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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.
| 7701. |
If the mean of the distribution is 2.6, then the value of y is 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 | |
| 7702. |
The mean of 100 observations is 50 and their standard deviation is 5. The sum of squares of all the observations is |
| A. | 50000 |
| B. | 250000 |
| C. | 252500 |
| D. | 255000 |
| Answer» D. 255000 | |
| 7703. |
If a variable takes the discrete values \[\alpha -4,\,\alpha -\frac{7}{2},\,\alpha -\frac{5}{2},\,\alpha -3,\,\alpha -2,\,\alpha +\frac{1}{2},\,\alpha -\frac{1}{2},\,\alpha +5\,(\alpha >0)\], then the median is [DCE 1997; Pb. CET 1988] |
| A. | \[\alpha -\frac{5}{4}\] |
| B. | \[\alpha -\frac{1}{2}\] |
| C. | \[\alpha -2\] |
| D. | \[\alpha +\frac{5}{4}\] |
| Answer» B. \[\alpha -\frac{1}{2}\] | |
| 7704. |
For a frequency distribution 7th decile is computed by the formula |
| A. | \[{{D}_{7}}=l+\frac{\left( \frac{N}{7}-C \right)}{f}\times i\] |
| B. | \[{{D}_{7}}=l+\frac{\left( \frac{N}{10}-C \right)}{f}\times i\] |
| C. | \[{{D}_{7}}=l+\frac{\left( \frac{7N}{10}-C \right)}{f}\times i\] |
| D. | \[{{D}_{7}}=l+\frac{\left( \frac{10N}{7}-C \right)}{f}\times i\] |
| Answer» D. \[{{D}_{7}}=l+\frac{\left( \frac{10N}{7}-C \right)}{f}\times i\] | |
| 7705. |
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 | |
| 7706. |
What is the standard deviation of the following series [DCE 1996] Measurements 0-10 10-20 20-30 30-40 Frequency 1 3 4 2 |
| A. | 81 |
| B. | 7.6 |
| C. | 9 |
| D. | 2.26 |
| Answer» D. 2.26 | |
| 7707. |
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. \[\frac{{{x}_{1}}+{{x}_{2}}+...+{{x}_{101}}}{101}\] | |
| 7708. |
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. | |
| 7709. |
If the variance of observations \[{{x}_{1}},\,{{x}_{2}},\,......{{x}_{n}}\] is \[{{\sigma }^{2}}\], then the variance of \[a{{x}_{1}},\,a{{x}_{2}}.......,\,a{{x}_{n}}\], a ¹ 0 is |
| A. | \[{{\sigma }^{2}}\] |
| B. | \[a\,{{\sigma }^{2}}\] |
| C. | \[{{a}^{2}}{{\sigma }^{2}}\] |
| D. | \[\frac{{{\sigma }^{2}}}{{{a}^{2}}}\] |
| Answer» D. \[\frac{{{\sigma }^{2}}}{{{a}^{2}}}\] | |
| 7710. |
If Q.D. is 16, the most likely value of S.D. will be |
| A. | 24 |
| B. | 42 |
| C. | 10 |
| D. | None of these |
| Answer» B. 42 | |
| 7711. |
\[{{d}_{i}}\] is the deviation of a class mark \[{{y}_{i}}\] from ?a? the assumed mean and \[{{f}_{i}}\] is the frequency, if \[{{M}_{g}}=x+\frac{1}{\sum {{f}_{i}}}(\sum {{f}_{i}}{{d}_{i}})\], then x is |
| A. | Lower limit |
| B. | Assumed mean |
| C. | Number of observations |
| D. | Class size |
| Answer» C. Number of observations | |
| 7712. |
If the mean of the set of numbers \[{{x}_{1}},\,{{x}_{2}},\,{{x}_{3}},\,.....,\,{{x}_{n}}\] is \[\bar{x}\], then the mean of the numbers \[{{x}_{i}}+2i\], \[1\le i\le n\] is [Pb. CET 1988] |
| A. | \[\bar{x}+2n\] |
| B. | \[\bar{x}+n+1\] |
| C. | \[\bar{x}+2\] |
| D. | \[\bar{x}+n\] |
| Answer» C. \[\bar{x}+2\] | |
| 7713. |
If \[{{\bar{x}}_{1}}\] and \[{{\bar{x}}_{2}}\] are the means of two distributions such that \[{{\bar{x}}_{1}} |
