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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.
| 2851. |
The median of a set of nine distinct observations is 20.5 if each of the largest four observations of the set is increased by 2, then the median of the new set |
| 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. | |
| 2852. |
Consider the following statements: I. Mode can be computed from histogram. II. Median is not independent of change of scale. III. Variance is independent of change of origin and scale. Which of these is/ are correct? |
| A. | only I |
| B. | only II |
| C. | only I and II |
| D. | I, II and III |
| Answer» D. I, II and III | |
| 2853. |
The mean deviation of the data 3, 10, 10, 4, 7, 10, 5 from the mean is |
| A. | 2 |
| B. | 2.57 |
| C. | 3 |
| D. | 3.75 |
| Answer» C. 3 | |
| 2854. |
Let\[{{x}_{1}},{{x}_{2}},{{x}_{3}},{{x}_{4}}\]and\[{{x}_{5}}\]be the observations with mean m and standard deviation s. The standard deviation of the observations \[k{{x}_{1}},\]\[k{{x}_{2}},\]\[k{{x}_{3}},\]\[k{{x}_{4}},\]and \[k{{x}_{5}},\] is |
| A. | \[k+s\] |
| B. | s/k |
| C. | ks |
| D. | s |
| Answer» D. s | |
| 2855. |
Standard deviation for first 10 natural numbers is |
| A. | 5.5 |
| B. | 3.87 |
| C. | 2.97 |
| D. | 2.87 |
| Answer» E. | |
| 2856. |
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. | 10 K |
| Answer» B. \[K+10\] | |
| 2857. |
For\[\left( 2n+1 \right)\] observations \[{{x}_{1}},{}^{-}{{x}_{1}},\,\,{{x}_{2}},{}^{-}{{x}_{2}},\,\,...,\,\,{{x}_{n}},\,{{\,}^{-}}{{x}_{n}}\] and 0, where all x's are distinct, let SD and MD denote the standard deviation and median, respectively. Then which of the following is always true? |
| A. | SD>MD |
| B. | SD>MD |
| C. | SD=MD |
| D. | Nothing can be said in general about the relationship between SD and MD |
| Answer» C. SD=MD | |
| 2858. |
The variance of the data 2, 4, 6, 8, 10 is |
| A. | 6 |
| B. | 7 |
| C. | 8 |
| D. | None of these |
| Answer» D. None of these | |
| 2859. |
The mean of a set of numbers is \[\bar{X}\]if each number is divided by 3, then the new mean is |
| A. | \[\bar{X}\] |
| B. | \[\bar{X}+3\] |
| C. | \[3\bar{X}\] |
| D. | \[\frac{{\bar{X}}}{3}\] |
| Answer» E. | |
| 2860. |
The following data give the distribution of heights of students: Height (in cm) 160 150 152 152 161 154 155 Name of students 12 8 4 4 3 3 7 The median of the distribution is |
| A. | 154 |
| B. | 155 |
| C. | 160 |
| D. | 161 |
| Answer» C. 160 | |
| 2861. |
If A = {2, 3, 7, 9}, B = {3, 7, 8}, then \[A\,\Delta \,B\]is |
