MCQOPTIONS
Saved Bookmarks
MCQOPTIONS
This section includes 31 Mcqs, each offering curated multiple-choice questions to sharpen your Mathematics knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
The value of\[{{a}^{{{\log }_{b}}x}}\], where \[a=0.2,\ b=\sqrt{5},\ x=\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+.........\]to \[\infty \] is |
| A. | 1 |
| B. | 2 |
| C. | \[\frac{1}{2}\] |
| D. | 4 |
| Answer» E. | |
| 2. |
The sum of infinity of a geometric progression is \[\frac{4}{3}\] and the first term is \[\frac{3}{4}\]. The common ratio is[MP PET 1994] |
| A. | 7/16 |
| B. | 9/16 |
| C. | 1/9 |
| D. | 7/9 |
| Answer» B. 9/16 | |
| 3. |
If \[a,\ b,\ c\] are \[{{p}^{th}},\ {{q}^{th}}\] and \[{{r}^{th}}\]terms of a G.P., then \[{{\left( \frac{c}{b} \right)}^{p}}{{\left( \frac{b}{a} \right)}^{r}}{{\left( \frac{a}{c} \right)}^{q}}\] is equal to |
| A. | 1 |
| B. | \[{{a}^{P}}{{b}^{q}}{{c}^{r}}\] |
| C. | \[{{a}^{q}}{{b}^{r}}{{c}^{p}}\] |
| D. | \[{{a}^{r}}{{b}^{p}}{{c}^{q}}\] |
| Answer» B. \[{{a}^{P}}{{b}^{q}}{{c}^{r}}\] | |
| 4. |
If\[i=\sqrt{-1}\],then\[\frac{{{e}^{xi}}+{{e}^{-xi}}}{2}=\] |
| A. | \[1+\frac{{{x}^{2}}}{2\,!}+\frac{{{x}^{4}}}{4\,!}+.....\infty \] |
| B. | \[1-\frac{{{x}^{2}}}{2\,!}+\frac{{{x}^{4}}}{4\,!}-.....\infty \] |
| C. | \[x+\frac{{{x}^{3}}}{3\,!}+\frac{{{x}^{5}}}{5\,!}+....\infty \] |
| D. | \[i\,\left[ x-\frac{{{x}^{3}}}{3\,!}+\frac{{{x}^{5}}}{5\,!}-.....\infty\right]\] |
| Answer» C. \[x+\frac{{{x}^{3}}}{3\,!}+\frac{{{x}^{5}}}{5\,!}+....\infty \] | |
| 5. |
The sum of the series \[\frac{1}{2\,!}-\frac{1}{3\,!}+\frac{1}{4\,!}-.....\] is [DCE 2002] |
| A. | e |
| B. | \[{{e}^{-\,\frac{1}{2}}}\] |
| C. | \[{{e}^{-\,2}}\] |
| D. | None of these |
| Answer» E. | |
| 6. |
\[\frac{{{1}^{2}}.2}{1\,!}+\frac{{{2}^{2}}.3}{2\,!}+\frac{{{3}^{2}}.4}{3\,!}+.....\infty =\] [UPSEAT 1999] |
| A. | \[6\,e\] |
| B. | \[7\,e\] |
| C. | \[8\,e\] |
| D. | \[9\,e\] |
| Answer» C. \[8\,e\] | |
| 7. |
\[1+\frac{1+2}{2\,!}+\frac{1+2+3}{3\,!}+\frac{1+2+3+4}{4\,!}+....\infty =\] [Roorkee 1999; MP PET 2003] |
| A. | \[e\] |
| B. | \[3\,e\] |
| C. | \[e/2\] |
| D. | \[3e/2\] |
| Answer» E. | |
| 8. |
The sum of \[1+\frac{2}{5}+\frac{3}{{{5}^{2}}}+\frac{4}{{{5}^{3}}}+...........\]upto \[n\] terms is [MP PET 1982] |
| A. | \[\frac{25}{16}-\frac{4n+5}{16\times {{5}^{n-1}}}\] |
| B. | \[\frac{3}{4}-\frac{2n+5}{16\times {{5}^{n+1}}}\] |
| C. | \[\frac{3}{7}-\frac{3n+5}{16\times {{5}^{n-1}}}\] |
| D. | \[\frac{1}{2}-\frac{5n+1}{3\times {{5}^{n+2}}}\] |
| Answer» B. \[\frac{3}{4}-\frac{2n+5}{16\times {{5}^{n+1}}}\] | |
