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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.
| 3201. |
The mode of the distribution [AMU 1988] Marks 4 5 6 7 8 No. of students 6 7 10 8 3 |
| A. | 5 |
| B. | 6 |
| C. | 8 |
| D. | 10 |
| Answer» C. 8 | |
| 3202. |
The mode of the following items is 0, 1, 6, 7, 2, 3, 7, 6, 6, 2, 6, 0, 5, 6, 0 [AMU 1995] |
| A. | 0 |
| B. | 5 |
| C. | 6 |
| D. | 2 |
| Answer» D. 2 | |
| 3203. |
A set of numbers consists of three 4?s, five 5?s, six 6?s, eight 8?s and seven 10?s. The mode of this set of numbers is [AMU 1989] |
| A. | 6 |
| B. | 7 |
| C. | 8 |
| D. | 10 |
| Answer» D. 10 | |
| 3204. |
For a continuous series the mode is computed by the formula |
| A. | \[l+\frac{{{f}_{m-1}}}{{{f}_{m}}-{{f}_{m-1}}-{{f}_{m+1}}}\times C\] or \[l+\left( \frac{{{f}_{1}}}{{{f}_{m}}-{{f}_{1}}-{{f}_{2}}} \right)\times i\] |
| B. | \[l=\frac{{{f}_{m}}-{{f}_{m-1}}}{{{f}_{m}}-{{f}_{m-1}}-{{f}_{m+1}}}\times C\] or \[l+\frac{{{f}_{m}}-{{f}_{1}}}{{{f}_{m}}-{{f}_{1}}-{{f}_{2}}}\times i\] |
| C. | \[l+\frac{{{f}_{m}}-{{f}_{m-1}}}{2{{f}_{m}}-{{f}_{m-1}}-{{f}_{m+1}}}\times C\] or \[l+\frac{{{f}_{m}}-{{f}_{1}}}{2{{f}_{m}}-{{f}_{1}}-{{f}_{2}}}\times i\] |
| D. | \[l+\frac{2{{f}_{m}}-{{f}_{m-1}}}{{{f}_{m}}-{{f}_{m-1}}-{{f}_{m+1}}}\times C\] or \[l+\frac{2{{f}_{m}}-{{f}_{1}}}{{{f}_{m}}-{{f}_{1}}-{{f}_{2}}}\times i\] |
| Answer» D. \[l+\frac{2{{f}_{m}}-{{f}_{m-1}}}{{{f}_{m}}-{{f}_{m-1}}-{{f}_{m+1}}}\times C\] or \[l+\frac{2{{f}_{m}}-{{f}_{1}}}{{{f}_{m}}-{{f}_{1}}-{{f}_{2}}}\times i\] | |
| 3205. |
The median of a set of 9 distinct observations is 20.5. If each of the largest 4 observation of the set is increased by 2, then the median of the new set [AIEEE 2003] |
| A. | Is increased by 2 |
| B. | Is decreased by 2 |
| C. | Is two times the original median |
| D. | Remains the same as that of the original set |
| Answer» E. | |
| 3206. |
Which one of the following measures of marks is the most suitable one of central location for computing intelligence of students? [Kurukshetra CEE 1995] |
| A. | Mode |
| B. | Arithmetic mean |
| C. | Geometric mean |
| D. | Median |
| Answer» E. | |
| 3207. |
Quartile deviation for a frequency distribution is [DCE 1998] |
| A. | \[Q={{Q}_{3}}-{{Q}_{1}}\] |
| B. | \[Q=\frac{1}{2}({{Q}_{3}}-{{Q}_{1}})\] |
| C. | \[Q=\frac{1}{3}({{Q}_{3}}-{{Q}_{1}})\] |
| D. | \[Q=\frac{1}{4}({{Q}_{2}}-{{Q}_{1}})\] |
| Answer» C. \[Q=\frac{1}{3}({{Q}_{3}}-{{Q}_{1}})\] | |
| 3208. |
If the standard deviation of 0, 1, 2, 3, ?..,9 is K, then the standard deviation of 10, 11, 12, 13 ?..19 is |
| A. | K |
| B. | K + 10 |
| C. | \[K+\sqrt{10}\] |
| D. | 10K |
| Answer» B. K + 10 | |
| 3209. |
For a frequency distribution mean deviation from mean is computed by [DCE 1994] |