| A. | {3, 7} |
| B. | {2, 8, 9} |
| C. | {2, 3, 7, 8, 9} |
| D. | {3, 8, 9} |
| Answer» C. {2, 3, 7, 8, 9} | |
| 2862. |
If A = {1, 2, 3, 4, 5} and B = {2, 3, 6, 7} then the number of elements in \[(A\times B)\cap (B\times A)\] is |
| A. | 20 |
| B. | 18 |
| C. | 6 |
| D. | 4 |
| Answer» E. | |
| 2863. |
If y =\[\left| x \right|+\left| x-1 \right|\]. then for x \[\le \] 0, y is equal to |
| A. | 2x-l |
| B. | 1 |
| C. | 1 - 2x |
| D. | x + 1 |
| Answer» D. x + 1 | |
| 2864. |
If. A={x|\[{{x}^{2}}\]-5x+6=0},B={0,3,4}, C= {x\[\in \] N and x\[\le \]3} then\[(A-B)\times (C-B)\]is |
| A. | {(2, 1), (2, 4)} |
| B. | {(2, 1), (2, 2)} |
| C. | {(2, 1), (2, 2), (3, 2)} |
| D. | {(2, 2), (3, 2)} |
| Answer» C. {(2, 1), (2, 2), (3, 2)} | |
| 2865. |
If A= {2, 3, 5}, B = {2, 6, 9}, C = {6, 7, 8} and U= {x|x \[\in \] N and x < 10} then\[A\cup (B\cap C)\] is |
| A. | {2, 3, 5, 6} |
| B. | {3, 5, 6, 9} |
| C. | {2, 3, 4, 5, 7, 8, 9} |
| D. | {2, 3, 5, 6, 7, 8, 9} |
| Answer» B. {3, 5, 6, 9} | |
| 2866. |
The number of non-trivial subsets of a set with 5 elements is |
| A. | 32 |
| B. | 34 |
| C. | 30 |
| D. | 35 |
| Answer» D. 35 | |
| 2867. |
The number of integral values of x if 5x-1 |
| A. | 4 |
| B. | 6 |
| C. | 2 |
| D. | 1 |
| Answer» E. | |
| 2868. |
Sum of solutions of the equation \[{{\left| x \right|}^{3}}-4{{\left| x \right|}^{2}}+3\left| x=0 \right|\] is _________. |
| A. | 5 |
| B. | 2 |
| C. | 3 |
| D. | 0 |
| Answer» E. | |
| 2869. |
in statistical survey of 1003 families of Kolkata, it was found that 63 families has neither a radio nor a TV. 794 families has a radio and 187 has TV. The number of families in that group having both a radio and a TV is ________. |
| A. | 40 |
| B. | 41 |
| C. | 42 |
| D. | 43 |
| Answer» C. 42 | |
| 2870. |
In a town of 10,000 families, it was found that 40% families buy newspaper A, 20% buy newspaper B and 10% buy newspaper C. Also, 5% families buy newspapers A and B 3% buy newspapers B and C and 4% buy newspapers A and C. if 2% families buy all the three newspapers, then number of families which buy newspaper A only is _________. |
| A. | 3300 |
| B. | 3200 |
| C. | 3000 |
| D. | 3400 |
| Answer» B. 3200 | |
| 2871. |
If A=\[\{x|{{x}^{3}}-3{{x}^{2}}+2x=0\}\],B=\[\{x|{{x}^{2}}-2x=0\}\], then B-A is |
| A. | {2} |
| B. | {0} |
| C. | \[\phi \] |
| D. | {1} |
| Answer» D. {1} | |
| 2872. |
Let U be the universal set and \[A\cup B\cup C=U\]. Then \[[(A-B)\cup (B-C)\cup (C-A)]'\]equals |
| A. | \[A\cup B\cup C\] |
