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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.
| 3401. |
For every positive integral value of n, \[{{3}^{n}}>{{n}^{3}}\] when |
| A. | n > 2 |
| B. | n ³ 3 |
| C. | n ³ 4 |
| D. | n < 4 |
| Answer» D. n < 4 | |
| 3402. |
For positive integer n, \[{{10}^{n-2}}>81n\], if |
| A. | n > 5 |
| B. | n ³ 5 |
| C. | n < 5 |
| D. | n > 6 |
| Answer» C. n < 5 | |
| 3403. |
For every positive integer n, \[{{2}^{n}} |
| A. | n < 4 |
| B. | n ³ 4 |
| C. | n < 3 |
| D. | None of these |
| Answer» C. n < 3 | |
| 3404. |
For all positive integral values of n, \[{{3}^{2n}}-2n+1\] is divisible by |
| A. | 2 |
| B. | 4 |
| C. | 8 |
| D. | 12 |
| Answer» B. 4 | |
| 3405. |
\[\left( \frac{a-b}{a} \right)+\frac{1}{2}{{\left( \frac{a-b}{a} \right)}^{2}}+\frac{1}{3}\,{{\left( \frac{a-b}{a} \right)}^{3}}+.....=\] [MNR 1979; MP PET 1990; UPSEAT 2001, 02; AMU 2005] |
| A. | \[{{\log }_{e}}(a-b)\] |
| B. | \[{{\log }_{e}}\left( \frac{a}{b} \right)\] |
| C. | \[{{\log }_{e}}\left( \frac{b}{a} \right)\] |
| D. | \[{{e}^{\left( \frac{a-b}{a} \right)}}\] |
| Answer» C. \[{{\log }_{e}}\left( \frac{b}{a} \right)\] | |
| 3406. |
\[{{\log }_{e}}(x+1)-{{\log }_{e}}(x-1)=\] |
| A. | \[2\,\left[ x+\frac{{{x}^{3}}}{3}+\frac{{{x}^{5}}}{5}+......\infty \right]\] |
| B. | \[\,\left[ x+\frac{{{x}^{3}}}{3}+\frac{{{x}^{5}}}{5}+......\infty \right]\] |
| C. | \[2\,\left[ \frac{1}{x}+\frac{1}{3{{x}^{3}}}+\frac{1}{5{{x}^{5}}}+...\infty \right]\] |
| D. | \[\,\left[ \frac{1}{x}+\frac{1}{3{{x}^{3}}}+\frac{1}{5{{x}^{5}}}+...\infty \right]\] |
| Answer» D. \[\,\left[ \frac{1}{x}+\frac{1}{3{{x}^{3}}}+\frac{1}{5{{x}^{5}}}+...\infty \right]\] | |
| 3407. |
\[\frac{1}{x+1}+\frac{1}{2\,{{(x+1)}^{2}}}+\frac{1}{3\,{{(x+1)}^{3}}}+....\infty =\] |
| A. | \[{{\log }_{e}}\left( 1+\frac{1}{x} \right)\] |
| B. | \[{{\log }_{e}}\left( 1-\frac{1}{x} \right)\] |
| C. | \[{{\log }_{e}}\left( \frac{x}{x+1} \right)\] |
| D. | None of these |
| Answer» B. \[{{\log }_{e}}\left( 1-\frac{1}{x} \right)\] | |
| 3408. |
\[{{\log }_{e}}\sqrt{\frac{1+x}{1-x}}=\] |
| A. | \[{{\log }_{e}}\frac{1}{2}\] |
| B. | \[2\,\left[ x+\frac{{{x}^{3}}}{3}+\frac{{{x}^{5}}}{5}+.....\infty \right]\] |
| C. | \[2\,\left[ {{x}^{2}}+\frac{{{x}^{4}}}{4}+\frac{{{x}^{6}}}{6}+.....\infty \right]\] |
| D. | None of these |
| Answer» B. \[2\,\left[ x+\frac{{{x}^{3}}}{3}+\frac{{{x}^{5}}}{5}+.....\infty \right]\] | |
| 3409. |
\[\frac{1}{1\,.\,2\,.\,3}+\frac{1}{3\,.\,4.\,5}+\frac{1}{5\,.\,6.\,7}+.....\infty =\] |