| A. | \[\bar{x}<{{\bar{x}}_{1}}\] |
| B. | \[\bar{x}>{{\bar{x}}_{2}}\] |
| C. | \[\bar{X}=\frac{{{{\bar{X}}}_{1}}+{{{\bar{X}}}_{2}}}{2}\] |
| D. | \[{{\bar{x}}_{1}}<\bar{x}<{{\bar{x}}_{2}}\] |
| Answer» E. | |
| 7714. |
The mean age of a combined group of men and women is 30 years. If the means of the age of men and women are respectively 32 and 27, then the percentage of women in the group is |
| A. | 30 |
| B. | 40 |
| C. | 50 |
| D. | 60 |
| Answer» C. 50 | |
| 7715. |
If the algebraic sum of deviations of 20 observations from 30 is 20, then the mean of observations is |
| A. | 30 |
| B. | 30.1 |
| C. | 29 |
| D. | 31 |
| Answer» E. | |
| 7716. |
If two sets A and B are having 99 elements in common, then the number of elements common to each of the sets \[A\times B\] and \[B\times A\] are [Kerala (Engg.) 2004] |
| A. | \[{{2}^{99}}\] |
| B. | \[{{99}^{2}}\] |
| C. | 100 |
| D. | 18 |
| Answer» C. 100 | |
| 7717. |
If \[A=\{1,\,2,\,3,\,4\}\]; \[B=\{a,\,b\}\] and f is a mapping such that \[f:A\to B\], then \[A\times B\] is [DCE 2005] |
| A. | {(a, 1), (3, b)} |
| B. | {(a, 2), (4, b)} |
| C. | {(1, a), (1, b), (2, a), (2, b), (3, a), (3, b), (4, a), (4, b)} |
| D. | None of these |
| Answer» D. None of these | |
| 7718. |
In a class of 30 pupils, 12 take needle work, 16 take physics and 18 take history. If all the 30 students take at least one subject and no one takes all three then the number of pupils taking 2 subjects is [J & K 2005] |
| A. | 16 |
| B. | 6 |
| C. | 8 |
| D. | 20 |
| Answer» B. 6 | |
| 7719. |
In a battle 70% of the combatants lost one eye, 80% an ear, 75% an arm, 85% a leg, x% lost all the four limbs. The minimum value of x is |
| A. | 10 |
| B. | 12 |
| C. | 15 |
| D. | None of these |
| Answer» B. 12 | |
| 7720. |
The number of proper subsets of the set {1, 2, 3} is [JMIEE 2000] |
| A. | 8 |
| B. | 7 |
| C. | 6 |
| D. | 5 |
| Answer» D. 5 | |
| 7721. |
The shaded region in the given figure is [NDA 2000] |
| A. | \[A\text{ }\cap \text{ }\left( B\text{ }\cup \text{ }C \right)\] |
| B. | \[A\text{ }\cup \text{ }\left( B\text{ }\cap \text{ }C \right)\] |
| C. | \[A\text{ }\cap \text{ }\left( B\text{ }-\text{ }C \right)\] |
| D. | \[A\text{ }-\text{ }\left( B\text{ }\cup \text{ }C \right)\] |
| Answer» E. | |
| 7722. |
If A and B are two sets, then \[A\cap (A\cup B{)}'\] is equal to |
| A. | A |
| B. | B |
| C. | \[\varphi \] |
| D. | None of these |
| Answer» D. None of these | |
| 7723. |
If A, B, C be three sets such that \[A\text{ }\cup \text{ }B\text{ }=\text{ }A\text{ }\cup \text{ }C\] and\[A\text{ }\cap \text{ }B\text{ }=\text{ }A\text{ }\cap \text{ }C,\] then [Roorkee 1991] |
| A. | A = B |
| B. | B = C |
| C. | A = C |
| D. | A = B = C |
| Answer» C. A = C | |
| 7724. |
If the set A has p elements, B has q elements, then the number of elements in A × B is [Karnataka CET 1999] |
| A. | \[p+q\] |
| B. | \[p+q+1\] |
| C. | \[pq\] |
| D. | \[{{p}^{2}}\] |
| Answer» D. \[{{p}^{2}}\] | |
| 7725. |
If A, B and C are any three sets, then A - (B U C) is equal to |
| A. | (A - B) U (A - C) |
