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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.
| 5151. |
The sum of the series\[\frac{1}{1.2}+\frac{1.3}{1.2.3.4}+\frac{1.3.5}{1.2.3.4.5.6}+.....\infty \] is [Kurukshetra CEE 2002] |
| A. | \[15e\] |
| B. | \[{{e}^{1/2}}+e\] |
| C. | \[{{e}^{1/2}}-1\] |
| D. | \[{{e}^{1/2}}-e\] |
| Answer» D. \[{{e}^{1/2}}-e\] | |
| 5152. |
The coefficient of \[{{x}^{r}}\] in the expansion of \[1+\frac{a+bx}{1\,!}+\frac{{{(a+bx)}^{2}}}{2\,!}+.....+\frac{{{(a+bx)}^{n}}}{n\,!}+.....\] is [MP PET 1989] |
| A. | \[\frac{{{(a+b)}^{r}}}{r\,!}\] |
| B. | \[\frac{{{b}^{r}}}{r\,!}\] |
| C. | \[\frac{{{e}^{a}}{{b}^{r}}}{r\,!}\] |
| D. | \[{{e}^{a+{{b}^{r}}}}\] |
| Answer» D. \[{{e}^{a+{{b}^{r}}}}\] | |
| 5153. |
The sum of \[\frac{2}{1\,!}+\frac{6}{2\,!}+\frac{12}{3\,!}+\frac{20}{4\,!}+\].......is [UPSEAT 2000] |
| A. | \[\frac{3e}{2}\] |
| B. | \[e\] |
| C. | \[2e\] |
| D. | \[3e\] |
| Answer» E. | |
| 5154. |
Sum of the infinite series \[1+2+\frac{1}{2!}+\frac{2}{3!}+\frac{1}{4!}+\frac{2}{5!}+.....\] is [Roorkee 2000] |
| A. | \[{{e}^{2}}\] |
| B. | \[e+{{e}^{-1}}\] |
| C. | \[\frac{e-{{e}^{-1}}}{2}\] |
| D. | \[\frac{3e-{{e}^{-1}}}{2}\] |
| Answer» E. | |
| 5155. |
The sum of the infinite series \[\frac{1}{2!}+\frac{2}{3!}+\frac{3}{4!}+\frac{4}{5!}+......\]is [AMU 1999] |
| A. | \[e-2\] |
| B. | \[\frac{2}{3}e-1\] |
| C. | 1 |
| D. | 44230 |
| Answer» D. 44230 | |
| 5156. |
The value of \[\sqrt{e}\] will be [UPSEAT 1999] |
| A. | 1.648 |
| B. | 1.547 |
| C. | 1.447 |
| D. | 1.348 |
| Answer» B. 1.547 | |
| 5157. |
The coefficient of \[{{x}^{n}}\] in the expansion of \[\frac{{{e}^{7x}}+{{e}^{x}}}{{{e}^{3x}}}\] is [MP PET 1999] |
| A. | \[\frac{{{4}^{n-1}}+{{(-2)}^{n}}}{n\,!}\] |
| B. | \[\frac{{{4}^{n-1}}+{{2}^{n}}}{n\,!}\] |
| C. | \[\frac{{{4}^{n-1}}+{{(-2)}^{n-1}}}{n\,!}\] |
| D. | \[\frac{{{4}^{n}}+{{(-2)}^{n}}}{n\,!}\] |
| Answer» E. | |
| 5158. |
If \[S=\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{3.4}-\frac{1}{4.5}+....+\infty ,\] then \[{{e}^{S}}=\] [MP PET 1999] |
| A. | \[{{\log }_{e}}\left( \frac{4}{e} \right)\] |
| B. | \[\frac{4}{e}\] |