| A. | \[{{\log }_{e}}\sqrt{2}\] |
| B. | \[{{\log }_{e}}2-\frac{1}{2}\] |
| C. | \[{{\log }_{e}}2\] |
| D. | \[{{\log }_{e}}4\] |
| Answer» C. \[{{\log }_{e}}2\] | |
| 3410. |
\[{{e}^{\left( x\,-\,\frac{1}{2}{{(x\,-\,1)}^{2}}\,+\,\frac{1}{3}{{(x\,-\,1)}^{3}}\,-\,\frac{1}{4}{{(x\,-\,1)}^{4}}+....... \right)}}\] is equal to [DCE 2001] |
| A. | \[\log x\] |
| B. | \[\log (x-1)\] |
| C. | x |
| D. | None of these |
| Answer» E. | |
| 3411. |
In \[n=(1999)\,!\] then \[\sum\limits_{x=1}^{1999}{{{\log }_{n}}x}\] is equal to [AMU 2002] |
| A. | 1 |
| B. | 0 |
| C. | \[\sqrt[1999]{1999}\] |
| D. | -1 |
| Answer» B. 0 | |
| 3412. |
The coefficient of \[{{n}^{-r}}\]in the expansion of \[{{\log }_{10}}\left( \frac{n}{n-1} \right)\] is |
| A. | \[\frac{1}{r\,{{\log }_{e}}10}\] |
| B. | \[-\frac{1}{r{{\log }_{e}}10}\] |
| C. | \[-\frac{1}{r!{{\log }_{e}}10}\] |
| D. | None of these |
| Answer» B. \[-\frac{1}{r{{\log }_{e}}10}\] | |
| 3413. |
The coefficient of \[{{x}^{n}}\] in the expansion of \[{{\log }_{e}}(1+3x+2{{x}^{2}})\] is [UPSEAT 2001] |
| A. | \[{{(-1)}^{n}}\left[ \frac{{{2}^{n}}+1}{n} \right]\] |
| B. | \[\frac{{{(-1)}^{n+1}}}{n}[{{2}^{n}}+1]\] |
| C. | \[\frac{{{2}^{n}}+1}{n}\] |
| D. | None of these |
| Answer» C. \[\frac{{{2}^{n}}+1}{n}\] | |
| 3414. |
The coefficient of \[{{x}^{n}}\] in the expansion of \[{{\log }_{a}}(1+x)\] is |
| A. | \[\frac{{{(-1)}^{n-1}}}{n}\] |
| B. | \[\frac{{{(-1)}^{n-1}}}{n}{{\log }_{a}}e\] |
| C. | \[\frac{{{(-1)}^{n-1}}}{n}{{\log }_{e}}a\] |
| D. | \[\frac{{{(-1)}^{n}}}{n}{{\log }_{a}}e\] |
| Answer» C. \[\frac{{{(-1)}^{n-1}}}{n}{{\log }_{e}}a\] | |
| 3415. |
\[(0.5)-\frac{{{(0.5)}^{2}}}{2}+\frac{{{(0.5)}^{3}}}{3}-\frac{{{(0.5)}^{4}}}{4}+....\] [MP PET 1995] |
| A. | \[{{\log }_{e}}\frac{3}{2}\] |
| B. | \[{{\log }_{10}}\frac{1}{2}\] |
| C. | \[{{\log }_{e}}n\,!\] |
| D. | \[{{\log }_{e}}\frac{1}{2}\] |
| Answer» B. \[{{\log }_{10}}\frac{1}{2}\] | |
| 3416. |
\[\frac{x-1}{(x+1)}+\frac{1}{2}\,.\,\frac{{{x}^{2}}-1}{{{(x+1)}^{2}}}+\frac{1}{3}\,.\,\frac{{{x}^{3}}-1}{{{(x+1)}^{3}}}+......\infty =\] |
| A. | \[{{\log }_{e}}x\] |
| B. | \[{{\log }_{e}}(1+x)\] |
| C. | \[{{\log }_{e}}(1-x)\] |
| D. | \[{{\log }_{e}}\frac{x}{1+x}\] |
| Answer» B. \[{{\log }_{e}}(1+x)\] | |
| 3417. |
The sum of the series \[{{\log }_{4}}2-{{\log }_{8}}2+{{\log }_{16}}2....\] is [MNR 1994; Roorkee 1994; MP PET 2000] |
| A. | \[{{e}^{2}}\] |
| B. | \[{{\log }_{e}}2\] |
| C. | \[{{\log }_{e}}3-2\] |
