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.
| 4601. |
The G.M. of the numbers \[3,\,{{3}^{2}},\,{{3}^{3}},....,\,{{3}^{n}}\] is [DCE 2002] |
| A. | \[{{3}^{\frac{2}{n}}}\] |
| B. | \[{{3}^{\frac{n+1}{2}}}\] |
| C. | \[{{3}^{\frac{n}{2}}}\] |
| D. | \[{{3}^{\frac{n-1}{2}}}\] |
| Answer» C. \[{{3}^{\frac{n}{2}}}\] | |
| 4602. |
The number which should be added to the numbers 2, 14, 62 so that the resulting numbers may be in G.P., is |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 4 |
| Answer» C. 3 | |
| 4603. |
If five G.M.?s are inserted between 486 and 2/3 then fourth G.M. will be [RPET 1999] |
| A. | 4 |
| B. | 6 |
| C. | 12 |
| D. | -6 |
| Answer» C. 12 | |
| 4604. |
If three geometric means be inserted between 2 and 32, then the third geometric mean will be |
| A. | 8 |
| B. | 4 |
| C. | 16 |
| D. | 12 |
| Answer» D. 12 | |
| 4605. |
If \[G\] be the geometric mean of \[x\] and \[y\], then \[\frac{1}{{{G}^{2}}-{{x}^{2}}}+\frac{1}{{{G}^{2}}-{{y}^{2}}}=\] |
| A. | \[{{G}^{2}}\] |
| B. | \[\frac{1}{{{G}^{2}}}\] |
| C. | \[\frac{2}{{{G}^{2}}}\] |
| D. | \[3{{G}^{2}}\] |
| Answer» C. \[\frac{2}{{{G}^{2}}}\] | |
| 4606. |
If the geometric mean between \[a\] and \[b\] is \[\frac{{{a}^{n+1}}+{{b}^{n+1}}}{{{a}^{n}}+{{b}^{n}}}\], then the value of n is |
| A. | 1 |
| B. | -0.5 |
| C. | 44228 |
| D. | 2 |
| Answer» C. 44228 | |
| 4607. |
If \[n\] geometric means be inserted between \[a\] and \[b\]then the \[{{n}^{th}}\] geometric mean will be |
| A. | \[a\,{{\left( \frac{b}{a} \right)}^{\frac{n}{n-1}}}\] |
| B. | \[a\,{{\left( \frac{b}{a} \right)}^{\frac{n-1}{n}}}\] |
| C. | \[a\,{{\left( \frac{b}{a} \right)}^{\frac{n}{n+1}}}\] |
| D. | \[a\,{{\left( \frac{b}{a} \right)}^{\frac{1}{n}}}\] |
| Answer» D. \[a\,{{\left( \frac{b}{a} \right)}^{\frac{1}{n}}}\] | |
| 4608. |
The first term of a G.P. is 7, the last term is 448 and sum of all terms is 889, then the common ratio is [MP PET 2003] |
| A. | 5 |
| B. | 4 |
| C. | 3 |
| D. | 2 |
| Answer» E. | |
| 4609. |
Three numbers are in G.P. such that their sum is 38 and their product is 1728. The greatest number among them is [UPSEAT 2004] |
| A. | 18 |
| B. | 16 |
| C. | 14 |
| D. | None of these |
| Answer» B. 16 | |
| 4610. |
The sum of the series \[3+33+333+...+n\] terms is [RPET 2000] |
| A. | \[\frac{1}{27}({{10}^{n+1}}+9n-28)\] |
| B. | \[\frac{1}{27}({{10}^{n+1}}-9n-10)\] |
| C. | \[\frac{1}{27}({{10}^{n+1}}+10n-9)\] |
| D. | None of these |
| Answer» C. \[\frac{1}{27}({{10}^{n+1}}+10n-9)\] | |
| 4611. |
The product of \[n\] positive numbers is unity. Their sum is [MP PET 2000] |
| A. | A positive integer |
| B. | Equal to \[n+\frac{1}{n}\] |
| C. | Divisible by \[n\] |