| B. | \[A\cap B\cap C\] |
| C. | \[A\cup (B\cap C)\] |
| D. | \[A\cap (B\cup C)\] |
| Answer» C. \[A\cup (B\cap C)\] | |
| 2873. |
if the sets A and B are defined as A=\[\{(x,y)|y=1/x,x\ne 0,x\in R\}\] B=\[\{(x,y)|y=-x,x\in R\}\] Then |
| A. | \[A\cap B=A\] |
| B. | \[A\cap B=B\] |
| C. | \[A\cap B=\phi \] |
| D. | \[A\cup B=A\] |
| Answer» D. \[A\cup B=A\] | |
| 2874. |
The set \[(A\cap B')'\cup (B\cap C)\]is equal to |
| A. | \[A'\cup B\cup C\] |
| B. | \[A'\cup B\] |
| C. | \[A'\cup C'\] |
| D. | \[A'\cap B\] |
| Answer» C. \[A'\cup C'\] | |
| 2875. |
Let \[{{F}_{1}}\]be the set of parallelograms, \[{{F}_{2}}\] the set of rectangles, \[{{F}_{3}}\] be the set of rhombuses, \[{{F}_{4}}\] be the set of squares and \[{{F}_{5}}\] be the set of trapeziums in a plane. Then \[{{F}_{1}}\] may be equal to |
| A. | \[{{F}_{2}}\cap {{F}_{3}}\] |
| B. | \[{{F}_{3}}\cap {{F}_{4}}\] |
| C. | \[{{F}_{2}}\cup {{F}_{5}}\] |
| D. | \[{{F}_{2}}\cup {{F}_{3}}\cup {{F}_{4}}\cup {{F}_{1}}\] |
| Answer» E. | |
| 2876. |
Number of integers satisfying the inequality, \[{{x}^{4}}-29{{x}^{2}}+100\le 0\]is |
| A. | 2 |
| B. | 4 |
| C. | 6 |
| D. | 8 |
| Answer» E. | |
| 2877. |
If A x B = {(1, 0), (1, 2), (2, 3), (1, 3), (0, 2)}, then A and B are respectively |
| A. | {1, 2} and {0, 2, 3} |
| B. | {1, 2, 0} and {0, 2} |
| C. | {1, 2, 0} and {0, 2, 3} |
| D. | {1, 2} and {2, 3} |
| Answer» D. {1, 2} and {2, 3} | |
| 2878. |
If A contains m elements and B contains n elements, then total number of distinct relations from a set A to a set B is |
| A. | \[mn\] |
| B. | \[{{2}^{n}}\] |
| C. | \[{{2}^{m}}\] |
| D. | \[{{2}^{mn}}\] |
| Answer» E. | |
| 2879. |
If A and B have n elements in common, then the number of elements common to A x B and B x is |
| A. | \[n\] |
| B. | \[2n\] |
| C. | \[{{n}^{2}}\] |
| D. | 0 |
| Answer» D. 0 | |
| 2880. |
If \[{{a}_{1}},{{a}_{2}},{{a}_{3}}....{{a}_{n}}\]are in H.P. and \[f(k)=\left( \sum\limits_{r=1}^{n}{{{a}_{r}}} \right)-{{a}_{k}}\]then \[\frac{{{a}_{1}}}{f(1)},\frac{{{a}_{2}}}{f(2)},\frac{{{a}_{3}}}{f(3)},...\frac{{{a}_{n}}}{f(n)}\]are in |
| A. | A.P |
| B. | G.P |
| C. | H.P |
| D. | none of these |
| Answer» D. none of these | |
| 2881. |
If a, b, and c are in A.P., p, q, and r are in H.P., and ap, bq, and cr are in G.P., then \[\frac{p}{r}+\frac{r}{p}\]is equal to |
| A. | \[\frac{a}{c}-\frac{c}{a}\] |
| B. | \[\frac{a}{c}+\frac{c}{a}\] |
| C. | \[\frac{b}{q}+\frac{q}{b}\] |
| D. | \[\frac{b}{q}-\frac{q}{b}\] |
| Answer» C. \[\frac{b}{q}+\frac{q}{b}\] | |
| 2882. |
