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.
| 4551. |
A polygon has 35 diagonals, then the number of its sides is [AMU 2002] |
| A. | 8 |
| B. | 9 |
| C. | 10 |
| D. | 11 |
| Answer» D. 11 | |
| 4552. |
Given six line segments of lengths 2, 3, 4, 5, 6, 7 units, the number of triangles that can be formed by these lines is [AMU 2002] |
| A. | \[^{6}{{C}_{3}}-7\] |
| B. | \[^{6}{{C}_{3}}-6\] |
| C. | \[^{6}{{C}_{3}}-5\] |
| D. | \[^{6}{{C}_{3}}-4\] |
| Answer» C. \[^{6}{{C}_{3}}-5\] | |
| 4553. |
There are n points in a plane of which p points are collinear. How many lines can be formed from these points [Karnataka CET 2002] |
| A. | \[^{(n-p)}{{C}_{2}}\] |
| B. | \[^{n}{{C}_{2}}-{{\,}^{p}}{{C}_{2}}\] |
| C. | \[^{n}{{C}_{2}}-{{\,}^{p}}{{C}_{2}}+1\] |
| D. | \[^{n}{{C}_{2}}-{{\,}^{p}}{{C}_{2}}-1\] |
| Answer» D. \[^{n}{{C}_{2}}-{{\,}^{p}}{{C}_{2}}-1\] | |
| 4554. |
Out of 10 points in a plane 6 are in a straight line. The number of triangles formed by joining these points are [RPET 2000] |
| A. | 100 |
| B. | 150 |
| C. | 120 |
| D. | None of these |
| Answer» B. 150 | |
| 4555. |
Let \[{{T}_{n}}\] denote the number of triangles which can be formed using the vertices of a regular polygon of \[n\] sides. If \[{{T}_{n+1}}-{{T}_{n}}=21,\] then \[n\] equals [IIT Screening 2001] |
| A. | 5 |
| B. | 7 |
| C. | 6 |
| D. | 4 |
| Answer» C. 6 | |
| 4556. |
The number of diagonals in a octagon will be [MP PET 1984; Pb. CET 1989, 2000] |
| A. | 28 |
| B. | 20 |
| C. | 10 |
| D. | 16 |
| Answer» C. 10 | |
| 4557. |
There are 16 points in a plane, no three of which are in a straight line except 8 which are all in a straight line. The number of triangles that can be formed by joining them equals [Kurukshetra CEE 1996, 1998] |
| A. | 504 |
| B. | 552 |
| C. | 560 |
| D. | 1120 |
| Answer» B. 552 | |
| 4558. |
The greatest possible number of points of intersection of 8 straight lines and 4 circles is |
| A. | 32 |
| B. | 64 |
| C. | 76 |
| D. | 104 |
| Answer» E. | |
| 4559. |
A parallelogram is cut by two sets of \[m\] lines parallel to its sides. The number of parallelograms thus formed is [Karnataka CET 1992] |
| A. | \[{{{{(}^{m}}{{C}_{2}})}^{2}}\] |
| B. | \[{{\left( ^{m+1}{{C}_{2}} \right)}^{2}}\] |
| C. | \[{{\left( ^{m+2}{{C}_{2}} \right)}^{2}}\] |
| D. | None of these |
| Answer» D. None of these | |
| 4560. |
There are \[n\] straight lines in a plane, no two of which are parallel and no three pass through the same point. Their points of intersection are joined. Then the number of fresh lines thus obtained is |
| A. | \[\frac{n(n-1)(n-2)}{8}\] |
| B. | \[\frac{n(n-1)(n-2)(n-3)}{6}\] |
| C. | \[\frac{n(n-1)(n-2)(n-3)}{8}\] |
| D. | None of these |
| Answer» D. None of these | |
