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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.
| 3251. |
The mean of a set of numbers is \[\bar{x}\]. If each number is multiplied by l, then the mean of new set is |
| A. | \[\bar{x}\] |
| B. | \[\lambda +\bar{x}\] |
| C. | \[\lambda \bar{x}\] |
| D. | None of these |
| Answer» D. None of these | |
| 3252. |
An automobile driver travels from plane to a hill station 120 km distant at an average speed of 30 km per hour. He then makes the return trip at an average speed of 25 km per hour. He covers another 120 km distance on plane at an average speed of 50 km per hour. His average speed over the entire distance of 360 km will be |
| A. | \[\frac{30+25+50}{3}\]km/hr |
| B. | \[{{(30,\,25,\,50)}^{\frac{1}{3}}}\] |
| C. | \[\frac{3}{\frac{1}{30}+\frac{1}{25}+\frac{1}{50}}\]km/hr |
| D. | None of these |
| Answer» D. None of these | |
| 3253. |
The A.M. of a 50 set of numbers is 38. If two numbers of the set, namely 55 and 45 are discarded, the A.M. of the remaining set of numbers is [Kurukshetra CEE 1993] |
| A. | 38.5 |
| B. | 37.5 |
| C. | 36.5 |
| D. | 36 |
| Answer» C. 36.5 | |
| 3254. |
A student obtain 75%, 80% and 85% in three subjects. If the marks of another subject are added, then his average cannot be less than |
| A. | 60% |
| B. | 65% |
| C. | 80% |
| D. | 90% |
| Answer» B. 65% | |
| 3255. |
The number of observations in a group is 40. If the average of first 10 is 4.5 and that of the remaining 30 is 3.5, then the average of the whole group is [AMU 1992; DCE 1996] |
| A. | \[\frac{1}{5}\] |
| B. | \[\frac{15}{4}\] |
| C. | 4 |
| D. | 8 |
| Answer» C. 4 | |
| 3256. |
If the values \[1,\,\frac{1}{2},\,\frac{1}{3},\,\frac{1}{4},\,\frac{1}{5},\,.....,\frac{1}{n}\] occur at frequencies 1, 2, 3, 4, 5, ?.,n in a distribution, then the mean is |
| A. | 1 |
| B. | n |
| C. | \[\frac{1}{n}\] |
| D. | \[\frac{2}{n+1}\] |
| Answer» E. | |
| 3257. |
The weighted mean of first n natural numbers whose weights are equal to the squares of corresponding numbers is [Pb. CET 1989] |
| A. | \[\frac{n+1}{2}\] |
| B. | \[\frac{3n(n+1)}{2(2n+1)}\] |
| C. | \[\frac{(n+1)(2n+1)}{6}\] |
| D. | \[\frac{n(n+1)}{2}\] |
| Answer» C. \[\frac{(n+1)(2n+1)}{6}\] | |
| 3258. |
The harmonic mean of 3, 7, 8, 10, 14 is |
| A. | \[\frac{3+7+8+10+14}{5}\] |
| B. | \[\frac{1}{3}+\frac{1}{7}+\frac{1}{8}+\frac{1}{10}+\frac{1}{14}\] |
| C. | \[\frac{\frac{1}{3}+\frac{1}{7}+\frac{1}{8}+\frac{1}{10}+\frac{1}{14}}{4}\] |
| D. | \[\frac{5}{\frac{1}{3}+\frac{1}{7}+\frac{1}{8}+\frac{1}{10}+\frac{1}{14}}\] |
| Answer» E. | |
| 3259. |
The reciprocal of the mean of the reciprocals of n observations is their [AMU 1985] |
| A. | A.M. |
| B. | G.M. |
| C. | H.M. |
| D. | None of these |
| Answer» D. None of these | |
| 3260. |
If the mean of 3, 4, x, 7, 10 is 6, then the value of x is |
| A. | 4 |