| D. | \[1-{{\log }_{e}}2\] |
| Answer» E. | |
| 3418. |
\[{{\log }_{e}}2+{{\log }_{e}}\left( 1+\frac{1}{2} \right)+{{\log }_{e}}\left( 1+\frac{1}{3} \right)+....+{{\log }_{e}}\left( 1+\frac{1}{n-1} \right)\] is equal to |
| A. | \[{{\log }_{e}}1\] |
| B. | \[{{\log }_{e}}n\] |
| C. | \[{{\log }_{e}}(1+n)\] |
| D. | \[{{\log }_{e}}(1-n)\] |
| Answer» C. \[{{\log }_{e}}(1+n)\] | |
| 3419. |
The sum to infinity of the given series \[\frac{1}{n}-\frac{1}{2{{n}^{2}}}+\frac{1}{3{{n}^{3}}}-\frac{1}{4{{n}^{4}}}+....\] is [MP PET 1994] |
| A. | \[{{\log }_{e}}\left( \frac{n+1}{n} \right)\] |
| B. | \[{{\log }_{e}}\left( \frac{n}{n+1} \right)\] |
| C. | \[{{\log }_{e}}\left( \frac{n-1}{n} \right)\] |
| D. | \[{{\log }_{e}}\left( \frac{n}{n-1} \right)\] |
| Answer» B. \[{{\log }_{e}}\left( \frac{n}{n+1} \right)\] | |
| 3420. |
\[{{\log }_{a}}x\] is defined for \[(a>0)\] [Roorkee 1990] |
| A. | All real x |
| B. | All negative real \[x\ne 1\] |
| C. | All positive real \[x\ne 0\] |
| D. | \[a\ge e\] |
| Answer» D. \[a\ge e\] | |
| 3421. |
If \[4\,\left[ {{x}^{2}}+\frac{{{x}^{6}}}{3}+\frac{{{x}^{10}}}{5}+..... \right]={{y}^{2}}+\frac{{{y}^{4}}}{2}+\frac{{{y}^{6}}}{3}+......,\]then |
| A. | \[{{x}^{2}}y=2x-y\] |
| B. | \[{{x}^{2}}y=2x+y\] |
| C. | \[x=2{{y}^{2}}-1\] |
| D. | \[{{x}^{2}}y=2x+{{y}^{2}}\] |
| Answer» B. \[{{x}^{2}}y=2x+y\] | |
| 3422. |
The sum of \[\frac{1}{2}+\frac{1}{3}.\frac{1}{{{2}^{3}}}+\frac{1}{5}.\frac{1}{{{2}^{5}}}+.....\infty \] is [MP PET 1991] |
| A. | \[{{\log }_{e}}\sqrt{\frac{3}{2}}\] |
| B. | \[{{\log }_{e}}\sqrt{3}\] |
| C. | \[{{\log }_{e}}\sqrt{\frac{1}{2}}\] |
| D. | \[{{\log }_{e}}3\] |
| Answer» C. \[{{\log }_{e}}\sqrt{\frac{1}{2}}\] | |
| 3423. |
\[\frac{1}{{{n}^{2}}}+\frac{1}{2{{n}^{4}}}+\frac{1}{3{{n}^{6}}}+......\infty =\] |
| A. | \[{{\log }_{e}}\left( \frac{{{n}^{2}}}{{{n}^{2}}+1} \right)\] |
| B. | \[{{\log }_{e}}\left( \frac{{{n}^{2}}+1}{{{n}^{2}}} \right)\] |
| C. | \[{{\log }_{e}}\left( \frac{{{n}^{2}}}{{{n}^{2}}-1} \right)\] |
| D. | None of these |
| Answer» D. None of these | |
| 3424. |
\[\frac{m-n}{m+n}+\frac{1}{3}{{\left( \frac{m-n}{m+n} \right)}^{3}}+\frac{1}{5}{{\left( \frac{m-n}{m+n} \right)}^{5}}+......\infty =\] |
| A. | \[{{\log }_{e}}\left( \frac{m}{n} \right)\] |
| B. | \[{{\log }_{e}}\left( \frac{n}{m} \right)\] |
| C. | \[{{\log }_{e}}\left( \frac{m-n}{m+n} \right)\] |
| D. | \[\frac{1}{2}{{\log }_{e}}\left( \frac{m}{n} \right)\] |
| Answer» E. | |
| 3425. |