| 4561. |
There are \[m\] points on a straight line \[AB\] and \[n\] points on another line \[AC\], none of them being the point \[A\]. Triangles are formed from these points as vertices when (i) \[A\]is excluded (ii) \[A\] is included. Then the ratio of the number of triangles in the two cases is |
| A. | \[\frac{m+n-2}{m+n}\] |
| B. | \[\frac{m+n-2}{2}\] |
| C. | \[\frac{m+n-2}{m+n+2}\] |
| D. | None of these |
| Answer» B. \[\frac{m+n-2}{2}\] | |
| 4562. |
Six points in a plane be joined in all possible ways by indefinite straight lines, and if no two of them be coincident or parallel, and no three pass through the same point (with the exception of the original 6 points). The number of distinct points of intersection is equal to |
| A. | 105 |
| B. | 45 |
| C. | 51 |
| D. | None of these |
| Answer» D. None of these | |
| 4563. |
The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is [WB JEE 1993; RPET 2001] |
| A. | 6 |
| B. | 18 |
| C. | 12 |
| D. | 9 |
| Answer» C. 12 | |
| 4564. |
The straight lines \[{{I}_{1}},\ {{I}_{2}},\ {{I}_{3}}\] are parallel and lie in the same plane. A total number of \[m\] points are taken on \[{{I}_{1}},\ n\] points on \[{{I}_{2}},\ k\] points on\[{{I}_{3}}\]. The maximum number of triangles formed with vertices at these points are [IIT Screening 1993; UPSEAT 2001] |
| A. | \[^{m+n+k}{{C}_{3}}\] |
| B. | \[^{m+n+k}{{C}_{3}}{{-}^{m}}{{C}_{3}}{{-}^{n}}{{C}_{3}}-{{}^{k}}{{C}_{3}}\] |
| C. | \[^{m}{{C}_{3}}{{+}^{n}}{{C}_{3}}{{+}^{k}}{{C}_{3}}\] |
| D. | None of these |
| Answer» C. \[^{m}{{C}_{3}}{{+}^{n}}{{C}_{3}}{{+}^{k}}{{C}_{3}}\] | |
| 4565. |
There are \[16\] points in a plane out of which 6 are collinear, then how many lines can be drawn by joining these points [RPET 1986; MP PET 1987] |
| A. | 106 |
| B. | 105 |
| C. | 60 |
| D. | 55 |
| Answer» B. 105 | |
| 4566. |
The number of triangles that can be formed by 5 points in a line and 3 points on a parallel line is |
| A. | \[^{8}{{C}_{3}}\] |
| B. | \[^{8}{{C}_{3}}{{-}^{5}}{{C}_{3}}\] |
| C. | \[^{8}{{C}_{3}}{{-}^{5}}{{C}_{3}}-1\] |
| D. | None of these |
| Answer» D. None of these | |
| 4567. |
If the ratio of the sum of first three terms and the sum of first six terms of a G.P. be 125 : 152, then the common ratio r is |
| A. | \[\frac{3}{5}\] |
| B. | \[\frac{5}{3}\] |
| C. | \[\frac{2}{3}\] |
| D. | \[\frac{3}{2}\] |
| Answer» B. \[\frac{5}{3}\] | |
| 4568. |
The product (32)(32) 1/6(32)1/36 ...... to \[\infty \] is [Kerala (Engg.) 2005] |
| A. | 16 |
| B. | 32 |
| C. | 64 |
| D. | 0 |
| E. | 62 |
| Answer» D. 0 | |
| 4569. |
The sum to infinity of the progression \[9-3+1-\frac{1}{3}+.....\] is [Karnataka CET 2005] |
| A. | 9 |
| B. | 44236 |
| C. | 44313 |