| B. | (A - B) U (A - C) |
| C. | (A - B) U C |
| D. | (A - B) U C |
| Answer» C. (A - B) U C | |
| 7726. |
Let \[A=[x:x\in R,\,|x|\, |
| A. | \[[x:1<x\le 2]\] |
| B. | \[[x:1\le x<2]\] |
| C. | \[[x:1\le x\le 2]\] |
| D. | None of these |
| Answer» C. \[[x:1\le x\le 2]\] | |
| 7727. |
Two finite sets have m and n elements, the total number of subsets of the first set is 56 more than the total number of subsets of the second set. Then: |
| A. | \[m=3,n=6\] |
| B. | \[m=6,n=3\] |
| C. | \[m=5,n=6\] |
| D. | None of these |
| Answer» C. \[m=5,n=6\] | |
| 7728. |
Given \[n(U)=20,n(A)=12,n(B)=9,n(A\cap B)=4,\]where U is the universal set, A and B are subsets of U, then \[n({{(A\cup B)}^{c}})=\] |
| A. | 17 |
| B. | 9 |
| C. | 11 |
| D. | 3 |
| Answer» E. | |
| 7729. |
If A and B are two disjoint sets, then which one of the following is correct? |
| A. | \[A-B=A-(A\cap B)\] |
| B. | \[B-A'=A\cap B\] |
| C. | \[A\cap B=(A-B)\cap B\] |
| D. | All of these |
| Answer» B. \[B-A'=A\cap B\] | |
| 7730. |
If A, B and C are three finite sets, then what is \[\left[ (A\cup B)\cap C \right]'\] equal to? |
| A. | \[A'\cup B'\cap C'\] |
| B. | \[A'\cap B'\cap C'\] |
| C. | \[A'\cap B'\cup C'\] |
| D. | \[A\cap B\cap C\] |
| Answer» D. \[A\cap B\cap C\] | |
| 7731. |
\[{{x}^{2}}=xy\] is a relation which is [Orissa JEE 2005] |
| A. | Symmetric |
| B. | Reflexive |
| C. | Transitive |
| D. | None of these |
| Answer» C. Transitive | |
| 7732. |
The relation R is defined on the set of natural numbers as {(a, b) : a = 2b}. Then \[{{R}^{-1}}\] is given by |
| A. | {(2, 1), (4, 2), (6, 3).....} |
| B. | {(1, 2), (2, 4), (3, 6)....} |
| C. | \[{{R}^{-1}}\] is not defined |
| D. | None of these |
| Answer» C. \[{{R}^{-1}}\] is not defined | |
| 7733. |
Let R be a relation over the set N × N and it is defined by \[(a,\,b)R(c,\,d)\Rightarrow a+d=b+c.\] Then R is |
| A. | Reflexive only |
| B. | Symmetric only |
| C. | Transitive only |
| D. | An equivalence relation |
| Answer» E. | |
| 7734. |
R is a relation over the set of real numbers and it is given by \[nm\ge 0\]. Then R is |
| A. | Symmetric and transitive |
| B. | Reflexive and symmetric |
| C. | A partial order relation |
| D. | An equivalence relation |
| Answer» E. | |
| 7735. |
The relation R defined on a set A is antisymmetric if \[(a,\,b)\in R\Rightarrow (b,\,a)\in R\] for |
| A. | Every (a, b) \[\in R\] |
| B. | No \[(a,\,b)\in R\] |
| C. | No \[(a,\,b),\,a\ne b,\,\in R\] |
| D. | None of these |
| Answer» D. None of these | |
| 7736. |
An integer m is said to be related to another integer n if m is a multiple of n. Then the relation is |
| A. | Reflexive and symmetric |
| B. | Reflexive and transitive |
| C. | Symmetric and transitive |
| D. | Equivalence relation |
| Answer» C. Symmetric and transitive | |
| 7737. |
Let A = {1, 2, 3}, B = {1, 3, 5}. If relation R from A to B is given by R ={(1, 3), (2, 5), (3, 3)}. Then \[{{R}^{-1}}\] is |
| A. | {(3, 3), (3, 1), (5, 2)} |
| B. | {(1, 3), (2, 5), (3, 3)} |
| C. | {(1, 3), (5, 2)} |
| D. | None of these |
| Answer» B. {(1, 3), (2, 5), (3, 3)} | |