| A. | M.D.\[=\frac{\sum d}{\sum f}\] |
| B. | M.D.\[=\frac{\sum fd}{\sum f}\] |
| C. | M.D.\[=\frac{\sum f|d|}{\sum f}\] |
| D. | M.D.\[=\frac{\sum f}{\sum f|d|}\] |
| Answer» D. M.D.\[=\frac{\sum f}{\sum f|d|}\] | |
| 3210. |
The mean deviation of the numbers 3, 4, 5, 6, 7 is [AMU 1993; DCE 1998] |
| A. | 0 |
| B. | 1.2 |
| C. | 5 |
| D. | 25 |
| Answer» C. 5 | |
| 3211. |
The variance of the data 2, 4, 6, 8, 10 is [AMU 1992] |
| A. | 6 |
| B. | 7 |
| C. | 8 |
| D. | None of these |
| Answer» D. None of these | |
| 3212. |
Karl-Pearson?s coefficient of skewness of a distribution is 0.32. Its S.D. is 6.5 and mean 39.6. Then the median of the distribution is given by [Kurukshetra CEE 1991] |
| A. | 28.61 |
| B. | 38.81 |
| C. | 29.13 |
| D. | 28.31 |
| Answer» C. 29.13 | |
| 3213. |
The quartile deviation of daily wages (in Rs.) of 7 persons given below 12, 7, 15, 10, 17, 19, 25 is [Pb. CET 1991, 96; Kurukshetra CEE 1997] |
| A. | 14.5 |
| B. | 5 |
| C. | 9 |
| D. | 4.5 |
| Answer» E. | |
| 3214. |
In an experiment with 15 observations on x, the following results were available \[\sum {{x}^{2}}=2830\], \[\sum x=170\]. On observation that was 20 was found to be wrong and was replaced by the correct value 30. Then the corrected variance is [AIEEE 2003] |
| A. | 78.00 |
| B. | 188.66 |
| C. | 177.33 |
| D. | 8.33 |
| Answer» B. 188.66 | |
| 3215. |
The variance of a, b and g is 9, then variance of 5a, 5b and 5g is [AMU 1998] |
| A. | 45 |
| B. | 9/5 |
| C. | 5/9 |
| D. | 225 |
| Answer» E. | |
| 3216. |
Suppose values taken by a variable x are such that \[a\le {{x}_{i}}\le b\], where \[{{x}_{i}}\] denotes the value of x in the ith case for i = 1, 2, n. Then [Kurukshetra CEE 1995, 2000] |
| A. | \[a\le \text{Var}(x)\le b\] |
| B. | \[{{a}^{2}}\le \text{Var}(x)\le {{b}^{2}}\] |
| C. | \[\frac{{{a}^{2}}}{4}\le \text{Var}(x)\] |
| D. | \[{{(b-a)}^{2}}\ge \text{Var}(x)\] |
| Answer» E. | |
| 3217. |
Consider any set of observations \[{{x}_{1}},\,{{x}_{2}},\,.{{x}_{3}},.\,...,{{x}_{101}}\]; it being given that \[{{x}_{1}} |
| A. | \[{{x}_{1}}\] |
| B. | \[{{x}_{51}}\] |
| C. | \[\frac{{{x}_{1}}+{{x}_{2}}+...+{{x}_{101}}}{101}\] |
| D. | \[{{x}_{50}}\] |
| Answer» C. \[\frac{{{x}_{1}}+{{x}_{2}}+...+{{x}_{101}}}{101}\] | |
| 3218. |
For (2n+1) observations \[{{x}_{1}},\,-{{x}_{1}}\], \[{{x}_{2}},\,-{{x}_{2}},\,.....{{x}_{n}},\,-{{x}_{n}}\] and 0 where x?s are all distinct. Let S.D. and M.D. denote the standard deviation and median respectively. Then which of the following is always true [Orissa JEE 2002] |
| A. | S.D. < M.D. |
| B. | S.D. > M.D. |
| C. | S.D. = M.D. |
| D. | Nothing can be said in general about the relationship of S.D. and M.D. |
| Answer» C. S.D. = M.D. | |
| 3219. |