| 9. |
The value of \[\sum\limits_{r=1}^{n}{\log \left( \frac{{{a}^{r}}}{{{b}^{r-1}}} \right)}\] is |
| A. | \[\frac{n}{2}\log \left( \frac{{{a}^{n}}}{{{b}^{n}}} \right)\] |
| B. | \[\frac{n}{2}\log \left( \frac{{{a}^{n+1}}}{{{b}^{n}}} \right)\] |
| C. | \[\frac{n}{2}\log \left( \frac{{{a}^{n+1}}}{{{b}^{n-1}}} \right)\] |
| D. | \[\frac{n}{2}\log \left( \frac{{{a}^{n+1}}}{{{b}^{n+1}}} \right)\] |
| Answer» D. \[\frac{n}{2}\log \left( \frac{{{a}^{n+1}}}{{{b}^{n+1}}} \right)\] | |
| 10. |
Let \[{{T}_{r}}\] be the \[{{r}^{th}}\] term of an A.P. for \[r=1,\ 2,\ 3,....\]. If for some positive integers \[m,\ n\] we have \[{{T}_{m}}=\frac{1}{n}\] and \[{{T}_{n}}=\frac{1}{m}\], then equals [IIT 1998] |
| A. | \[\frac{1}{mn}\] |
| B. | \[\frac{1}{m}+\frac{1}{n}\] |
| C. | 1 |
| D. | 0 |
| Answer» D. 0 | |
| 11. |
The \[{{9}^{th}}\] term of the series \[27+9+5\frac{2}{5}+3\frac{6}{7}+........\] will be [MP PET 1983] |
| A. | \[1\frac{10}{17}\] |
| B. | \[\frac{10}{17}\] |
| C. | \[\frac{16}{27}\] |
| D. | \[\frac{17}{27}\] |
| Answer» B. \[\frac{10}{17}\] | |
| 12. |
\[0.5737373......=\] [Karnataka CET 2004] |
| A. | \[\frac{284}{497}\] |
| B. | \[\frac{284}{495}\] |
| C. | \[\frac{568}{990}\] |
| D. | \[\frac{567}{990}\] |
| Answer» D. \[\frac{567}{990}\] | |
| 13. |
If \[x=\sum\limits_{n=0}^{\infty }{{{a}^{n}}},\ y=\sum\limits_{n=0}^{\infty }{{{b}^{n}},\ z=\sum\limits_{n=0}^{\infty }{{{(ab)}^{n}}}}\], where, then |
| A. | \[xyz=x+y+z\] |
| B. | \[xz+yz=xy+z\] |
| C. | \[xy+yz=xz+y\] |
| D. | \[xy+xz=yz+x\] |
| Answer» C. \[xy+yz=xz+y\] | |
| 14. |
The G.M. of roots of the equation \[{{x}^{2}}-18x+9=0\] is [RPET 1997] |
| A. | 3 |
| B. | 4 |
| C. | 2 |
| D. | 1 |
| Answer» B. 4 | |
| 15. |
The sum of few terms of any ratio series is 728, if common ratio is 3 and last term is 486, then first term of series will be [UPSEAT 1999] |
| A. | 2 |
| B. | 1 |
| C. | 3 |
| D. | 4 |
| Answer» B. 1 | |
| 16. |
The sum of first two terms of a G.P. is 1 and every term of this series is twice of its previous term, then the first term will be [RPET 1988] |
| A. | 1/4 |
| B. | 1/3 |
| C. | 2/3 |
| D. | 3/4 |
| Answer» C. 2/3 | |
| 17. |
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 | |
| 18. |
Inthe expansion of \[(1+x+{{x}^{2}}){{e}^{-x}}\],the coefficient of\[{{x}^{2}}\] is |
| A. | 1 |
| B. | \[-1\] |
| C. | 1/2 |
| D. | -1/2 |
| Answer» D. -1/2 | |
| 19. |
\[1+3+7+15+31+..........\]to \[n\]terms = [IIT 1963] |
| A. | \[{{2}^{n+1}}-n\] |
| B. | \[{{2}^{n+1}}-n-2\] |
| C. | \[{{2}^{n}}-n-2\] |