\[{{\log }_{e}}\frac{4}{5}+\frac{1}{4}-\frac{1}{2}{{\left( \frac{1}{4} \right)}^{2}}+\frac{1}{3}\,{{\left( \frac{1}{4} \right)}^{3}}+.....\] |
| A. | \[2{{\log }_{e}}\frac{4}{5}\] |
| B. | \[{{\log }_{e}}\frac{5}{4}\] |
| C. | 1 |
| D. | 0 |
| Answer» E. | |
| 3426. |
\[{{\log }_{e}}x-{{\log }_{e}}(x-1)=\] |
| A. | \[\frac{1}{x}-\frac{1}{2{{x}^{2}}}+\frac{1}{3{{x}^{3}}}-.....\infty \] |
| B. | \[\frac{1}{x}+\frac{1}{2{{x}^{2}}}+\frac{1}{3{{x}^{3}}}+.....\infty \] |
| C. | \[2\,\left( \frac{1}{x}+\frac{1}{3{{x}^{3}}}+\frac{1}{5{{x}^{5}}}+...\infty \right)\] |
| D. | \[2\,\left( \frac{1}{x}-\frac{1}{3{{x}^{3}}}+\frac{1}{5{{x}^{5}}}-...\infty \right)\] |
| Answer» C. \[2\,\left( \frac{1}{x}+\frac{1}{3{{x}^{3}}}+\frac{1}{5{{x}^{5}}}+...\infty \right)\] | |
| 3427. |
\[\frac{1}{1\,.\,3}+\frac{1}{2}\,.\,\frac{1}{3\,.\,5}+\frac{1}{3}\,.\,\frac{1}{5\,.\,7}+......\infty =\] |
| A. | \[2\,{{\log }_{e}}2-1\] |
| B. | \[{{\log }_{e}}2-1\] |
| C. | \[{{\log }_{e}}2\] |
| D. | None of these |
| Answer» B. \[{{\log }_{e}}2-1\] | |
| 3428. |
\[\frac{1}{1\,.\,2}-\frac{1}{2\,.\,3}+\frac{1}{3\,.\,4}-\frac{1}{4\,.\,5}+.....\infty =\] [Roorkee 1992; AIEEE 2003] |
| A. | \[{{\log }_{e}}\frac{4}{e}\] |
| B. | \[{{\log }_{e}}\frac{e}{4}\] |
| C. | \[{{\log }_{e}}4\] |
| D. | \[{{\log }_{e}}2\] |
| Answer» B. \[{{\log }_{e}}\frac{e}{4}\] | |
| 3429. |
\[1+\left( \frac{1}{2}+\frac{1}{3} \right)\,\frac{1}{4}+\left( \frac{1}{4}+\frac{1}{5} \right)\,\frac{1}{{{4}^{2}}}+\left( \frac{1}{6}+\frac{1}{7} \right)\,\frac{1}{{{4}^{3}}}+....\infty =\] |
| A. | \[{{\log }_{e}}(2\sqrt{3})\] |
| B. | \[2\,\,{{\log }_{e}}2\] |
| C. | \[{{\log }_{e}}2\] |
| D. | \[{{\log }_{e}}\left( \frac{2}{\sqrt{3}} \right)\] |
| Answer» B. \[2\,\,{{\log }_{e}}2\] | |
| 3430. |
If \[b=a-\frac{{{a}^{2}}}{2}+\frac{{{a}^{3}}}{3}-\frac{{{a}^{4}}}{4}+..\]then \[b+\frac{{{b}^{2}}}{2\,!}+\frac{{{b}^{3}}}{3\,!}+\frac{{{b}^{4}}}{4\,!}+...\infty =\] |
| A. | \[{{\log }_{e}}a\] |
| B. | \[{{\log }_{e}}b\] |
| C. | \[a\] |
| D. | \[{{e}^{a}}\] |
| Answer» D. \[{{e}^{a}}\] | |
| 3431. |
The sum of the series\[\frac{1}{2\,.\,3}+\frac{1}{4\,.\,5}+\frac{1}{6\,.\,7}+...=\] [MP PET 1998] |
| A. | \[\log \,(2/e)\] |
| B. | \[\log \,(e/2)\] |
| C. | 2/e |
| D. | e/2 |
| Answer» C. 2/e | |
| 3432. |
In the expansion of \[2{{\log }_{e}}x-{{\log }_{e}}(x+1)-{{\log }_{e}}(x-1)\], the coefficient of \[{{x}^{-4}}\] is |
| A. | 44228 |
| B. | \[-1\] |
| C. | 1 |
| D. | None of these |
| Answer» B. \[-1\] | |
| 3433. |