| B. | 5 |
| C. | 6 |
| D. | 7 |
| Answer» D. 7 | |
| 3261. |
Area of the greatest rectangle that can be inscribed in the ellipse \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\] is [AIEEE 2005] |
| A. | \[\sqrt{ab}\] |
| B. | \[\frac{a}{b}\] |
| C. | \[2ab\] |
| D. | \[ab\] |
| Answer» D. \[ab\] | |
| 3262. |
If \[P=(1,\,1)\], \[Q=(3,\,2)\] and R is a point on x-axis then the value of \[PR+RQ\] will be minimum at [AMU 2005] |
| A. | \[\left( \frac{5}{3},\,0 \right)\] |
| B. | \[\left( \frac{1}{3},\,0 \right)\] |
| C. | (3, 0) |
| D. | (1, 0) |
| Answer» B. \[\left( \frac{1}{3},\,0 \right)\] | |
| 3263. |
The minimum value of \[P(1,\,1)\] is [DCE 2005] |
| A. | \[\frac{15}{2}\] |
| B. | \[\frac{11}{2}\] |
| C. | \[\frac{-13}{2}\] |
| D. | \[\frac{71}{8}\] |
| Answer» E. | |
| 3264. |
The maximum value of xy when \[x+2y=8\] is [Kerala (Engg.) 2005] |
| A. | 20 |
| B. | 16 |
| C. | 24 |
| D. | 8 |
| E. | 4 |
| Answer» E. 4 | |
| 3265. |
The point \[(0,\,5)\]is closest to the curve \[{{x}^{2}}=2y\] at [MNR 1983] |
| A. | \[(2\sqrt{2},0)\] |
| B. | (0, 0) |
| C. | \[(2,\,2)\] |
| D. | None of these |
| Answer» E. | |
| 3266. |
The maximum value of \[{{x}^{1/x}}\] is [MP PET 2004] |
| A. | \[\frac{1}{e}\] |
| B. | \[{{e}^{1/e}}\] |
| C. | e |
| D. | \[\frac{1}{{{e}^{e}}}\] |
| Answer» C. e | |
| 3267. |
The minimum value of function \[f(x)=3{{x}^{4}}-8{{x}^{3}}+12{{x}^{2}}-48x+25\] on [0, 3] is equal to [Pb. CET 2004] |
| A. | 25 |
| B. | ? 39 |
| C. | ? 25 |
| D. | 39 |
| Answer» C. ? 25 | |
| 3268. |
The function \[f(x)=|px-q|+r|x|,\] \[x\in (-\infty ,\infty )\] where \[p>0,q>0,r>0\]assumes its minimum value only at one point if [Pb. CET 2003] |
| A. | \[p\ne q\] |
| B. | \[q\ne r\] |
| C. | \[r\ne p\] |
| D. | \[p=q=r\] |
| Answer» E. | |
| 3269. |
Local maximum value of the function \[\frac{\log x}{x}\]is [MNR 1984; RPET 1997, 2002; DCE 2002; Karnataka CET 2000; UPSEAT 2001; MP PET 2002] |
| A. | e |
| B. | 1 |
| C. | \[\frac{1}{e}\] |
| D. | 2e |
| Answer» D. 2e | |
| 3270. |
The minimum value of \[2x+3y,\] when \[xy=6,\] is [MP PET 2003] |
| A. | 12 |
| B. | 9 |
| C. | 8 |
| D. | 6 |
| Answer» B. 9 | |
| 3271. |
If \[x-2y=4,\] the minimum value of \[xy\] is [UPSEAT 2003] |
| A. | ? 2 |
| B. | 2 |
| C. | 0 |
| D. | ? 3 |
| Answer» B. 2 | |
| 3272. |
The minimum value of \[{{x}^{2}}+\frac{1}{1+{{x}^{2}}}\] is at [UPSEAT 2003] |
| A. | \[x=0\] |
| B. | \[x=1\] |
| C. | \[x=4\] |
| D. | \[x=3\] |
| Answer» B. \[x=1\] | |
| 3273. |
The minimum value of \[\left( {{x}^{2}}+\frac{250}{x} \right)\] is [Kurukshetra CEE 2002] |
| A. | 75 |
| B. | 50 |
| C. | 25 |
| D. | 55 |
| Answer» B. 50 | |
| 3274. |
If PQ and PR are the two sides of a triangle, then the angle between them which gives maximum area of the triangle is [Kerala (Engg.) 2002] |
| A. | \[\pi \] |
| B. | \[\pi /3\] |
| C. | \[\pi /4\] |
| D. | \[\pi /2\] |