| D. | 44242 |
| Answer» D. 44242 | |
| 4570. |
If s is the sum of an infinite G.P., the first term a then the common ratio r given by [J & K 2005] |
| A. | \[\frac{a-s}{s}\] |
| B. | \[\frac{s-a}{s}\] |
| C. | \[\frac{a}{1-s}\] |
| D. | \[\frac{s-a}{a}\] |
| Answer» C. \[\frac{a}{1-s}\] | |
| 4571. |
If \[x\] is added to each of numbers 3, 9, 21 so that the resulting numbers may be in G.P., then the value of \[x\] will be [MP PET 1986] |
| A. | 3 |
| B. | \[\frac{1}{2}\] |
| C. | 2 |
| D. | \[\frac{1}{3}\] |
| Answer» B. \[\frac{1}{2}\] | |
| 4572. |
The value of \[\overline{0.037}\] where, \[\overline{.037}\] stands for the number 0.037037037........ is [MP PET 2004] |
| A. | \[\frac{37}{1000}\] |
| B. | \[\frac{1}{27}\] |
| C. | \[\frac{1}{37}\] |
| D. | \[\frac{37}{999}\] |
| Answer» E. | |
| 4573. |
If the sum of the series \[1+\frac{2}{x}+\frac{4}{{{x}^{2}}}+\frac{8}{{{x}^{3}}}+....\infty \] is a finite number, then [UPSEAT 2002] |
| A. | \[x>2\] |
| B. | \[x>-2\] |
| C. | \[x>\frac{1}{2}\] |
| D. | None of these |
| Answer» B. \[x>-2\] | |
| 4574. |
If in an infinite G.P. first term is equal to the twice of the sum of the remaining terms, then its common ratio is [RPET 2002] |
| A. | 1 |
| B. | 2 |
| C. | 44256 |
| D. | -0.333333333333333 |
| Answer» D. -0.333333333333333 | |
| 4575. |
If \[x,\,2x+2,\,3x+3,\]are in G.P., then the fourth term is [MNR 1981] |
| A. | 27 |
| B. | \[-27\] |
| C. | 13.5 |
| D. | \[-13.5\] |
| Answer» E. | |
| 4576. |
Sum of infinite number of terms in G.P. is 20 and sum of their square is 100. The common ratio of G.P. is [AIEEE 2002] |
| A. | 5 |
| B. | 44319 |
| C. | 44324 |
| D. | 44317 |
| Answer» C. 44324 | |
| 4577. |
The sum of infinite terms of the geometric progression \[\frac{\sqrt{2}+1}{\sqrt{2}-1},\frac{1}{2-\sqrt{2}},\frac{1}{2}.....\] is [Kerala (Engg.) 2002] |
| A. | \[\sqrt{2}{{(\sqrt{2}+1)}^{2}}\] |
| B. | \[{{(\sqrt{2}+1)}^{2}}\] |
| C. | \[5\sqrt{2}\] |
| D. | \[3\sqrt{2}+\sqrt{5}\] |
| Answer» B. \[{{(\sqrt{2}+1)}^{2}}\] | |
| 4578. |
If sum of infinite terms of a G.P. is 3 and sum of squares of its terms is 3, then its first term and common ratio are [RPET 1999] |
| A. | 3/2, 1/2 |
| B. | 1, 1/2 |
| C. | 3/2, 2 |
| D. | None of these |
| Answer» B. 1, 1/2 | |
| 4579. |
If \[y=x+{{x}^{2}}+{{x}^{3}}+.......\,\infty ,\,\text{then}\,\,x=\] [DCE 1999] |
| A. | \[\frac{y}{1+y}\] |
| B. | \[\frac{1-y}{y}\] |
| C. | \[\frac{y}{1-y}\] |
| D. | None of these |
| Answer» B. \[\frac{1-y}{y}\] | |
| 4580. |
The value of \[{{4}^{1/3}}{{.4}^{1/9}}{{.4}^{1/27}}...........\infty \] is [RPET 2003] |
| A. | 2 |
| B. | 3 |
| C. | 4 |
| D. | 9 |
| Answer» B. 3 | |
| 4581. |