The S.D. of 5 scores 1, 2, 3, 4, 5 is [AMU 1991; DCE 2000] |
| A. | \[\frac{2}{5}\] |
| B. | \[\frac{3}{5}\] |
| C. | \[\sqrt{2}\] |
| D. | \[\sqrt{3}\] |
| Answer» D. \[\sqrt{3}\] | |
| 3220. |
The means of five observations is 4 and their variance is 5.2. If three of these observations are 1, 2 and 6, then the other two are [AMU 1994] |
| A. | 2 and 9 |
| B. | 3 and 8 |
| C. | 4 and 7 |
| D. | 5 and 6 |
| Answer» D. 5 and 6 | |
| 3221. |
The sum of squares of deviations for 10 observations taken from mean 50 is 250. The co-efficient of variation is [DCE 1996] |
| A. | 50% |
| B. | 10% |
| C. | 40% |
| D. | None of these |
| Answer» C. 40% | |
| 3222. |
The quartile deviation for the following data is x : 2 3 4 5 6 f : 3 4 8 4 1 [AMU 1988; Kurukshetra CEE 1999] |
| A. | 0 |
| B. | \[\frac{1}{4}\] |
| C. | \[\frac{1}{2}\] |
| D. | 1 |
| Answer» E. | |
| 3223. |
The standard deviation of 25 numbers is 40. If each of the numbers is increased by 5, then the new standard deviation will be [DCE 1995] |
| A. | 40 |
| B. | 45 |
| C. | \[40+\frac{21}{25}\] |
| D. | None of these |
| Answer» B. 45 | |
| 3224. |
The mean and S.D. of 1, 2, 3, 4, 5, 6 is |
| A. | \[\frac{7}{2},\,\sqrt{\frac{35}{12}}\] |
| B. | 3, 3 |
| C. | \[\frac{7}{2},\,\sqrt{3}\] |
| D. | \[3,\,\frac{35}{12}\] |
| Answer» B. 3, 3 | |
| 3225. |
The mean deviation from the mean for the set of observations ?1, 0, 4 is |
| A. | \[\sqrt{\frac{14}{3}}\] |
| B. | 2 |
| C. | \[\frac{2}{3}\] |
| D. | None of these |
| Answer» C. \[\frac{2}{3}\] | |
| 3226. |
For a given distribution of marks mean is 35.16 and its standard deviation is 19.76. The co-efficient of variation is |
| A. | \[\frac{35.16}{19.76}\] |
| B. | \[\frac{19.76}{35.16}\] |
| C. | \[\frac{35.16}{19.76}\times 100\] |
| D. | \[\frac{19.76}{35.16}\times 100\] |
| Answer» E. | |
| 3227. |
If 25% of the item are less than 20 and 25% are more than 40, the quartile deviation is |
| A. | 20 |
| B. | 30 |
| C. | 40 |
| D. | 10 |
| Answer» E. | |
| 3228. |
If v is the variance and s is the standard deviation, then [Kurukshetra CEE 1995] |
| A. | \[{{v}^{2}}=\sigma \] |
| B. | \[v={{\sigma }^{2}}\] |
| C. | \[v=\frac{1}{\sigma }\] |
| D. | \[v=\frac{1}{{{\sigma }^{2}}}\] |
| Answer» C. \[v=\frac{1}{\sigma }\] | |
| 3229. |
The range of following set of observations 2, 3, 5, 9, 8, 7, 6, 5, 7, 4, 3 is [DCE 1998] |
| A. | 11 |
| B. | 7 |
| C. | 5.5 |
| D. | 6 |
| Answer» C. 5.5 | |
| 3230. |
If M.D. is 12, the value of S.D. will be |
| A. | 15 |
| B. | 12 |
| C. | 24 |
| D. | None of these |
| Answer» B. 12 | |
| 3231. |
For a frequency distribution standard deviation is computed by applying the formula [Kurukshetra CEE 1999] |
| A. | \[\sigma =\sqrt{\left( \frac{\sum \,fd}{\sum \,f} \right)-\frac{\sum \,f{{d}^{2}}}{\sum \,f}}\] |
