta \] be the roots of the equation \[2{{x}^{2}}-2({{m}^{2}}+1)x+{{m}^{4}}+{{m}^{2}}+1=0\], then \[{{\alpha }^{2}}+{{\beta }^{2}}\]= |
| A. | 0 |
| B. | 1 |
| C. | m |
| D. | \[{{m}^{2}}\] |
| Answer» E. | |
| 1966. |
If \[\alpha \] and \[\beta \] are the roots of the equation \[{{x}^{2}}-a(x+1)-b=0\] then \[(\alpha +1)(\beta +1)=\] |
| A. | b |
| B. | |
| C. | \[1-b\] |
| D. | \[b-1\] |
| Answer» D. \[b-1\] | |
| 1967. |
If \[\alpha \] and \[\beta \] are the roots of the equation \[2{{x}^{2}}-3x+4=0\], then the equation whose roots are \[{{\alpha }^{2}}\] and \[{{\beta }^{2}}\] is |
| A. | \[4{{x}^{2}}+7x+16=0\] |
| B. | \[4{{x}^{2}}+7x+6=0\] |
| C. | \[4{{x}^{2}}+7x+1=0\] |
| D. | \[4{{x}^{2}}-7x+16=0\] |
| Answer» B. \[4{{x}^{2}}+7x+6=0\] | |
| 1968. |
If \[3{{p}^{2}}=5p+2\] and \[3{{q}^{2}}=5q+2\] where \[p\ne q\], then the equation whose roots are \[3p-2q\] and \[3q-2p\] is [Kerala (Engg.) 2005] |
| A. | \[3{{x}^{2}}-5x-100=0\] |
| B. | \[5{{x}^{2}}+3x+100=0\] |
| C. | \[3{{x}^{2}}-5x+100=0\] |
| D. | \[5{{x}^{2}}-3x-100=0\] \[5{{x}^{2}}-3x-100=0\] |
| Answer» B. \[5{{x}^{2}}+3x+100=0\] | |
| 1969. |
\[2{{x}^{2}}-(p+1)x+(p-1)=0\]. If \[\alpha -\beta =\alpha \beta \], then what is the value of p [Orissa JEE 2005] |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | -2 |
| Answer» C. 3 | |
| 1970. |
If \[\alpha ,\beta \] are the roots of \[a{{x}^{2}}+bx+c=0\] and \[\alpha +\beta ,\] \[\,{{\alpha }^{2}}+{{\beta }^{2}},\] \[\,{{\alpha }^{3}}+{{\beta }^{3}}\] are in G.P., where \[\Delta ={{b}^{2}}-4ac\], then [IIT Screening 2005] |
| A. | \[\Delta \ne 0\] |
| B. | \[b\Delta =0\] |
| C. | \[cb\ne 0\] |
| D. | \[c\Delta =0\] |
| Answer» E. | |
| 1971. |
If one root of the equation \[{{x}^{2}}+px+q=0\]is the square of the other, then [IIT Screening 2004] |
| A. | \[{{p}^{3}}+{{q}^{2}}-q(3p+1)=0\] |
| B. | \[{{p}^{3}}+{{q}^{2}}+q(1+3p)=0\] |
| C. | \[{{p}^{3}}+{{q}^{2}}+q(3p-1)=0\] |
| D. | \[{{p}^{3}}+{{q}^{2}}+q(1-3p)=0\] |
| Answer» E. | |
| 1972. |
If one of the roots of equation \[{{x}^{2}}+ax+3=0\] is 3 and one of the roots of the equation \[{{x}^{2}}+ax+b=0\] is three times the other root, then the value of b is equal to [J & K 2005] |
| A. | 3 |
| B. | 4 |
| C. | 2 |
| D. | 1 |
| Answer» B. 4 | |
| 1973. |
If a and b are roots of \[{{x}^{2}}-px+q=0\], then \[\frac{1}{a}+\frac{1}{b}=\] [Orissa JEE 2004] |
| A. | \[\frac{1}{p}\] |
| B. | \[\frac{1}{q}\] |
| C. | \[\frac{1}{2p}\] |
| D. | \[\frac{p}{q}\] |
| Answer» E. | |
| 1974. |
Let two numbers have arithmetic mean 9 and geometric mean 4. Then these numbers are the roots of the quadratic equation [AIEEE 2004] |
| A. | \[{{x}^{2}}-18x-16=0\] |
| B. | \[{{x}^{2}}-18x+16=0\] |
| C. | \[{{x}^{2}}+18x-16=0\] |
| D. | \[{{x}^{2}}+18x+16=0\] |
| Answer» C. \[{{x}^{2}}+18x-16=0\] | |
| 1975. |
If one root of \[5{{x}^{2}}+13x+k=0\] is reciprocal of the other, then \[k\]= [MNR 1980, 1983] |
| A. | 0 |
| B. | 5 |
| C. | 44348 |
| D. | 6 |
| Answer» C. 44348 | |
| 1976. |
The mortality in a town during 4 quarters of a year due to various causes is given below: Based on this data, the percentage increase in mortality in the third quarter is |