| D. | Never less than |
| Answer» E. | |
| 4612. |
If the first term of a G.P. be 5 and common ratio be \[-5\], then which term is 3125 |
| A. | \[{{6}^{th}}\] |
| B. | \[{{5}^{th}}\] |
| C. | \[{{7}^{th}}\] |
| D. | \[{{8}^{th}}\] |
| Answer» C. \[{{7}^{th}}\] | |
| 4613. |
If in a geometric progression \[\left\{ {{a}_{n}} \right\},\ {{a}_{1}}=3,\ {{a}_{n}}=96\] and \[{{S}_{n}}=189\] then the value of \[n\] is |
| A. | 5 |
| B. | 6 |
| C. | 7 |
| D. | 8 |
| Answer» C. 7 | |
| 4614. |
The solution of the equation \[1+a+{{a}^{2}}+{{a}^{3}}+.......+{{a}^{x}}\] \[=(1+a)(1+{{a}^{2}})(1+{{a}^{4}})\] is given by \[x\] is equal to |
| A. | 3 |
| B. | 5 |
| C. | 7 |
| D. | None of these |
| Answer» D. None of these | |
| 4615. |
For a sequence \[,\ {{a}_{1}}=2\] and \[\frac{{{a}_{n+1}}}{{{a}_{n}}}=\frac{1}{3}\]. Then \[\sum\limits_{r=1}^{20}{{{a}_{r}}}\] is |
| A. | \[\frac{20}{2}[4+19\times 3]\] |
| B. | \[3\left( 1-\frac{1}{{{3}^{20}}} \right)\] |
| C. | \[2(1-{{3}^{20}})\] |
| D. | None of these |
| Answer» C. \[2(1-{{3}^{20}})\] | |
| 4616. |
The number \[111..............1\] (91 times) is a |
| A. | Even number |
| B. | Prime number |
| C. | Not prime |
| D. | None of these |
| Answer» D. None of these | |
| 4617. |
The sum of \[n\] terms of the following series \[1+(1+x)+(1+x+{{x}^{2}})+..........\]will be [IIT 1962] |
| A. | \[\frac{1-{{x}^{n}}}{1-x}\] |
| B. | \[\frac{x(1-{{x}^{n}})}{1-x}\] |
| C. | \[\frac{n(1-x)-x(1-{{x}^{n}})}{{{(1-x)}^{2}}}\] |
| D. | None of these |
| Answer» D. None of these | |
| 4618. |
If the sum of first 6 term is 9 times to the sum of first 3 terms of the same G.P., then the common ratio of the series will be [RPET 1985] |
| A. | \[-2\] |
| B. | 2 |
| C. | 1 |
| D. | 44228 |
| Answer» C. 1 | |
| 4619. |
If the sum of \[n\] terms of a G.P. is 255 and \[{{n}^{th}}\]terms is 128 and common ratio is 2, then first term will be [RPET 1990] |
| A. | 1 |
| B. | 3 |
| C. | 7 |
| D. | None of these |
| Answer» B. 3 | |
| 4620. |
If every term of a G.P. with positive terms is the sum of its two previous terms, then the common ratio of the series is [RPET 1986] |
| A. | 1 |
| B. | \[\frac{2}{\sqrt{5}}\] |
| C. | \[\frac{\sqrt{5}-1}{2}\] |
| D. | \[\frac{\sqrt{5}+1}{2}\] |
| Answer» E. | |
| 4621. |
If the \[{{4}^{th}},\ {{7}^{th}}\] and \[{{10}^{th}}\] terms of a G.P. be \[a,\ b,\ c\] respectively, then the relation between \[a,\ b,\ c\] is [MNR 1995; Karnataka CET 1999] |
| A. | \[b=\frac{a+c}{2}\] |
| B. | \[{{a}^{2}}=bc\] |
| C. | \[{{b}^{2}}=ac\] |
| D. | \[{{c}^{2}}=ab\] |
| Answer» D. \[{{c}^{2}}=ab\] | |
| 4622. |
The sum of the series \[6+66+666+..........\]upto \[n\] terms is [IIT 1974] |
| A. | \[({{10}^{n-1}}-9n+10)/81\] |