| C. | \[{{\log }_{e}}\left( \frac{e}{4} \right)\] |
| D. | \[\frac{e}{4}\] |
| Answer» C. \[{{\log }_{e}}\left( \frac{e}{4} \right)\] | |
| 5159. |
The value of \[1-\log 2+\frac{{{(\log 2)}^{2}}}{2\,!}-\frac{{{(\log 2)}^{3}}}{3\,!}+....\] is [MP PET 1998; Pb. CET 2000] |
| A. | 2 |
| B. | \[\frac{1}{2}\] |
| C. | \[\log 3\] |
| D. | None of these |
| Answer» C. \[\log 3\] | |
| 5160. |
\[1+\frac{{{({{\log }_{e}}n)}^{2}}}{2\,!}+\frac{{{({{\log }_{e}}n)}^{4}}}{4\,!}+....=\] [MP PET 1996] |
| A. | \[n\] |
| B. | \[1/n\] |
| C. | \[\frac{1}{2}(n+{{n}^{-1}})\] |
| D. | \[\frac{1}{2}({{e}^{n}}+{{e}^{-n}})\] |
| Answer» D. \[\frac{1}{2}({{e}^{n}}+{{e}^{-n}})\] | |
| 5161. |
Which of the following is not true [Kurukshetra CEE 1996] |
| A. | \[\log (1+x)<x\] for \[x>0\] |
| B. | \[\frac{x}{1+x}<\log (1+x)\]for \[x>0\] |
| C. | \[{{e}^{x}}>1+x\] for \[x>0\] |
| D. | \[{{e}^{-x}}<1-x\] for \[x>0\] |
| Answer» E. | |
| 5162. |
\[\frac{1\,.\,2}{1\,!}+\frac{2\,.\,3}{2\,!}+\frac{3\,.\,4}{3\,!}+\frac{4\,.\,5}{4\,!}+.....\infty =\] |
| A. | \[2\,e\] |
| B. | \[3\,e\] |
| C. | \[3\,e-1\] |
| D. | \[e\] |
| Answer» C. \[3\,e-1\] | |
| 5163. |
Sum to infinity of the series is \[1+\frac{{{x}^{2}}}{2\,!}+\frac{{{x}^{4}}}{4\,!}+......\] is [MP PET 1994] |
| A. | \[\frac{{{e}^{x}}-{{e}^{-x}}}{2}\] |
| B. | \[\frac{{{e}^{x}}+{{e}^{-x}}}{2}\] |
| C. | \[\frac{{{e}^{-x}}-{{e}^{x}}}{2}\] |
| D. | \[\frac{-({{e}^{x}}+{{e}^{-x}})}{2}\] |
| Answer» C. \[\frac{{{e}^{-x}}-{{e}^{x}}}{2}\] | |
| 5164. |
If \[{{T}_{n}}=\frac{{{3}^{n}}}{2\,(n\,!)}-\frac{1}{2\,(n\,!)},\] then \[{{S}_{\infty }}=\] |
| A. | \[\frac{{{e}^{3}}-1}{2}\] |
| B. | \[\frac{{{e}^{3}}-e}{2}\] |
| C. | \[\frac{e-3}{2}\] |
| D. | None of these |
| Answer» C. \[\frac{e-3}{2}\] | |
| 5165. |
The coefficient of \[{{x}^{r}}\] in the expansion of \[{{e}^{{{e}^{x}}}}\] is |
| A. | \[\frac{{{1}^{r}}}{1\,!}+\frac{{{2}^{r}}}{2\,!}+\frac{{{3}^{r}}}{3\,!}+.....\] |
| B. | \[1+\frac{1}{1\,!}+\frac{1}{2\,!}+....+\frac{1}{r\,!}\] |
| C. | \[\frac{1}{r\,!}\left[ \frac{{{1}^{r}}}{1\,!}+\frac{{{2}^{r}}}{2\,!}+\frac{{{3}^{r}}}{3\,!}+.... \right]\] |
| D. | \[\frac{{{e}^{r}}}{r!}\] |
| Answer» D. \[\frac{{{e}^{r}}}{r!}\] | |