| A. | 40 |
| B. | 50 |
| C. | 60 |
| D. | 75 |
| Answer» D. 75 | |
| 1977. |
The following data was collected from the newspaper : (percentage distribution) Country Agriculture Industry Services Others India 45 19 28 8 U.K. 3 40 44 13 Japan 6 48 43 3 U.S.A. 3 35 61 1 It is an example of |
| A. | Data given in text form |
| B. | Data given in diagrammatic form |
| C. | Primary data |
| D. | Secondary data |
| Answer» D. Secondary data | |
| 1978. |
Which of the following average is most affected of extreme observations [DCE 1995] |
| A. | Mode |
| B. | Median |
| C. | Arithmetic mean |
| D. | Geometric mean |
| Answer» D. Geometric mean | |
| 1979. |
The most stable measure of central tendency is [AMU 1994] |
| A. | Mean |
| B. | Median |
| C. | Mode |
| D. | None of these |
| Answer» B. Median | |
| 1980. |
If in a moderately asymmetrical distribution mode and mean of the data are 6l and 9l respectively, then median is [Pb. CET 1988] |
| A. | 8l |
| B. | 7l |
| C. | 6l |
| D. | 5l |
| Answer» B. 7l | |
| 1981. |
In a moderately asymmetrical distribution the mode and mean are 7 and 4 respectively. The median is |
| A. | 4 |
| B. | 5 |
| C. | 6 |
| D. | 7 |
| Answer» C. 6 | |
| 1982. |
If in a frequency distribution, the mean and median are 21 and 22 respectively, then its mode is approximately [AIEEE 2005] |
| A. | 25.5 |
| B. | 24.0 |
| C. | 22.0 |
| D. | 20.5 |
| Answer» C. 22.0 | |
| 1983. |
The expenditure of a family for a certain month were as follows: Food ? Rs.560, Rent ? Rs.420, Clothes ? Rs.180, Education ? Rs.160, Other items ? Rs.120 A pie graph representing this data would show the expenditure for clothes by a sector whose angle equals |
| A. | 180° |
| B. | 90° |
| C. | 45° |
| D. | 64° |
| Answer» D. 64° | |
| 1984. |
The total expenditure incurred by an industry under different heads is best presented as a [NDA 2000] |
| A. | Bar diagram |
| B. | Pie diagram |
| C. | Histogram |
| D. | Frequency polygon |
| Answer» C. Histogram | |
| 1985. |
If mean = (3 median ? mode) k, then the value of k is |
| A. | 1 |
| B. | 2 |
| C. | 1/2 |
| D. | 3/2 |
| Answer» D. 3/2 | |
| 1986. |
If A.M and G.M of x and y are in the ratio p : q, then x : y is [Kerala (Engg.) 2005] |
| A. | \[p-\sqrt{{{p}^{2}}+{{q}^{2}}}\]:\[p+\sqrt{{{p}^{2}}+{{q}^{2}}}\] |
| B. | \[p+\sqrt{{{p}^{2}}-{{q}^{2}}}\]:\[p-\sqrt{{{p}^{2}}-{{q}^{2}}}\] |
| C. | \[p:q\] |
| D. | \[p+\sqrt{{{p}^{2}}+{{q}^{2}}}\]:\[p-\sqrt{{{p}^{2}}+{{q}^{2}}}\] |
| E. | \[q+\sqrt{{{p}^{2}}-{{q}^{2}}}\]:\[q-\sqrt{{{p}^{2}}-{{q}^{2}}}\] |
| Answer» C. \[p:q\] | |
| 1987. |
If \[{{a}^{2}},\,{{b}^{2}},\,{{c}^{2}}\] be in A.P., then \[\frac{a}{b+c},\,\frac{b}{c+a},\,\frac{c}{a+b}\] will be in |
| A. | A.P. |
| B. | G.P. |
| C. | H.P. |
| D. | None of these |
| Answer» B. G.P. | |
| 1988. |
The harmonic mean between two numbers is and the geometric mean 24. The greater number them is [UPSEAT 2004] |
| A. | 72 |
| B. | 54 |
| C. | 36 |
| D. | None of these |
| Answer» B. 54 | |
| 1989. |