| B. | \[\sigma =\sqrt{\frac{\sum \,f{{d}^{2}}}{\sum \,f}-{{\left( \frac{\sum \,f{{d}^{2}}}{\sum \,f} \right)}^{2}}}\] |
| C. | \[\sigma =\sqrt{{{\left( \frac{\sum \,fd}{\sum \,f} \right)}^{2}}-\frac{\sum \,f{{d}^{2}}}{\sum \,f}}\] |
| D. | \[\sigma =\sqrt{\frac{\sum \,f{{d}^{2}}}{\sum \,f}-{{\left( \frac{\sum \,fd}{\sum \,f} \right)}^{2}}}\] |
| Answer» E. | |
| 3232. |
For a moderately skewed distribution, quartile deviation and the standard deviation are related by [AMU 1996] |
| A. | S.D.\[=\frac{2}{3}\]Q.D. |
| B. | S.D.\[=\frac{3}{2}\]Q.D. |
| C. | S.D.\[=\frac{3}{4}\]Q.D. |
| D. | S.D.\[=\frac{4}{3}\]Q.D. |
| Answer» C. S.D.\[=\frac{3}{4}\]Q.D. | |
| 3233. |
The variance of the first n natural numbers is [AMU 1994; SCRA 2001] |
| A. | \[\frac{{{n}^{2}}-1}{12}\] |
| B. | \[\frac{{{n}^{2}}-1}{6}\] |
| C. | \[\frac{{{n}^{2}}+1}{6}\] |
| D. | \[\frac{{{n}^{2}}+1}{12}\] |
| Answer» B. \[\frac{{{n}^{2}}-1}{6}\] | |
| 3234. |
The measure of dispersion is [DCE 1998] |
| A. | Mean deviation |
| B. | S.D. |
| C. | Quartile deviation |
| D. | All of these |
| Answer» E. | |
| 3235. |
The G.M. of the numbers \[3,\,{{3}^{2}},\,{{3}^{3}},\,......,\,{{3}^{n}}\] is [Pb. CET 1997] |
| A. | \[{{3}^{2/n}}\] |
| B. | \[{{3}^{(n-1)/2}}\] |
| C. | \[{{3}^{n/2}}\] |
| D. | \[{{3}^{(n+1)/2}}\] |
| Answer» E. | |
| 3236. |
If the arithmetic mean of the numbers \[{{x}_{1}},{{x}_{2}},{{x}_{3}},\,......,\,{{x}_{n}}\] is \[\bar{x}\], then the arithmetic mean of numbers \[a{{x}_{1}}+b,\,a{{x}_{2}}+b,\,a{{x}_{3}}+b,\,........,a{{x}_{n}}+b\], where a, b are two constants would be |
| A. | \[\bar{x}\] |
| B. | \[n\,a\bar{x}+nb\] |
| C. | \[a\bar{x}\] |
| D. | \[a\bar{x}+b\] |
| Answer» E. | |
| 3237. |
Consider the frequency distribution of the given numbers Value : 1 2 3 4 Frequency : 5 4 6 f If the mean is known to be 3, then the value of f is |
| A. | 3 |
| B. | 7 |
| C. | 10 |
| D. | 14 |
| Answer» E. | |
| 3238. |
The mean of a set of observation is \[\bar{x}\]. If each observation is divided by a, a ¹ 0 and then is increased by 10, then the mean of the new set is |
| A. | \[\frac{{\bar{x}}}{\alpha }\] |
| B. | \[\frac{\bar{x}+10}{\alpha }\] |
| C. | \[\frac{\bar{x}+10\alpha }{\alpha }\] |
| D. | \[\alpha \bar{x}+10\] |
| Answer» D. \[\alpha \bar{x}+10\] | |
| 3239. |
If the mean of the numbers \[27+x\], \[31+x\], \[89+x\], \[107+x,\,156+x\] is 82, then the mean of \[130+x,\,126+x,\,68+x,\,50+x,\,1+x\] is [Pb. CET 1989; Kurukshetra CEE 2000; Kerala (Engg.) 2001] |
| A. | 75 |
| B. | 157 |
| C. | 82 |
| D. | 80 |
| Answer» B. 157 | |
| 3240. |
Let \[{{x}_{1}},\,{{x}_{2}},....,{{x}_{n}}\] be n observations such that \[\sum x_{i}^{2}=400\] and \[\sum x_{i}^{{}}=80\]. Then a possible value of n among the following is [AIEEE 2005] |