| B. | \[2({{10}^{n+1}}-9n-10)/27\] |
| C. | \[2({{10}^{n}}-9n-10)/27\] |
| D. | None of these |
| Answer» C. \[2({{10}^{n}}-9n-10)/27\] | |
| 4623. |
The value of \[0.\overset{\,\,\,\,\,\,\bullet \,\,\,\,\bullet \,\,\,}{\mathop{234}}\,\] is [MNR 1986; UPSEAT 2000] |
| A. | \[\frac{232}{990}\] |
| B. | \[\frac{232}{9990}\] |
| C. | \[\frac{232}{990}\] |
| D. | \[\frac{232}{9909}\] |
| Answer» B. \[\frac{232}{9990}\] | |
| 4624. |
The sum of 100 terms of the series \[.9+.09+.009.........\]will be |
| A. | \[1-{{\left( \frac{1}{10} \right)}^{100}}\] |
| B. | \[1+{{\left( \frac{1}{10} \right)}^{100}}\] |
| C. | \[\]\[1-{{\left( \frac{1}{10} \right)}^{106}}\] |
| D. | \[1+{{\left( \frac{1}{10} \right)}^{100}}\] |
| Answer» B. \[1+{{\left( \frac{1}{10} \right)}^{100}}\] | |
| 4625. |
The sum of the first five terms of the series \[3+4\frac{1}{2}+6\frac{3}{4}+......\] will be |
| A. | \[39\frac{9}{16}\] |
| B. | \[18\frac{3}{16}\] |
| C. | \[39\frac{7}{16}\] |
| D. | \[13\frac{9}{16}\] |
| Answer» B. \[18\frac{3}{16}\] | |
| 4626. |
If the sum of an infinite G.P. be 9 and the sum of first two terms be 5, then the common ratio is |
| A. | 44256 |
| B. | 44230 |
| C. | 44289 |
| D. | 44257 |
| Answer» E. | |
| 4627. |
Fifth term of a G.P. is 2, then the product of its 9 terms is [Pb. CET 1990, 94; AIEEE 2002] |
| A. | 256 |
| B. | 512 |
| C. | 1024 |
| D. | None of these |
| Answer» C. 1024 | |
| 4628. |
The third term of a G.P. is the square of first term. If the second term is 8, then the \[{{6}^{th}}\] term is [MP PET 1997] |
| A. | 120 |
| B. | 124 |
| C. | 128 |
| D. | 132 |
| Answer» D. 132 | |
| 4629. |
If the nth term of geometric progression \[5,-\frac{5}{2},\frac{5}{4},-\frac{5}{8},...\] is \[\frac{5}{1024}\], then the value of n is [Kerala (Engg.) 2002] |
| A. | 11 |
| B. | 10 |
| C. | 9 |
| D. | 4 |
| Answer» B. 10 | |
| 4630. |
\[{{7}^{th}}\] term of the sequence \[\sqrt{2},\ \sqrt{10},\ 5\sqrt{2},\ .......\]is |
| A. | \[125\sqrt{10}\] |
| B. | \[25\sqrt{2}\] |
| C. | 125 |
| D. | \[125\sqrt{2}\] |
| Answer» E. | |
| 4631. |
If the \[{{10}^{th}}\] term of a geometric progression is 9 and \[{{4}^{th}}\] term is 4, then its \[{{7}^{th}}\] term is [MP PET 1996] |
| A. | 6 |
| B. | 36 |
| C. | \[\frac{4}{9}\] |
| D. | \[\frac{9}{4}\] |
| Answer» B. 36 | |
| 4632. |
If the roots of the cubic equation \[a{{x}^{3}}+b{{x}^{2}}+cx+d=0\] are in G.P., then |
| A. | \[{{c}^{3}}a={{b}^{3}}d\] |
| B. | \[c{{a}^{3}}=b{{d}^{3}}\] |
| C. | \[{{a}^{3}}b={{c}^{3}}d\] |
| D. | \[a{{b}^{3}}=c{{d}^{3}}\] |
| Answer» B. \[c{{a}^{3}}=b{{d}^{3}}\] | |
| 4633. |
If \[{{\log }_{x}}a,\ {{a}^{x/2}}\] and \[{{\log }_{b}}x\] are in G.P., then \[x=\] |