If \[{{S}_{n}}\]denotes the sum of first n terms of an A.P. whose first term is a and \[{{S}_{nx}}/{{S}_{x}}\]is independent of x, then \[{{S}_{p}}=\] |
| A. | \[{{p}^{3}}\] |
| B. | \[{{p}^{2}}a\] |
| C. | \[p{{a}^{2}}\] |
| D. | \[{{a}^{3}}\] |
| Answer» C. \[p{{a}^{2}}\] | |
| 2883. |
The largest term common to the sequences 1, 11, 21, 31 ,..to 100 terms and 31, 36, 41, 46,..to 100 terms is |
| A. | 381 |
| B. | 471 |
| C. | 281 |
| D. | none of these |
| Answer» E. | |
| 2884. |
If the sum of n terms of an A.P. is cn (n - 1), where \[c\ne 0\]then the sum of the squares of these term is |
| A. | \[{{c}^{n}}n{{(n+1)}^{2}}\] |
| B. | \[\frac{2}{3}{{c}^{2}}n(n-1)(2n-1)\] |
| C. | \[\frac{2{{c}^{2}}}{3}n(n+1)(2n+1)\] |
| D. | none of these |
| Answer» C. \[\frac{2{{c}^{2}}}{3}n(n+1)(2n+1)\] | |
| 2885. |
If \[{{a}_{1}},{{a}_{2}}....{{a}_{n}}\]are in H.P., then the expression \[{{a}_{1}}{{a}_{2}}+{{a}_{2}}{{a}_{3}}\]+...+\[{{a}_{n}}{{-}_{1}}{{a}_{n}}\]is equal to |
| A. | \[n({{a}_{1}}-{{a}_{n}})\] |
| B. | \[(n-1)({{a}_{1}}-{{a}_{n}})\] |
| C. | \[n{{a}_{1}}{{a}_{n}}\] |
| D. | \[(n-1){{a}_{1}}{{a}_{n}}\] |
| Answer» E. | |
| 2886. |
If x, y, z are real and \[4{{x}^{2}}+9{{y}^{2}}+16{{z}^{2}}-6xy-12yz-8zx=0\], then x, y, z are in |
| A. | A.P |
| B. | G.P. |
| C. | H.P. |
| D. | none of these |
| Answer» D. none of these | |
| 2887. |
If a, b, c and d are in H.P. then |
| A. | \[{{a}^{2}}+{{c}^{2}}>{{b}^{2}}+{{d}^{2}}\] |
| B. | \[{{a}^{2}}+{{d}^{2}}>{{b}^{2}}+{{c}^{2}}\] |
| C. | \[ac+bd>{{b}^{2}}+{{c}^{2}}\] |
| D. | \[ac+bd>{{b}^{2}}+{{d}^{2}}\] |
| Answer» D. \[ac+bd>{{b}^{2}}+{{d}^{2}}\] | |
| 2888. |
The sum of the series \[\frac{x}{1-{{x}^{2}}}+\frac{{{x}^{2}}}{1-{{x}^{4}}}+\frac{{{x}^{4}}}{1-{{x}^{8}}}+...\]to infinite terms, if \[\left| x \right| |
| A. | \[\frac{x}{1-x}\] |
| B. | \[\frac{1}{1-x}\] |
| C. | \[\frac{1+x}{1-x}\] |
| D. | 1 |
| Answer» B. \[\frac{1}{1-x}\] | |
| 2889. |
Let \[S=\frac{4}{19}+\frac{44}{{{19}^{2}}}+\frac{444}{{{19}^{3}}}+...\]up to \[\infty \]. Then S is equal to |
| A. | 40/9 |
| B. | 38/81 |
| C. | 36/171 |
| D. | none of these |
| Answer» C. 36/171 | |
| 2890. |
Sum of the series \[\frac{2}{3}+\frac{8}{9}+\frac{26}{27}+\frac{80}{81}+...\]to n terms is |
| A. | \[n-\frac{1}{2}({{3}^{n}}-1)\] |
| B. | \[n+\frac{1}{2}({{3}^{n}}-1)\] |
| C. | \[n+\frac{1}{2}(1-{{3}^{-n}})\] |
| D. | \[n+\frac{1}{2}({{3}^{-n}}-1)\] |
| Answer» E. | |
| 2891. |
If \[{{x}_{1}},{{x}_{2}},.....{{x}_{20}}\]are in H.P. and \[{{x}_{1}},2,{{x}_{20}}\]are in G.P., then \[\sum\limits_{r=1}^{19}{{{x}_{r}}{{x}_{r+1}}}\]= |