\[{{\log }_{e}}\,[{{(1+x)}^{1+x}}{{(1-x)}^{1-x}}]\,=\] |
| A. | \[\frac{{{x}^{2}}}{2}+\frac{{{x}^{4}}}{4}+\frac{{{x}^{6}}}{6}+....\infty \] |
| B. | \[\frac{{{x}^{2}}}{1.2}+\frac{{{x}^{4}}}{3.4}+\frac{{{x}^{6}}}{5.6}+....\infty \] |
| C. | \[2\,\,\left[ \frac{{{x}^{2}}}{1.2}+\frac{{{x}^{4}}}{3.4}+\frac{{{x}^{6}}}{5.6}+..\infty \right]\] |
| D. | None of these |
| Answer» D. None of these | |
| 3434. |
\[\frac{1}{5}+\frac{1}{2}\,.\,\frac{1}{{{5}^{2}}}+\frac{1}{3}.\frac{1}{{{5}^{3}}}+.....\infty =\] |
| A. | \[{{\log }_{e}}\frac{4}{5}\] |
| B. | \[{{\log }_{e}}\frac{\sqrt{5}}{2}\] |
| C. | \[2{{\log }_{e}}\frac{\sqrt{5}}{2}\] |
| D. | None of these |
| Answer» D. None of these | |
| 3435. |
\[\frac{(a-1)-\frac{{{(a-1)}^{2}}}{2}+\frac{{{(a-1)}^{3}}}{3}-....\infty }{(b-1)-\frac{{{(b-1)}^{2}}}{2}+\frac{{{(b-1)}^{3}}}{3}-.....\infty }=\] |
| A. | \[{{\log }_{b}}a\] |
| B. | \[{{\log }_{a}}b\] |
| C. | \[{{\log }_{e}}a-{{\log }_{e}}b\] |
| D. | \[{{\log }_{e}}a+{{\log }_{e}}b\] |
| Answer» B. \[{{\log }_{a}}b\] | |
| 3436. |
\[\frac{2}{1}\,.\,\frac{1}{3}+\frac{3}{2}.\frac{1}{9}+\frac{4}{3}.\frac{1}{27}+\frac{5}{4}.\frac{1}{81}+......\infty =\] |
| A. | \[\frac{1}{2}-{{\log }_{e}}\frac{2}{3}\] |
| B. | \[-{{\log }_{e}}\frac{2}{3}\] |
| C. | \[\frac{1}{2}+{{\log }_{e}}\left( \frac{2}{3} \right)\] |
| D. | None of these |
| Answer» B. \[-{{\log }_{e}}\frac{2}{3}\] | |
| 3437. |
The feasible solution of a L.P.P. belongs to |
| A. | First and second quadrant |
| B. | First and third quadrant |
| C. | Second quadrant |
| D. | Only first quadrant |
| Answer» E. | |
| 3438. |
The graph of \[x\le 2\] and \[y\ge 2\] will be situated in the |
| A. | First and second quadrant |
| B. | Second and third quadrant |
| C. | First and third quadrant |
| D. | Third and fourth quadrant |
| Answer» B. Second and third quadrant | |
| 3439. |
The maximum value of \[\mu =3x+4y\], subject to the conditions \[x+y\le 40,x+2y\le 60,x,y\ge 0\] is [MP PET 2004] |
| A. | 130 |
| B. | 120 |
| C. | 40 |
| D. | 140 |
| Answer» E. | |
| 3440. |
The co-ordinates of the point for minimum value of \[z=7x-8y\]subject to the conditions\[x+y-20\le 0\], \[y\ge 5,\,\] \[x\ge 0\], \[y\ge 0\] is [DCE 2005] |
| A. | (20, 0) |
| B. | (15, 5) |
| C. | (0, 5) |
| D. | (0, 20) |
| Answer» E. | |
| 3441. |
The minimum value of\[z=2{{x}_{1}}+3{{x}_{2}}\] subject to the constraints\[2{{x}_{1}}+7{{x}_{2}}\ge 22\],\[{{x}_{1}}+{{x}_{2}}\ge 6\],\[5{{x}_{1}}+{{x}_{2}}\ge 10\] and \[{{x}_{1}},\ {{x}_{2}}\ge 0\] is [MP PET 2003] |