| Answer» E. | |
| 3275. |
If \[ab=2a+3b,\,a>0,\,\,b>0\] then the minimum value of ab is [Orissa JEE 2002] |
| A. | 12 |
| B. | 24 |
| C. | \[\frac{1}{4}\] |
| D. | None of these |
| Answer» C. \[\frac{1}{4}\] | |
| 3276. |
The function \[f(x)={{x}^{-x}},\,(x\,\in \,R)\] attains a maximum value at x = [EAMCET 2002] |
| A. | 2 |
| B. | 3 |
| C. | 1/e |
| D. | 1 |
| Answer» D. 1 | |
| 3277. |
On [1, e] the greatest value of \[{{x}^{2}}\log x\] [AMU 2002] |
| A. | \[{{e}^{2}}\] |
| B. | \[\frac{1}{e}\log \frac{1}{\sqrt{e}}\] |
| C. | \[{{e}^{2}}\log \sqrt{e}\] |
| D. | None of these |
| Answer» B. \[\frac{1}{e}\log \frac{1}{\sqrt{e}}\] | |
| 3278. |
The minimum value of \[|x|+|x+\frac{1}{2}|+|x-3|+|x-\frac{5}{2}|\] is |
| A. | 0 |
| B. | 2 |
| C. | 4 |
| D. | 6 |
| Answer» E. | |
| 3279. |
v If \[y=a\,\,\log x+b{{x}^{2}}+x\]has its extremum value at \[x=1\]and \[x=2,\]then \[(a,b)\]= [UPSEAT 2002] |
| A. | \[\left( 1,\,\,\frac{1}{2} \right)\] |
| B. | \[\left( \frac{1}{2},\,2 \right)\] |
| C. | \[\left( 2,\,\,\frac{-1}{2} \right)\] |
| D. | \[\left( \frac{-2}{3},\,\,\frac{-1}{6} \right)\] |
| Answer» E. | |
| 3280. |
The perimeter of a sector is p. The area of the sector is maximum when its radius is [Karnataka CET 2002] |
| A. | \[\sqrt{p}\] |
| B. | \[\frac{1}{\sqrt{p}}\] |
| C. | \[\frac{p}{2}\] |
| D. | \[\frac{p}{4}\] |
| Answer» E. | |
| 3281. |
If \[f(x)=\frac{1}{4{{x}^{2}}+2x+1}\], then its maximum value is [RPET 2002] |
| A. | 4/3 |
| B. | 2/3 |
| C. | 1 |
| D. | ¾ |
| Answer» B. 2/3 | |
| 3282. |
The function \[f(x)=2{{x}^{3}}-3{{x}^{2}}-12x+4\] has [DCE 2002] |
| A. | No maxima and minima |
| B. | One maximum and one minimum |
| C. | Two maxima |
| D. | Two minima |
| Answer» C. Two maxima | |
| 3283. |
Maximum slope of the curve \[y=-{{x}^{3}}+3{{x}^{2}}+9x-27\] is [MP PET 2001] |
| A. | 0 |
| B. | 12 |
| C. | 16 |
| D. | 32 |
| Answer» C. 16 | |
| 3284. |
The function \[f(x)=2{{x}^{3}}-15{{x}^{2}}+36x+4\] is maximum at [Karnataka CET 2001] |
| A. | \[x=2\] |
| B. | \[x=4\] |
| C. | \[x=0\] |
| D. | \[x=3\] |
| Answer» B. \[x=4\] | |
| 3285. |
If \[xy={{c}^{2}},\] then minimum value of \[ax+by\] is [RPET 2001] |
| A. | \[c\sqrt{ab}\] |
| B. | \[2c\sqrt{ab}\] |
| C. | \[-c\sqrt{ab}\] |
| D. | \[-2c\sqrt{ab}\] |
| Answer» C. \[-c\sqrt{ab}\] | |
| 3286. |
If \[{{a}^{2}}{{x}^{4}}+{{b}^{2}}{{y}^{4}}={{c}^{6}},\] then maximum value of xy is [RPET 2001] |
| A. | \[\frac{{{c}^{2}}}{\sqrt{ab}}\] |
| B. | \[\frac{{{c}^{3}}}{ab}\] |
| C. | \[\frac{{{c}^{3}}}{\sqrt{2ab}}\] |
| D. | \[\frac{{{c}^{3}}}{2ab}\] |
| Answer» D. \[\frac{{{c}^{3}}}{2ab}\] | |
| 3287. |
The function \[f(x)=ax+\frac{b}{x};a,\,b,x>0\] takes on the least value at x equal to [AMU 2000] |
| A. | b |
| B. | \[\sqrt{a}\] |
| C. | \[\sqrt{b}\] |
| D. | \[\sqrt{b/a}\] |
| Answer» E. | |
| 3288. |
The function \[{{x}^{2}}\log x\]in the interval (1, e) has |