| 5166. |
The value of \[\frac{2\frac{1}{2}}{1\,!}+\frac{3\frac{1}{2}}{2\,!}+\frac{4\frac{1}{2}}{3\,!}+\frac{5\frac{1}{2}}{4\,!}+......\infty \] is |
| A. | \[1+e\] |
| B. | \[\frac{1+e}{e}\] |
| C. | \[\frac{e-1}{e}\] |
| D. | None of these |
| Answer» E. | |
| 5167. |
\[\frac{1}{2}+\frac{1}{4}+\frac{1}{8(2)\,!}+\frac{1}{16\,(3)\,!}+\frac{1}{32(4)\,!}+......\infty =\] |
| A. | \[e\] |
| B. | \[\sqrt{e}\] |
| C. | \[\frac{\sqrt{e}}{2}\] |
| D. | None of these |
| Answer» D. None of these | |
| 5168. |
\[\left( 1+\frac{1}{2\,!}+\frac{1}{4\,!}+.... \right)\,\,\left( 1+\frac{1}{3\,!}+\frac{1}{5\,!}+.... \right)\,=\] |
| A. | \[{{e}^{4}}\] |
| B. | \[\frac{{{e}^{2}}-1}{{{e}^{2}}}\] |
| C. | \[\frac{{{e}^{4}}-1}{4\,{{e}^{2}}}\] |
| D. | \[\frac{{{e}^{4}}+1}{4\,{{e}^{2}}}\] |
| Answer» D. \[\frac{{{e}^{4}}+1}{4\,{{e}^{2}}}\] | |
| 5169. |
\[1+\frac{1+3}{2\,!}+\frac{1+3+5}{3\,!}+\frac{1+3+5+7}{4\,!}+.......\infty =\] |
| A. | \[e/2\] |
| B. | \[e\] |
| C. | \[2\,e\] |
| D. | \[3e\] |
| Answer» D. \[3e\] | |
| 5170. |
\[\frac{{{e}^{2}}+1}{2\,e}=\] |
| A. | \[1+\frac{2}{2\,!}+\frac{{{2}^{2}}}{3\,!}+\frac{{{2}^{3}}}{4\,!}+.....\infty \] |
| B. | \[1+\frac{1}{2\,!}+\frac{1}{4\,!}+\frac{1}{6\,!}+.....\infty \] |
| C. | \[\frac{1}{2}\left( 1+\frac{1}{2\,!}+\frac{1}{4\,!}+....\infty \right)\] |
| D. | \[\frac{1}{2}\left( 1+\frac{1}{1\,!}+\frac{1}{2\,!}+\frac{1}{3\,!}+....\infty \right)\] |
| Answer» C. \[\frac{1}{2}\left( 1+\frac{1}{2\,!}+\frac{1}{4\,!}+....\infty \right)\] | |
| 5171. |
\[1+\frac{a-bx}{1\,!}+\frac{{{(a-bx)}^{2}}}{2\,!}+\frac{{{(a-bx)}^{3}}}{3\,!}+....\infty =\] |
| A. | \[{{e}^{a-bx}}\] |
| B. | \[{{e}^{a-bx}}-1\] |
| C. | \[1+a{{\log }_{e}}(a-bx)\] |
| D. | \[{{e}^{-bx}}\] |
| Answer» B. \[{{e}^{a-bx}}-1\] | |
| 5172. |
In the expansion of \[\frac{{{e}^{4x}}-1}{{{e}^{2x}}}\], the coefficient of \[{{x}^{2}}\] is |
| A. | \[\frac{1}{2}\] |
| B. | 1 |
| C. | 0 |
| D. | None of these |
| Answer» D. None of these | |
| 5173. |
\[3+\frac{5}{1\,!}+\frac{7}{2\,!}+\frac{9}{3\,!}+.....\infty =\] |
| A. | \[3\,e\] |
| B. | \[5\,e\] |
| C. | \[5\,e-1\] |
| D. | None of these |
| Answer» C. \[5\,e-1\] | |