| A. | 9 |
| B. | 12 |
| C. | 15 |
| D. | 18 |
| Answer» E. | |
| 3241. |
The class marks of a distribution are 6,10, 14, 18, 22, 26, 30 then the class size is [Pb. CET 2004] |
| A. | 4 |
| B. | 2 |
| C. | 5 |
| D. | 8 |
| Answer» B. 2 | |
| 3242. |
The mean weight per student in a group of seven students is 55 kg If the individual weights of 6 students are 52, 58, 55, 53, 56 and 54; then weights of the seventh student is [Pb. CET 2002] |
| A. | 55kg |
| B. | 60kg |
| C. | 57kg |
| D. | 50kg |
| Answer» D. 50kg | |
| 3243. |
The mean of discrete observations \[{{y}_{1}},\,{{y}_{2}},\,......,\,{{y}_{n}}\] is given by [DCE 1999] |
| A. | \[\frac{\sum\limits_{i=1}^{n}{{{y}_{i}}}}{n}\] |
| B. | \[\frac{\sum\limits_{i=1}^{n}{{{y}_{i}}}}{\sum\limits_{i=1}^{n}{i}}\] |
| C. | \[\frac{\sum\limits_{i=1}^{n}{{{y}_{i}}{{f}_{i}}}}{n}\] |
| D. | \[\frac{\sum\limits_{i=1}^{n}{{{y}_{i}}{{f}_{i}}}}{\sum\limits_{i=1}^{n}{{{f}_{i}}}}\] |
| Answer» B. \[\frac{\sum\limits_{i=1}^{n}{{{y}_{i}}}}{\sum\limits_{i=1}^{n}{i}}\] | |
| 3244. |
The mean of 5 numbers is 18. If one number is excluded, their mean becomes 16. Then the excluded number is [Pb. CET 2001] |
| A. | 18 |
| B. | 25 |
| C. | 26 |
| D. | 30 |
| Answer» D. 30 | |
| 3245. |
A school has four sections of chemistry in class XII having 40, 35, 45 and 42 students. The mean marks obtained in chemistry test are 50, 60, 55 and 45 respectively for the four sections, the over all average of marks per students is [Pb. CET 2000] |
| A. | 53 |
| B. | 45 |
| C. | 55.3 |
| D. | 52. 25 |
| Answer» E. | |
| 3246. |
Mean of 100 items is 49. It was discovered that three items which should have been 60, 70, 80 were wrongly read as 40, 20, 50 respectively. The correct mean is [Kurukshetra CEE 1994] |
| A. | 48 |
| B. | \[82\frac{1}{2}\] |
| C. | 50 |
| D. | 80 |
| Answer» D. 80 | |
| 3247. |
The harmonic mean of 4, 8, 16 is [AMU 1995] |
| A. | 6.4 |
| B. | 6.7 |
| C. | 6.85 |
| D. | 7.8 |
| Answer» D. 7.8 | |
| 3248. |
In a class of 100 students there are 70 boys whose average marks in a subject are 75. If the average marks of the complete class are 72, then what are the average marks of the girls [AIEEE 2002] |
| A. | 73 |
| B. | 65 |
| C. | 68 |
| D. | 74 |
| Answer» C. 68 | |
| 3249. |
If the mean of the distribution is 2.6, then the value of y is [Kurukshetra CEE 2001] Variate x 1 2 3 4 5 Frequency f of x 4 5 y 1 2 |
| A. | 24 |
| B. | 13 |
| C. | 8 |
| D. | 3 |
| Answer» D. 3 | |
| 3250. |
The A.M. of n observations is M. If the sum of \[n-4\] observations is a, then the mean of remaining 4 observations is |
| A. | \[\frac{n\,M-a}{4}\] |
| B. | \[\frac{n\,M+a}{2}\] |
| C. | \[\frac{n\,M-A}{2}\] |
| D. | n M + a |
| Answer» B. \[\frac{n\,M+a}{2}\] | |