| A. | \[-\log ({{\log }_{b}}a)\] |
| B. | \[-{{\log }_{a}}({{\log }_{a}}b)\] |
| C. | \[{{\log }_{a}}({{\log }_{e}}a)-{{\log }_{a}}({{\log }_{e}}b)\] |
| D. | \[{{\log }_{a}}({{\log }_{e}}b)-{{\log }_{a}}({{\log }_{e}}a)\] |
| Answer» D. \[{{\log }_{a}}({{\log }_{e}}b)-{{\log }_{a}}({{\log }_{e}}a)\] | |
| 4634. |
The first and last terms of a G.P. are \[a\] and \[l\] respectively; \[r\] being its common ratio; then the number of terms in this G.P. is |
| A. | \[\frac{\log l-\log a}{\log r}\] |
| B. | \[1-\frac{\log l-\log a}{\log r}\] |
| C. | \[\frac{\log a-\log l}{\log r}\] |
| D. | \[1+\frac{\log l-\log a}{\log r}\] |
| Answer» E. | |
| 4635. |
The \[{{20}^{th}}\] term of the series \[2\times 4+4\times 6+6\times 8+.......\]will be [Pb. CET 1988] |
| A. | 1600 |
| B. | 1680 |
| C. | 420 |
| D. | 840 |
| Answer» C. 420 | |
| 4636. |
If the \[{{5}^{th}}\] term of a G.P. is \[\frac{1}{3}\] and \[{{9}^{th}}\] term is \[\frac{16}{243}\], then the \[{{4}^{th}}\] term will be [MP PET 1982] |
| A. | \[\frac{3}{4}\] |
| B. | \[\frac{1}{2}\] |
| C. | \[\frac{1}{3}\] |
| D. | \[\frac{2}{5}\] |
| Answer» C. \[\frac{1}{3}\] | |
| 4637. |
If the \[{{p}^{th}}\],\[{{q}^{th}}\] and \[{{r}^{th}}\]term of a G.P. are \[a,\ b,\ c\] respectively, then \[{{a}^{q-r}}.\ {{b}^{r-p}}.\ {{c}^{p-q}}\] is equal to [Roorkee 1955, 63, 73; Pb. CET 1991, 95] |
| A. | 0 |
| B. | 1 |
| C. | \[abc\] |
| D. | \[pqr\] |
| Answer» C. \[abc\] | |
| 4638. |
If \[x,\ y,\ z\] are in G.P. and \[{{a}^{x}}={{b}^{y}}={{c}^{z}}\], then [IIT 1966, 68] |
| A. | \[{{\log }_{a}}c={{\log }_{b}}a\] |
| B. | \[{{\log }_{b}}a={{\log }_{c}}b\] |
| C. | \[{{\log }_{c}}b={{\log }_{a}}c\] |
| D. | None of these |
| Answer» C. \[{{\log }_{c}}b={{\log }_{a}}c\] | |
| 4639. |
If \[a,\,b,\,c\] are in G.P., then |
| A. | \[a({{b}^{2}}+{{a}^{2}})=c({{b}^{2}}+{{c}^{2}})\] |
| B. | \[a({{b}^{2}}+{{c}^{2}})=c({{a}^{2}}+{{b}^{2}})\] |
| C. | \[{{a}^{2}}(b+c)={{c}^{2}}(a+b)\] |
| D. | None of these |
| Answer» C. \[{{a}^{2}}(b+c)={{c}^{2}}(a+b)\] | |
| 4640. |
If the \[{{(r+1)}^{th}}\] term in the expansion of \[{{\left( \sqrt[3]{\frac{a}{\sqrt{b}}}+\sqrt{\frac{b}{\sqrt[3]{a}}} \right)}^{21}}\] has the same power of a and b, then the value of r is |
| A. | 9 |
| B. | 10 |
| C. | 8 |
| D. | 6 |
| Answer» B. 10 | |
| 4641. |
The middle term in the expression of \[{{\left( x-\frac{1}{x} \right)}^{18}}\] is [Karnataka CET 2005] |
| A. | \[^{18}{{C}_{9}}\] |
| B. | \[{{-}^{18}}{{C}_{9}}\] |
| C. | \[^{18}{{C}_{0}}\] |
| D. | \[{{-}^{18}}{{C}_{10}}\] |
| Answer» C. \[^{18}{{C}_{0}}\] | |
| 4642. |
The middle term in the expansion of \[{{\left( x+\frac{1}{2x} \right)}^{2n}}\], is [MP PET 1995] |
| A. | \[\frac{1.3.5....(2n-3)}{n!}\] |