| 5174. |
\[1+\frac{a-b}{a}+\frac{1}{2\,!}{{\left( \frac{a-b}{a} \right)}^{2}}+\frac{1}{3\,!}{{\left( \frac{a-b}{a} \right)}^{3}}+......\infty =\] |
| A. | \[x=\] |
| B. | \[{{e}^{a}}\] |
| C. | \[\frac{e}{{{e}^{b/a}}}\] |
| D. | \[\frac{e}{{{e}^{a/b}}}\] |
| Answer» D. \[\frac{e}{{{e}^{a/b}}}\] | |
| 5175. |
\[\frac{2}{3\,!}+\frac{4}{5\,!}+\frac{6}{7\,!}+......\infty =\] [MNR 1979; MP PET 1995, 2002; Pb. CET 2002] |
| A. | \[e\] |
| B. | \[2\,e\] |
| C. | \[{{e}^{2}}\] |
| D. | \[1/e\] |
| Answer» E. | |
| 5176. |
\[1+\frac{{{2}^{3}}}{2\,!}+\frac{{{3}^{3}}}{3\,!}+\frac{{{4}^{3}}}{4\,!}+....\infty \] = [MNR 1976; MP PET 1997] |
| A. | \[2\,e\] |
| B. | \[3\,e\] |
| C. | \[4\,e\] |
| D. | \[5\,e\] |
| Answer» E. | |
| 5177. |
\[1+\frac{1}{3\,!}+\frac{1}{5\,!}+\frac{1}{7\,!}+.....\infty =\] [MP PET 1991] |
| A. | \[{{e}^{-1}}\] |
| B. | \[e\] |
| C. | \[\frac{e+{{e}^{-1}}}{2}\] |
| D. | \[\frac{e-{{e}^{-1}}}{2}\] |
| Answer» E. | |
| 5178. |
\[{{\left[ 1+\frac{1}{2\,!}+\frac{1}{4\,!}+....\infty \right]}^{2}}-{{\left[ 1+\frac{1}{3\,!}+\frac{1}{5\,!}+.....\infty \right]}^{2}}=\] |
| A. | 0 |
| B. | 1 |
| C. | \[-1\] |
| D. | 2 |
| Answer» C. \[-1\] | |
| 5179. |
If \[y=1+\frac{x}{1\,!}+\frac{{{x}^{2}}}{2\,!}+\frac{{{x}^{3}}}{3\,!}+......\infty \], then \[x=\] |
| A. | \[{{\log }_{e}}y\] |
| B. | \[{{\log }_{e}}\frac{1}{y}\] |
| C. | \[{{e}^{y}}\] |
| D. | \[{{e}^{-y}}\]! |
| Answer» B. \[{{\log }_{e}}\frac{1}{y}\] | |
| 5180. |
The value of \[\left| \,\begin{matrix} 41 & 42 & 43 \\ 44 & 45 & 46 \\ 47 & 48 & 49 \\ \end{matrix}\, \right|=\] [Karnataka CET 2001] |
| A. | 2 |
| B. | 4 |
| C. | 0 |
| D. | 1 |
| Answer» D. 1 | |
| 5181. |
If \[\left| \,\begin{matrix} {{(b+c)}^{2}} & {{a}^{2}} & {{a}^{2}} \\ {{b}^{2}} & {{(c+a)}^{2}} & {{b}^{2}} \\ {{c}^{2}} & {{c}^{2}} & {{(a+b)}^{2}} \\ \end{matrix}\, \right|=k\,abc{{(a+b+c)}^{3}}\], then the value of k is [Tamilnadu (Engg.) 2001] |
| A. | -1 |
| B. | 1 |
| C. | 2 |
| D. | -2 |
| Answer» D. -2 | |
| 5182. |
Let \[\omega =-\frac{1}{2}+i\frac{\sqrt{3}}{2}\]. Then the value of the determinant \[\left| \,\begin{matrix} 1 & 1 & 1 \\ 1 & -1-{{\omega }^{2}} & {{\omega }^{2}} \\ 1 & {{\omega }^{2}} & {{\omega }^{4}} \\ \end{matrix}\, \right|\]is [IIT Screening 2002] |