| A. | 76 |
| B. | 80 |
| C. | 84 |
| D. | none of these |
| Answer» B. 80 | |
| 2892. |
if a, b, c are in A.P., then\[\frac{a}{bc},\frac{1}{c},\frac{2}{b}\] will be in |
| A. | A.P. |
| B. | G.P. |
| C. | H.P. |
| D. | none of these |
| Answer» E. | |
| 2893. |
a, b, c, d,\[\in {{R}^{+}}\] such that a, b, and c are in A.P. and b, c and , d are in H.P., then |
| A. | ab = cd |
| B. | ac = bd |
| C. | bc = ad |
| D. | None of these |
| Answer» D. None of these | |
| 2894. |
If \[{{S}_{n}}\]denotes the sum of first n terms of an A.P. and \[\frac{{{S}_{3n}}-{{S}_{n-1}}}{{{S}_{2n}}-{{S}_{2n-1}}}=31\], then the value of n is |
| A. | 21 |
| B. | 15 |
| C. | 16 |
| D. | 19 |
| Answer» C. 16 | |
| 2895. |
If \[f(x)\] is an invertible function and \[g\left( x \right)=2f\left( x \right)+5,\] then the value of \[{{g}^{-1}}(x)\] is |
| A. | \[2{{f}^{-1}}(x)-5\] |
| B. | \[\frac{1}{2{{f}^{-1}}(x)+5}\] |
| C. | \[\frac{1}{2}{{f}^{-1}}(x)=5\] |
| D. | \[{{f}^{-1}}\left( \frac{x-5}{2} \right)\] |
| Answer» E. | |
| 2896. |
The function \[f:(-\infty ,-1)\to \left( 0,{{e}^{5}} \right]\] defined by \[f(x)={{e}^{{{x}^{3-3x+2}}}}\] is |
| A. | many-one and onto |
| B. | many-one and into |
| C. | one-one and onto |
| D. | one-one and into |
| Answer» E. | |
| 2897. |
The range of the function \[f(x)=\left| x-1 \right|+\left| x-2 \right|,-1\le x\le 3\] is |
| A. | \[\left[ 1,\text{ }3 \right]\] |
| B. | \[[1\text{ },5]\] |
| C. | \[\left[ 3,\text{ }5 \right]\] |
| D. | none of these |
| Answer» C. \[\left[ 3,\text{ }5 \right]\] | |
| 2898. |
The range of \[f(x)=si{{n}^{-1}}(\sqrt{{{x}^{2}}+x+1})\] is |
| A. | \[\left( 0,\frac{\pi }{2} \right]\] |
| B. | \[\left( 0,\frac{\pi }{3} \right]\] |
| C. | \[\left[ \frac{\pi }{3},\frac{\pi }{2} \right]\] |
| D. | \[\left[ \frac{\pi }{6},\frac{\pi }{3} \right]\] |
| Answer» D. \[\left[ \frac{\pi }{6},\frac{\pi }{3} \right]\] | |
| 2899. |
The domain of the function \[f(x)={{\left[ {{\log }_{10}}\left( \frac{5x-{{x}^{2}}}{4} \right) \right]}^{1/2}}\]is |
| A. | \[-\infty <x<\infty \] |
| B. | \[1\le x\le 4\] |
| C. | \[4\le x\le 16\] |
| D. | \[-1\le x\le 3\] |
| Answer» C. \[4\le x\le 16\] | |
| 2900. |
Let \[R=\left\{ \left( 1,3 \right),\left( 4,2 \right),\left( 2,4 \right),\left( 2,3 \right),\left( 3,1 \right) \right\}\] be a relation on the set \[A=\left\{ 1,2,3,4 \right\}.\]The relation R is |
| A. | a function |
| B. | reflexive |
| C. | not symmetric |
| D. | transitive |
| Answer» D. transitive | |