| A. | A point of maximum |
| B. | A point of minimum |
| C. | Points of maximum as well as of minimum |
| D. | Neither a point of maximum nor minimum |
| Answer» E. | |
| 3289. |
The function \[f(x)=x+\sin x\] has [AMU 2000] |
| A. | A minimum but no maximum |
| B. | A maximum but no minimum |
| C. | Neither maximum nor minimum |
| D. | Both maximum and minimum |
| Answer» D. Both maximum and minimum | |
| 3290. |
The ratio of height of cone of maximum volume inscribed in a sphere to its radius is [Orissa JEE 2004] |
| A. | \[\frac{3}{4}\] |
| B. | \[\frac{4}{3}\] |
| C. | \[\frac{1}{2}\] |
| D. | \[\frac{2}{3}\] |
| Answer» C. \[\frac{1}{2}\] | |
| 3291. |
A cone of maximum volume is inscribed in a given sphere, then ratio of the height of the cone to diameter of the sphere is [MNR 1985; UPSEAT 2000] |
| A. | 2/3 |
| B. | 3/4 |
| C. | 1/3 |
| D. | ¼ |
| Answer» B. 3/4 | |
| 3292. |
The maximum value of \[f(x)=\frac{x}{4+x+{{x}^{2}}}\] on \[[-1,\,1]\] is [MP PET 2000] |
| A. | \[-1/4\] |
| B. | \[-1/3\] |
| C. | \[1/6\] |
| D. | \[1/5\] |
| Answer» D. \[1/5\] | |
| 3293. |
The real number which most exceeds its cube is [MP PET 2000] |
| A. | \[\frac{1}{2}\] |
| B. | \[\frac{1}{\sqrt{3}}\] |
| C. | \[\frac{1}{\sqrt{2}}\] |
| D. | None of these |
| Answer» C. \[\frac{1}{\sqrt{2}}\] | |
| 3294. |
The denominator of a fraction number is greater than 16 of the square of numerator, then least value of the number is [RPET 2000] |
| A. | \[-1/4\] |
| B. | \[-1/8\] |
| C. | \[1/12\] |
| D. | \[1/16\] |
| Answer» C. \[1/12\] | |
| 3295. |
The real number x when added to its inverse gives the minimum value of the sum at x equal to [RPET 2000; AIEEE 2003] |
| A. | ? 2 |
| B. | 2 |
| C. | 1 |
| D. | ? 1 |
| Answer» D. ? 1 | |
| 3296. |
If \[A+B=\frac{\pi }{2},\] the maximum value of \[\cos A\cos B\]is [AMU 1999] |
| A. | \[\frac{1}{2}\] |
| B. | \[\frac{3}{4}\] |
| C. | 1 |
| D. | \[\frac{4}{3}\] |
| Answer» B. \[\frac{3}{4}\] | |
| 3297. |
The maximum value of \[{{x}^{4}}{{e}^{-{{x}^{2}}}}\]is [AMU 1999] |
| A. | \[{{e}^{2}}\] |
| B. | \[{{e}^{-2}}\] |
| C. | \[12{{e}^{-2}}\] |
| D. | \[4{{e}^{-2}}\] |
| Answer» E. | |
| 3298. |
The minimum value of \[\frac{\log x}{x}\] in the interval \[[2,\,\infty )\] is [Roorkee 1999] |
| A. | \[\frac{\log 2}{2}\] |
| B. | Zero |
| C. | \[\frac{1}{e}\] |
| D. | Does not exist |
| Answer» E. | |
| 3299. |
If x is real, then greatest and least values of \[\frac{{{x}^{2}}-x+1}{{{x}^{2}}+x+1}\] are [RPET 1999; AMU 1999; UPSEAT 2002] |
| A. | \[3,\,-\frac{1}{2}\] |
| B. | \[3,\frac{1}{3}\] |
| C. | \[-3,\,-\frac{1}{3}\] |
| D. | None of these |
| Answer» C. \[-3,\,-\frac{1}{3}\] | |
| 3300. |
\[\frac{x}{1+x\,\tan x}\] is maxima at [UPSEAT 1999] |
| A. | \[x=\sin x\] |
| B. | \[x=\cos x\] |
| C. | \[x=\frac{\pi }{3}\] |
| D. | \[x=\tan x\] |
| Answer» C. \[x=\frac{\pi }{3}\] | |