| A. | \[3\omega \] |
| B. | \[3\omega (\omega -1)\] |
| C. | \[3{{\omega }^{2}}\] |
| D. | \[3\omega (1-\omega )\] |
| Answer» C. \[3{{\omega }^{2}}\] | |
| 5183. |
At what value of \[x,\]will \[\left| \,\begin{matrix} x+{{\omega }^{2}} & \omega & 1 \\ \omega & {{\omega }^{2}} & 1+x \\ 1 & x+\omega & {{\omega }^{2}} \\ \end{matrix}\, \right|=0\] [DCE 2000, 01] |
| A. | \[x=0\] |
| B. | \[x=1\] |
| C. | \[x=-1\] |
| D. | None of these |
| Answer» B. \[x=1\] | |
| 5184. |
The value of \[\left| \,\begin{matrix} {{5}^{2}} & {{5}^{3}} & {{5}^{4}} \\ {{5}^{3}} & {{5}^{4}} & {{5}^{5}} \\ {{5}^{4}} & {{5}^{5}} & {{5}^{7}} \\ \end{matrix}\, \right|\]is |
| A. | \[{{5}^{2}}\] |
| B. | 0 |
| C. | \[{{5}^{13}}\] |
| D. | \[{{5}^{9}}\] |
| Answer» C. \[{{5}^{13}}\] | |
| 5185. |
If \[\left| \,\begin{matrix} {{a}_{1}} & {{b}_{1}} & {{c}_{1}} \\ {{a}_{2}} & {{b}_{2}} & {{c}_{2}} \\ {{a}_{3}} & {{b}_{3}} & {{c}_{3}} \\ \end{matrix}\, \right|=5\]; then the value of \[\left| \,\begin{matrix} {{b}_{2}}{{c}_{3}}-{{b}_{3}}{{c}_{2}} & {{c}_{2}}{{a}_{3}}-{{c}_{3}}{{a}_{2}} & {{a}_{2}}{{b}_{3}}-{{a}_{3}}{{b}_{2}} \\ {{b}_{3}}{{c}_{1}}-{{b}_{1}}{{c}_{3}} & {{c}_{3}}{{a}_{1}}-{{c}_{1}}{{a}_{3}} & {{a}_{3}}{{b}_{1}}-{{a}_{1}}{{b}_{3}} \\ {{b}_{1}}{{c}_{2}}-{{b}_{2}}{{c}_{1}} & {{c}_{1}}{{a}_{2}}-{{c}_{2}}{{a}_{1}} & {{a}_{1}}{{b}_{2}}-{{a}_{2}}{{b}_{1}} \\ \end{matrix}\, \right|\] is [Tamilnadu (Engg.) 2002] |
| A. | 5 |
| B. | 25 |
| C. | 125 |
| D. | 0 |
| Answer» C. 125 | |
| 5186. |
If \[\left| \,\begin{matrix} a & b & c \\ m & n & p \\ x & y & z \\ \end{matrix}\, \right|=k\], then \[\left| \,\begin{matrix} 6a & 2b & 2c \\ 3m & n & p \\ 3x & y & z \\ \end{matrix}\, \right|=\] [Tamilnadu (Engg.) 2002] |
| A. | \[k/6\] |
| B. | \[2k\] |
| C. | \[3k\] |
| D. | \[6k\] |
| Answer» E. | |
| 5187. |
If \[A=\left| \,\begin{matrix} -1 & 2 & 4 \\ 3 & 1 & 0 \\ -2 & 4 & 2 \\ \end{matrix}\, \right|\]and \[B=\left| \,\begin{matrix} -2 & 4 & 2 \\ 6 & 2 & 0 \\ -2 & 4 & 8 \\ \end{matrix}\, \right|\], then B is given by [Tamilnadu (Engg.) 2002] |
| A. | \[B=4A\] |