| B. | \[\frac{1.3.5....(2n-1)}{n!}\] |
| C. | \[\frac{1.3.5....(2n+1)}{n!}\] |
| D. | None of these |
| Answer» C. \[\frac{1.3.5....(2n+1)}{n!}\] | |
| 4643. |
The coefficient of \[{{x}^{n}}\]in expansion of \[(1+x)\,{{(1-x)}^{n}}\] is [AIEEE 2004] |
| A. | \[{{(-1)}^{n-1}}n\] |
| B. | \[{{(-1)}^{n}}(1-n)\] |
| C. | \[{{(-1)}^{n-1}}{{(n-1)}^{2}}\] |
| D. | \[(n-1)\] |
| Answer» C. \[{{(-1)}^{n-1}}{{(n-1)}^{2}}\] | |
| 4644. |
The coefficient of \[{{t}^{24}}\] in the expansion of \[{{(1+{{t}^{2}})}^{12}}(1+{{t}^{12}})\,(1+{{t}^{24}})\] is [IIT Screening 2003] |
| A. | \[^{12}{{C}_{6}}+2\] |
| B. | \[^{12}{{C}_{5}}\] |
| C. | \[^{12}{{C}_{6}}\] |
| D. | \[^{12}{{C}_{7}}\] |
| Answer» B. \[^{12}{{C}_{5}}\] | |
| 4645. |
The coefficient of \[{{x}^{4}}\] in the expansion of \[{{(1+x+{{x}^{2}}+{{x}^{3}})}^{n}}\] is [MNR 1993; RPET 2001; DCE 1998] |
| A. | \[^{n}{{C}_{4}}\] |
| B. | \[^{n}{{C}_{4}}{{+}^{n}}{{C}_{2}}\] |
| C. | \[^{n}{{C}_{4}}+{{\,}^{n}}{{C}_{2}}+\,{{\,}^{n}}{{C}_{4}}{{.}^{n}}{{C}_{2}}\] |
| D. | \[^{n}{{C}_{4}}+{{\,}^{n}}{{C}_{2}}+{{\,}^{n}}{{C}_{1}}.{{\,}^{n}}{{C}_{2}}\] |
| Answer» E. | |
| 4646. |
If coefficient of \[{{(2r+3)}^{th}}\] and \[{{(r-1)}^{th}}\] terms in the expansion of \[{{(1+x)}^{15}}\] are equal, then value of r is [RPET 1995, 2003; UPSEAT 2001] |
| A. | 5 |
| B. | 6 |
| C. | 4 |
| D. | 3 |
| Answer» B. 6 | |
| 4647. |
The greatest coefficient in the expansion of \[{{(1+x)}^{2n+1}}\] is [RPET 1997] |
| A. | \[\frac{(2n+1)\,!}{n!(n+1)!}\] |
| B. | \[\frac{(2n+2)!}{n!(n+1)!}\] |
| C. | \[\frac{(2n+1)!}{{{[(n+1)!]}^{2}}}\] |
| D. | \[\frac{(2n)!}{{{(n!)}^{2}}}\] |
| Answer» B. \[\frac{(2n+2)!}{n!(n+1)!}\] | |
| 4648. |
The interval in which x must lie so that the greatest term in the expansion of \[{{(1+x)}^{2n}}\]has the greatest coefficient, is |
| A. | \[\left( \frac{n-1}{n},\frac{n}{n-1} \right)\] |
| B. | \[\left( \frac{n}{n+1},\frac{n+1}{n} \right)\] |
| C. | \[\left( \frac{n}{n+2},\frac{n+2}{n} \right)\] |
| D. | None of these |
| Answer» C. \[\left( \frac{n}{n+2},\frac{n+2}{n} \right)\] | |
| 4649. |
If n is even positive integer, then the condition that the greatest term in the expansion of \[{{(1+x)}^{n}}\]may have the greatest coefficient also, is |
| A. | \[\frac{n}{n+2}<x<\frac{n+2}{n}\] |
| B. | \[\frac{n+1}{n}<x<\frac{n}{n+1}\] |
| C. | \[\frac{n}{n+4}<x<\frac{n+4}{4}\] |
| D. | None of these |
| Answer» B. \[\frac{n+1}{n}<x<\frac{n}{n+1}\] | |
| 4650. |
The greatest term in the expansion of \[\sqrt{3}{{\left( 1+\frac{1}{\sqrt{3}} \right)}^{20}}\]is |
| A. | \[\frac{25840}{9}\] |
| B. | \[\frac{24840}{9}\] |
| C. | \[\frac{26840}{9}\] |
| D. | None of these |
| Answer» B. \[\frac{24840}{9}\] | |