| 7738. |
Let \[X=\{1,\,2,\,3,\,4,\,5\}\] and \[Y=\{1,\,3,\,5,\,7,\,9\}\]. Which of the following is/are relations from X to Y |
| A. | \[{{R}_{1}}=\{(x,\,y)|y=2+x,\,x\in X,\,y\in Y\}\] |
| B. | \[{{R}_{2}}=\{(1,\,1),\,(2,\,1),\,(3,\,3),\,(4,\,3),\,(5,\,5)\}\] |
| C. | \[{{R}_{3}}=\{(1,\,1),\,(1,\,3)(3,\,5),\,(3,\,7),\,(5,\,7)\}\] |
| D. | \[{{R}_{4}}=\{(1,\,3),\,(2,\,5),\,(2,\,4),\,(7,\,9)\}\] |
| Answer» C. \[{{R}_{3}}=\{(1,\,1),\,(1,\,3)(3,\,5),\,(3,\,7),\,(5,\,7)\}\] | |
| 7739. |
Let n = n. Then the number of all relations on A is |
| A. | \[{{2}^{n}}\] |
| B. | \[{{2}^{(n)!}}\] |
| C. | \[{{2}^{{{n}^{2}}}}\] |
| D. | None of these |
| Answer» D. None of these | |
| 7740. |
If A={0},B={l, 2}, and C={3}, then\[A\times B\times C\]is |
| A. | {(0, 1, 3), (0, 2, 3)} |
| B. | {(0, 1, 2), (0, 2, 3)} |
| C. | \[\phi \] |
| D. | {(0, 2, 3), (1, 2, 3)} |
| Answer» B. {(0, 1, 2), (0, 2, 3)} | |
| 7741. |
Number of solutions of the equation \[\left| 2-\left| x \right| \right|=x+4\] is _________. |
| A. | 2 |
| B. | 4 |
| C. | 1 |
| D. | 5 |
| Answer» D. 5 | |
| 7742. |
If A = {x|x \[\in \] N and x \[\le \] 5}, B = {2, 3, 6, 7} then \[(A-B)\cap (B-A)\] |
| A. | {1, 4, 5, 6, 7} |
| B. | {1, 4, 5} |
| C. | {6, 7} |
| D. | \[\phi \] |
| Answer» E. | |
| 7743. |
If A=\[\{x|x\in \,N\,\]and \[({{x}^{2}}-4)\]\[({{x}^{2}}-5)\]=0} and B=\[\{x|x\in {{l}^{+}}\]and \[x(x-1)\]\[(x-2)\]=0} then \[(A\cup B)\]-\[(A\cap B)\]is |
| A. | {1, 2} |
| B. | {1} |
| C. | {2} |
| D. | \[\phi \] |
| Answer» C. {2} | |
| 7744. |
The roots of the equation \[{{(x-1)}^{2}}-4\left| x-1 \right|+3=0\] |
| A. | Form an A.P. |
| B. | Form a G.P. |
| C. | Form an H.P. |
| D. | Do not form any progression |
| Answer» B. Form a G.P. | |
| 7745. |
The least value of n (a natural number), for which the sum S of the series \[1+\frac{1}{2}+\frac{1}{{{2}^{2}}}+\frac{1}{{{2}^{3}}}+.....\]differs from \[{{S}_{n}}\] by a quantity \[ |
| A. | 21 |
| B. | 20 |
| C. | 19 |
| D. | None |
| Answer» B. 20 | |
| 7746. |
The sum of \[\frac{\frac{1}{2}.\frac{2}{2}}{{{1}^{3}}}+\frac{\frac{2}{2}.\frac{3}{2}}{{{1}^{3}}+{{2}^{3}}}+\frac{\frac{3}{2}.\frac{4}{2}}{{{1}^{3}}+{{2}^{3}}+{{3}^{3}}}+.....\] upto n terms is equal to |
| A. | \[\frac{n-1}{n}\] |
| B. | \[\frac{n}{n+1}\] |
| C. | \[\frac{n+1}{n+2}\] |
| D. | \[\frac{n+1}{n}\] |
| Answer» C. \[\frac{n+1}{n+2}\] | |
| 7747. |
The 100th term of the sequence 1, 2, 2, 3, 3, 3, 4, 4, 4, 4,... is |
| A. | 12 |
| B. | 13 |
| C. | 14 |
| D. | 15 |
| Answer» D. 15 | |
| 7748. |
If the positive integers a, b, c, d are in AP, then the numbers abc, abd, acd, bcd are in |
| A. | HP |
| B. | AP |
| C. | GP |
| D. | None of the above |
| Answer» B. AP | |
| 7749. |
If the nth term of an arithmetic progression is\[3n+7\], then what is the sum of its first 50 terms? |
| A. | 3925 |
| B. | 4100 |
| C. | 4175 |
| D. | 8200 |
| Answer» D. 8200 | |
| 7750. |
If a, b, c are positive numbers, then least value of\[(a+b+c)\left( \frac{1}{a}+\frac{1}{b}+\frac{1}{c} \right)\] is |
| A. | 1 |
| B. | 6 |
| C. | 9 |
| D. | None |
| Answer» D. None | |