| B. | \[B=-4A\] |
| C. | \[B=-A\] |
| D. | \[B=6A\] |
| Answer» C. \[B=-A\] | |
| 5188. |
If \[ab+bc+ca=0\] and \[\left| \,\begin{matrix} a-x & c & b \\ c & b-x & a \\ b & a & c-x \\ \end{matrix}\, \right|=0\], then one of the value of x is [AMU 2000] |
| A. | \[{{({{a}^{2}}+{{b}^{2}}+{{c}^{2}})}^{\frac{1}{2}}}\] |
| B. | \[{{\left[ \frac{3}{2}({{a}^{2}}+{{b}^{2}}+{{c}^{2}}) \right]}^{\frac{1}{2}}}\] |
| C. | \[{{\left[ \frac{1}{2}({{a}^{2}}+{{b}^{2}}+{{c}^{2}}) \right]}^{\frac{1}{2}}}\] |
| D. | None of these |
| Answer» E. | |
| 5189. |
If \[\omega \] is the cube root of unity, then \[\left| \begin{matrix} 1 & \omega & {{\omega }^{2}} \\ \omega & {{\omega }^{2}} & 1 \\ {{\omega }^{2}} & 1 & \omega \\ \end{matrix} \right|\]= [RPET 1985, 93, 94; MP PET 1990, 2002; Karnataka CET 1992; 93, 02, 05] |
| A. | 1 |
| B. | 0 |
| C. | \[\omega \] |
| D. | \[{{\omega }^{2}}\] |
| Answer» C. \[\omega \] | |
| 5190. |
If \[\left| \,\begin{matrix} a & b & a+b \\ b & c & b+c \\ a+b & b+c & 0 \\ \end{matrix}\, \right|=0\]; then \[a,b,c\] are in [AMU 2000] |
| A. | A. P. |
| B. | G. P. |
| C. | H. P. |
| D. | None of these |
| Answer» C. H. P. | |
| 5191. |
The value of the determinant given below \[\left| \text{ }\begin{matrix} 1 & 2 & 3 \\ 3 & 5 & 7 \\ 8 & 14 & 20 \\ \end{matrix} \right|\] is [UPSEAT 2000] |
| A. | 20 |
| B. | 10 |
| C. | 0 |
| D. | 5 |
| Answer» D. 5 | |
| 5192. |
The sum of the products of the elements of any row of a determinant A with the same row is always equal to [Karnataka CET 2000] |
| A. | 1 |
| B. | 0 |
| C. | |A| |
| D. | \[\frac{1}{2}|A|\] |
| Answer» D. \[\frac{1}{2}|A|\] | |
| 5193. |
\[\left| \,\begin{matrix} {{a}^{2}}+{{x}^{2}} & ab & ca \\ ab & {{b}^{2}}+{{x}^{2}} & bc \\ ca & bc & {{c}^{2}}+{{x}^{2}} \\ \end{matrix}\, \right|\] is divisor of [RPET 2000] |
| A. | \[{{a}^{2}}\] |
| B. | \[{{b}^{2}}\] |
| C. | \[{{c}^{2}}\] |
| D. | \[{{x}^{2}}\] |
| Answer» E. | |
| 5194. |
If \[{{a}^{-1}}+{{b}^{-1}}+{{c}^{-1}}=0\] such that \[\left| \,\begin{matrix} 1+a & 1 & 1 \\ 1 & 1+b & 1 \\ 1 & 1 & 1+c \\ \end{matrix}\, \right|=\lambda \], then the value of \[\lambda \]is [RPET 2000] |
| A. | 0 |
| B. | abc |