| A. | 14 |
| B. | 20 |
| C. | 10 |
| D. | 16 |
| Answer» B. 20 | |
| 3442. |
The maximum value of \[z=3x+4y\] subject to the constraints \[x+y\le 40,\ x+2y\le 60,\ x\ge 0\] and \[y\ge 0\] is [MP PET 2002, 04] |
| A. | 120 |
| B. | 140 |
| C. | 100 |
| D. | 160 |
| Answer» C. 100 | |
| 3443. |
The maximum value of \[z=5x+2y\], subject to the constraints \[x+y\le 7,\ x+2y\le 10\], \[x,\ y\ge 0\] is [AMU 1999] |
| A. | 10 |
| B. | 26 |
| C. | 35 |
| D. | 70 |
| Answer» D. 70 | |
| 3444. |
If \[3{{x}_{1}}+5{{x}_{2}}\le 15\], \[5{{x}_{1}}+2{{x}_{2}}\le 10\], \[{{x}_{1}},\ {{x}_{2}}\ \ \ge 0\] then the maximum value of \[5{{x}_{1}}+3{{x}_{2}}\], by graphical method is |
| A. | \[12\frac{7}{19}\] |
| B. | \[12\frac{1}{7}\] |
| C. | \[12\frac{3}{5}\] |
| D. | 12 |
| Answer» B. \[12\frac{1}{7}\] | |
| 3445. |
The solution of set of constraints \[x+2y\ge 11,\] \[3x+4y\le 30,\ \ 2x+5y\le 30,\ x\ge 0,\ \ y\ge 0\] includes the point [MP PET 1993] |
| A. | (2, 3) |
| B. | (3, 2) |
| C. | (3, 4) |
| D. | (4, 3) |
| Answer» D. (4, 3) | |
| 3446. |
The maximum value of \[10x+5y\] under the constraints \[3x+y\le 15,\ x+2y\le 8,\] \[x,\ y\ge 0\] is |
| A. | 20 |
| B. | 50 |
| C. | 53 |
| D. | 70 |
| Answer» D. 70 | |
| 3447. |
The maximum value of \[(x+2y)\] under the constraints \[2x+3y\le 6,\ x+4y\le 4,\ \ x,\ y\ge 0\] is |
| A. | 3 |
| B. | 3.2 |
| C. | 2 |
| D. | 4 |
| Answer» C. 2 | |
| 3448. |
The point at which the maximum value of \[(x+y)\] subject to the constraints \[2x+5y\le 100\], \[\frac{x}{25}+\frac{y}{49}\le 1\], \[x,\ y\ge 0\] is obtained, is |
| A. | (10, 20) |
| B. | (20, 10) |
| C. | (15, 15) |
| D. | \[\left( \frac{50}{3},\ \frac{40}{3} \right)\] |
| Answer» E. | |
| 3449. |
By graphical method, the solution of linear programming problem Maximize \[z=3{{x}_{1}}+5{{x}_{2}}\] Subject to \[3{{x}_{1}}+2{{x}_{2}}\le 18\], \[{{x}_{1}}\le 4\], \[{{x}_{2}}\le 6\],\[{{x}_{1}}\ge 0\],\[{{x}_{2}}\ge 0\] is [MP PET 1996] |
| A. | \[{{x}_{1}}=2,\ {{x}_{2}}=0,\ z=6\] |
| B. | \[{{x}_{1}}=2,\ {{x}_{2}}=6,\ z=36\] |
| C. | \[{{x}_{1}}=4,\ {{x}_{2}}=3,\ z=27\] |
| D. | \[{{x}_{1}}=4,\ {{x}_{2}}=6,\ z=42\] |
| Answer» C. \[{{x}_{1}}=4,\ {{x}_{2}}=3,\ z=27\] | |
| 3450. |
\[z=ax+by,\ a,\ b\] being positive, under constraints \[y\ge 1\], \[x-4y+8\ge 0\], \[x,\ y\ge 0\] has |
| A. | Finite maximum |
| B. | Finite minimum |
| C. | An unbounded minimum solution |
| D. | An unbounded maximum solution |
| Answer» C. An unbounded minimum solution | |