Consider an infinite G.P. with first term a and common ratio r, its sum is 4 and the second term is 3/4, then [IIT Screening 2000; DCE 2001] |
| A. | \[a=\frac{7}{4},\,r=\frac{3}{7}\] |
| B. | \[a=\frac{3}{2},\,r=\frac{1}{2}\] |
| C. | \[a=2,\,r=\frac{3}{8}\] |
| D. | \[a=3,\,r=\frac{1}{4}\] |
| Answer» E. | |
| 4582. |
The sum of an infinite geometric series is 3. A series, which is formed by squares of its terms, have the sum also 3. First series will be [UPSEAT 1999] |
| A. | \[\frac{3}{2},\frac{3}{4},\frac{3}{8},\frac{3}{16},.....\] |
| B. | \[\frac{1}{2},\frac{1}{4},\frac{1}{8},\frac{1}{16},.....\] |
| C. | \[\frac{1}{3},\frac{1}{9},\frac{1}{27},\frac{1}{81},.....\] |
| D. | \[1,-\frac{1}{3},\,\frac{1}{{{3}^{2}}},-\frac{1}{{{3}^{3}}},.....\] |
| Answer» B. \[\frac{1}{2},\frac{1}{4},\frac{1}{8},\frac{1}{16},.....\] | |
| 4583. |
The sum of the series \[5.05+1.212+0.29088+...\,\infty \] is [AMU 2000] |
| A. | 6.93378 |
| B. | 6.87342 |
| C. | 6.74384 |
| D. | 6.64474 |
| Answer» E. | |
| 4584. |
0.14189189189?. can be expressed as a rational number [AMU 2000] |
| A. | \[\frac{7}{3700}\] |
| B. | \[\frac{7}{50}\] |
| C. | \[\frac{525}{111}\] |
| D. | \[\frac{21}{148}\] |
| Answer» E. | |
| 4585. |
The terms of a G.P. are positive. If each term is equal to the sum of two terms that follow it, then the common ratio is |
| A. | \[\frac{\sqrt{5}-1}{2}\] |
| B. | \[\frac{1-\sqrt{5}}{2}\] |
| C. | 1 |
| D. | \[2\sqrt{5}\] |
| Answer» B. \[\frac{1-\sqrt{5}}{2}\] | |
| 4586. |
If \[S\] is the sum to infinity of a G.P., whose first term is \[a\], then the sum of the first \[n\] terms is [UPSEAT 2002] |
| A. | \[S{{\left( 1-\frac{a}{S} \right)}^{n}}\] |
| B. | \[S\left[ 1-{{\left( 1-\frac{a}{S} \right)}^{n}} \right]\] |
| C. | \[a\left[ 1-{{\left( 1-\frac{a}{S} \right)}^{n}} \right]\] |
| D. | None of these |
| Answer» C. \[a\left[ 1-{{\left( 1-\frac{a}{S} \right)}^{n}} \right]\] | |
| 4587. |
The sum of infinite terms of a G.P. is and on squaring the each term of it, the sum will be , then the common ratio of this series is [RPET 1988] |
| A. | \[\frac{{{x}^{2}}-{{y}^{2}}}{{{x}^{2}}+{{y}^{2}}}\] |
| B. | \[\frac{{{x}^{2}}+{{y}^{2}}}{{{x}^{2}}-{{y}^{2}}}\] |
| C. | \[\frac{{{x}^{2}}-y}{{{x}^{2}}+y}\] |
| D. | \[\frac{{{x}^{2}}+y}{{{x}^{2}}-y}\] |
| Answer» D. \[\frac{{{x}^{2}}+y}{{{x}^{2}}-y}\] | |
| 4588. |
If the sum of an infinite G.P. and the sum of square of its terms is 3, then the common ratio of the first series is [Roorkee 1972] |
| A. | 1 |
| B. | \[\frac{1}{2}\] |
| C. | \[\frac{2}{3}\] |
| D. | \[\frac{3}{2}\] |
| Answer» C. \[\frac{2}{3}\] | |
| 4589. |
If \[y=x-{{x}^{2}}+{{x}^{3}}-{{x}^{4}}+......\infty \], then value of x will be [MNR 1975; RPET 1988; MP PET 2002] |
| A. | \[y+\frac{1}{y}\] |
| B. | \[\frac{y}{1+y}\] |