| D. | None of these |
| Answer» C. \[{{2}^{n}}-n-2\] | |
| 20. |
If \[1,\ {{\log }_{y}}x,\ {{\log }_{z}}y,\ -15{{\log }_{x}}z\] are in A.P., then |
| A. | \[{{z}^{3}}=x\] |
| B. | \[x={{y}^{-1}}\] |
| C. | \[{{z}^{-3}}=y\] |
| D. | \[x={{y}^{-1}}={{z}^{3}}\] |
| E. | All the above |
| Answer» F. | |
| 21. |
The number of terms in the series \[101+99+97+.....+47\] is |
| A. | 25 |
| B. | 28 |
| C. | 30 |
| D. | 20 |
| Answer» C. 30 | |
| 22. |
If the sum of two extreme numbers of an A.P. with four terms is 8 and product of remaining two middle term is 15, then greatest number of the series will be [Roorkee 1965] |
| A. | 5 |
| B. | 7 |
| C. | 9 |
| D. | 11 |
| Answer» C. 9 | |
| 23. |
The sum of the first four terms of an A.P. is 56. The sum of the last four terms is 112. If its first term is 11, the number of terms is |
| A. | 10 |
| B. | 11 |
| C. | 12 |
| D. | None of these |
| Answer» C. 12 | |
| 24. |
\[{{7}^{th}}\] term of an A.P. is 40, then the sum of first 13 terms is [Karnataka CET 2003] |
| A. | 53 |
| B. | 520 |
| C. | 1040 |
| D. | 2080 |
| Answer» C. 1040 | |
| 25. |
The sum of \[1+3+5+7+.........\]upto \[n\] terms is [MP PET 1984] |
| A. | \[{{(n+1)}^{2}}\] |
| B. | \[{{(2n)}^{2}}\] |
| C. | \[{{n}^{2}}\] |
| D. | \[{{(n-1)}^{2}}\] |
| Answer» D. \[{{(n-1)}^{2}}\] | |
| 26. |
The ratio of the sums of first \[n\] even numbers and \[n\] odd numbers will be |
| A. | \[1:n\] |
| B. | \[(n+1):1\] |
| C. | \[(n+1):n\] |
| D. | \[(n-1):1\] |
| Answer» D. \[(n-1):1\] | |
| 27. |
If the 9th term of an A.P. be zero, then the ratio of its29thand 19thterm is |
| A. | 1 : 2 |
| B. | 2 : 1 |
| C. | 1 : 3 |
| D. | 3 : 1 |
| Answer» C. 1 : 3 | |
| 28. |
The first term of an A.P. is 2 and common difference is 4. The sum of its 40 terms will be [MNR 1978; MP PET 2002] |
| A. | 3200 |
| B. | 1600 |
| C. | 200 |
| D. | 2800 |
| Answer» B. 1600 | |
| 29. |
If the \[{{p}^{th}},\ {{q}^{th}}\] and \[{{r}^{th}}\] term of an arithmetic sequence are a , b and \[c\] respectively, then the value of \[[a(q-r)\] + \[b(r-p)\] \[+c(p-q)]=\] [MP PET 1985] |
| A. | 1 |
| B. | \[-1\] |
| C. | 0 |
| D. | 1/2 |
| Answer» D. 1/2 | |
| 30. |
If . terms of the series \[63+65+67+69+.........\] and \[3+10+17+24+......\] be equal, then [Kerala (Engg.) 2002] |
| A. | 11 |
| B. | 12 |
| C. | 13 |
| D. | 15 |
| Answer» D. 15 | |
| 31. |
If twice the 11th term of an A.P. is equal to 7 times of its 21st term, then its 25th term is equal to [J & K 2005] |
| A. | 24 |
| B. | 120 |
| C. | 0 |
| D. | None of these |
| Answer» D. None of these | |