When \[\frac{1}{a}+\frac{1}{c}+\frac{1}{a-b}+\frac{1}{c-d}=0\] and \[b\ne a\ne c\], then \[a,\ b,\ c\] are [MP PET 2004] |
| A. | In H.P. |
| B. | In G.P. |
| C. | In A.P. |
| D. | None of these |
| Answer» B. In G.P. | |
| 1990. |
If arithmetic mean of two positive numbers is \[A\], their geometric mean is \[G\] and harmonic mean is \[H\], then \[H\]is equal to [MP PET 2004] |
| A. | \[1.2+2.3+3.4+4.5+.........\] |
| B. | \[\frac{G}{{{A}^{2}}}\] |
| C. | \[\frac{{{A}^{2}}}{G}\] |
| D. | \[\frac{A}{{{G}^{2}}}\] |
| Answer» B. \[\frac{G}{{{A}^{2}}}\] | |
| 1991. |
If the arithmetic and geometric means of a and b be \[A\] and \[G\] respectively, then the value of \[A-G\] will be |
| A. | \[\frac{a-b}{a}\] |
| B. | \[\frac{a+b}{2}\] |
| C. | \[{{\left[ \frac{\sqrt{a}-\sqrt{b}}{\sqrt{2}} \right]}^{2}}\] |
| D. | \[\frac{2ab}{a+b}\] |
| Answer» D. \[\frac{2ab}{a+b}\] | |
| 1992. |
If \[(y-x),\,\,2(y-a)\] and \[(y-z)\] are in H.P., then \[x-a,\] \[y-a,\] \[z-a\] are in [RPET 2001] |
| A. | A.P. |
| B. | G.P. |
| C. | H.P. |
| D. | None of these |
| Answer» C. H.P. | |
| 1993. |
If \[a,\,b,\,c\] are in A.P. and \[{{a}^{2}},\,{{b}^{2}},{{c}^{2}}\]are in H.P., then [UPSEAT 2001] |
| A. | \[a\ne b\ne c\] |
| B. | \[{{a}^{2}}={{b}^{2}}=\frac{{{c}^{2}}}{2}\] |
| C. | \[a,\,b,\,c\] are in G.P. |
| D. | \[\frac{-a}{2},b,c\]are in G.P |
| Answer» E. | |
| 1994. |
If \[a,b,c\]are in G.P. then \[{{\log }_{a}}x,{{\log }_{b}}x,{{\log }_{c}}x\] are in [RPET 2002] |
| A. | A.P. |
| B. | G.P. |
| C. | H.P. |
| D. | None of these |
| Answer» D. None of these | |
| 1995. |
If the altitudes of a triangle are in A.P., then the sides of the triangle are in [EAMCET 2002] |
| A. | A.P. |
| B. | H.P. |
| C. | G.P. |
| D. | Arithmetico-geometric progression |
| Answer» C. G.P. | |
| 1996. |
If A is the A.M. of the roots of the equation \[{{x}^{2}}-2ax+b=0\] and \[G\] is the G.M. of the roots of the equation \[{{x}^{2}}-2bx+{{a}^{2}}=0,\] then [UPSEAT 2001] |
| A. | \[A>G\] |
| B. | \[A\ne G\] |
| C. | \[A=G\] |
| D. | None of these |
| Answer» D. None of these | |
| 1997. |
If A and G are arithmetic and geometric means and \[{{x}^{2}}-2Ax+{{G}^{2}}=0\], then [UPSEAT 2001] |
| A. | \[A=G\] |
| B. | \[A>G\] |
| C. | \[A<G\] |
| D. | \[A=-\,G\] |
| Answer» C. \[A<G\] | |
| 1998. |
If \[\frac{a}{b},\frac{b}{c},\frac{c}{a}\] are in H.P., then [UPSEAT 2002] |
| A. | \[{{a}^{2}}b,\,{{c}^{2}}a,\,{{b}^{2}}c\] are in A.P. |
| B. | \[{{a}^{2}}b,\,{{b}^{2}}c,\,{{c}^{2}}a\]are in H.P. |
| C. | \[{{a}^{2}}b,\,{{b}^{2}}c,\,{{c}^{2}}a\]are in G.P. |
| D. | None of these |
| Answer» B. \[{{a}^{2}}b,\,{{b}^{2}}c,\,{{c}^{2}}a\]are in H.P. | |
| 1999. |
If \[b+c,\] \[c+a,\] \[a+b\] are in H.P., then \[\frac{a}{b+c},\frac{b}{c+a},\frac{c}{a+b}\] are in [RPET 2000] |
| A. | A.P. |
| B. | G.P. |
| C. | H.P. |
| D. | None of these |
| Answer» B. G.P. | |
| 2000. |
If \[{{p}^{th}},\ {{q}^{th}},\ {{r}^{th}}\] and \[{{s}^{th}}\] terms of an A.P. be in G.P., then \[(p-q),\ (q-r),\ (r-s)\] will be in [MP PET 1993] |
| A. | G.P. |
| B. | A.P. |
| C. | H.P. |
| D. | None of these |
| Answer» B. A.P. | |