| C. | |
| D. | None of these |
| Answer» C. | |
| 5195. |
If \[a\ne 6,b,c\]satisfy \[\left| \,\begin{matrix} a & 2b & 2c \\ 3 & b & c \\ 4 & a & b \\ \end{matrix}\, \right|=0,\]then \[abc=\] [EAMCET 2000] |
| A. | \[a+b+c\] |
| B. | 0 |
| C. | \[{{b}^{3}}\] |
| D. | \[ab+bc\] |
| Answer» D. \[ab+bc\] | |
| 5196. |
If \[\Delta =\left| \,\begin{matrix} x & y & z \\ p & q & r \\ a & b & c \\ \end{matrix}\, \right|,\]then \[\left| \,\begin{matrix} x & 2y & z \\ 2p & 4q & 2r \\ a & 2b & c \\ \end{matrix}\, \right|\]equals [RPET 1999] |
| A. | \[{{\Delta }^{2}}\] |
| B. | \[4\Delta \] |
| C. | \[3\Delta \] |
| D. | None of these |
| Answer» C. \[3\Delta \] | |
| 5197. |
If \[a,b,c\] are in A.P., then the value of \[\left| \,\begin{matrix} x+2 & x+3 & x+a \\ x+4 & x+5 & x+b \\ x+6 & x+7 & x+c \\ \end{matrix}\, \right|\] is [RPET 1999] |
| A. | \[x-(a+b+c)\] |
| B. | \[9{{x}^{2}}+a+b+c\] |
| C. | \[a+b+c\] |
| D. | 0 |
| Answer» E. | |
| 5198. |
If \[\left| \,\begin{matrix} 3x-8 & 3 & 3 \\ 3 & 3x-8 & 3 \\ 3 & 3 & 3x-8 \\ \end{matrix}\, \right|=0,\]then the values of x are [RPET 1997] |
| A. | 0, 2/3 |
| B. | 2/3, 11/3 |
| C. | 1/2, 1 |
| D. | 11/3, 1 |
| Answer» C. 1/2, 1 | |
| 5199. |
The determinant \[\,\left| \,\begin{matrix} 1 & 1 & 1 \\ 1 & 2 & 3 \\ 1 & 3 & 6 \\ \end{matrix}\, \right|\]is not equal to [MP PET 1988] |
| A. | \[\left| \,\begin{matrix} 2 & 1 & 1 \\ 2 & 2 & 3 \\ 2 & 3 & 6 \\ \end{matrix}\, \right|\] |
| B. | \[\left| \,\begin{matrix} 2 & 1 & 1 \\ 3 & 2 & 3 \\ 4 & 3 & 6 \\ \end{matrix}\, \right|\] |
| C. | \[\left| \begin{matrix} 1 & 2 & 1 \\ 1 & 5 & 3 \\ 1 & 9 & 6 \\ \end{matrix} \right|\] |
| D. | \[\left| \,\begin{matrix} 3 & 1 & 1 \\ 6 & 2 & 3 \\ 10 & 3 & 6 \\ \end{matrix} \right|\,\] |
| Answer» B. \[\left| \,\begin{matrix} 2 & 1 & 1 \\ 3 & 2 & 3 \\ 4 & 3 & 6 \\ \end{matrix}\, \right|\] | |
| 5200. |
If \[{{\left| \,\begin{matrix} 4 & 1 \\ 2 & 1 \\ \end{matrix}\, \right|}^{2}}=\left| \,\begin{matrix} 3 & 2 \\ 1 & x \\ \end{matrix}\, \right|-\left| \,\begin{matrix} x & 3 \\ -2 & 1 \\ \end{matrix}\, \right|\], then x = [RPET 1996] |
| A. | -14 |
| B. | 2 |
| C. | 6 |
| D. | 7 |
| Answer» D. 7 | |