| C. | \[y-\frac{1}{y}\] |
| D. | \[\frac{y}{1-y}\] |
| Answer» E. | |
| 4590. |
\[0.\overset{\,\,\,\,\bullet \,\,\,\bullet \,}{\mathop{423}}\,=\] [Roorkee 1961; IIT 1973] |
| A. | \[\frac{419}{990}\] |
| B. | \[\frac{419}{999}\] |
| C. | \[\frac{417}{990}\] |
| D. | \[\frac{417}{999}\] |
| Answer» B. \[\frac{419}{999}\] | |
| 4591. |
If \[A=1+{{r}^{z}}+{{r}^{2z}}+{{r}^{3z}}+.......\infty \], then the value of r will be |
| A. | \[A{{(1-A)}^{z}}\] |
| B. | \[{{\left( \frac{A-1}{A} \right)}^{1/z}}\] |
| C. | \[{{\left( \frac{1}{A}-1 \right)}^{1/z}}\] |
| D. | \[A{{(1-A)}^{1/z}}\] |
| Answer» C. \[{{\left( \frac{1}{A}-1 \right)}^{1/z}}\] | |
| 4592. |
\[x=1+a+{{a}^{2}}+....\infty \,(a |
| A. | \[\frac{xy}{x+y-1}\] |
| B. | \[\frac{xy}{x+y+1}\] |
| C. | \[\frac{xy}{x-y-1}\] |
| D. | \[\frac{xy}{x-y+1}\] |
| Answer» B. \[\frac{xy}{x+y+1}\] | |
| 4593. |
The sum can be found of a infinite G.P. whose common ratio is \[r\] [AMU 1982] |
| A. | For all values of \[r\] |
| B. | For only positive value of \[r\] |
| C. | Only for \[0<r<1\] |
| D. | Only for \[-1<r<1(r\ne 0)\] |
| Answer» E. | |
| 4594. |
If \[{{(p+q)}^{th}}\] term of a G.P. be \[m\] and \[{{(p-q)}^{th}}\]term be \[n\], then the \[{{p}^{th}}\] term will be [RPET 1997; MP PET 1985, 99] |
| A. | \[m/n\] |
| B. | \[\sqrt{mn}\] |
| C. | \[mn\] |
| D. | 0 |
| Answer» C. \[mn\] | |
| 4595. |
If \[3+3\alpha +3{{\alpha }^{2}}+.........\infty =\frac{45}{8}\], then the value of \[\alpha \] will be [Pb. CET 1989] |
| A. | 15/23 |
| B. | 42186 |
| C. | 44415 |
| D. | 44392 |
| Answer» C. 44415 | |
| 4596. |
If the product of three consecutive terms of G.P. is 216 and the sum of product of pair-wise is 156, then the numbers will be [MNR 1978] |
| A. | 1, 3, 9 |
| B. | 2, 6, 18 |
| C. | 3, 9, 27 |
| D. | 2, 4, 8 |
| Answer» C. 3, 9, 27 | |
| 4597. |
The sum of 3 numbers in geometric progression is 38 and their product is 1728. The middle number is [MP PET 1994] |
| A. | 12 |
| B. | 8 |
| C. | 18 |
| D. | 6 |
| Answer» B. 8 | |
| 4598. |
If \[a,\ b,\ c\] are in G.P., then [RPET 1995] |
| A. | \[{{a}^{2}},\ {{b}^{2}},\ {{c}^{2}}\] are in G.P. |
| B. | \[{{a}^{2}}(b+c),\ {{c}^{2}}(a+b),\ {{b}^{2}}(a+c)\] are in G.P. |
| C. | \[\frac{a}{b+c},\ \frac{b}{c+a},\ \frac{c}{a+b}\] are in G.P. |
| D. | None of the above |
| Answer» B. \[{{a}^{2}}(b+c),\ {{c}^{2}}(a+b),\ {{b}^{2}}(a+c)\] are in G.P. | |
| 4599. |
The two geometric means between the number 1 and 64 are [Kerala (Engg.) 2002] |
| A. | 1 and 64 |
| B. | 4 and 16 |
| C. | 2 and 16 |
| D. | 8 and 16 |
| Answer» C. 2 and 16 | |
| 4600. |
The product of three geometric means between 4 and \[\frac{1}{4}\] will be |
| A. | 4 |
| B. | 2 |
| C. | \[-1\] |
| D. | 1 |
| Answer» E. | |