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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.
| 7851. |
An anti-aircraft gun can take a maximum of four shots at any plane moving away from it. The probabilities of hitting the plane at the 1st, 2nd, 3rd and 4th shots are 0.4, 0.3, 0.2 and 0.1 respectively. What is the probability that at least one shot hits the plane? |
| A. | \[0.6976\] |
| B. | \[0.3024\] |
| C. | 0.72 |
| D. | 0.6431 |
| Answer» B. \[0.3024\] | |
| 7852. |
For k=1, 2, 3 the box \[{{B}_{k}}\] contains k red balls and \[(k+1)\] white balls. Let \[P({{B}_{1}})=\frac{1}{2},P({{B}_{2}})=\frac{1}{3}\]and \[P({{B}_{3}})=\frac{1}{6}.\] A box is selected at random and a ball is drawn from it, if a red ball is drawn, then the probability that it has come from box \[{{B}_{2}}\], is |
| A. | \[\frac{35}{78}\] |
| B. | \[\frac{14}{39}\] |
| C. | \[\frac{10}{13}\] |
| D. | \[\frac{12}{13}\] |
| Answer» C. \[\frac{10}{13}\] | |
| 7853. |
The mode of the binomial distribution for which mean and standard deviation are 10 and \[\sqrt{5}\] respectively is |
| A. | 7 |
| B. | 8 |
| C. | 9 |
| D. | 10 |
| Answer» E. | |
| 7854. |
If A and B are two events such that \[P(A)\ne 0\] and \[P(B)\ne 1,\] then \[P\left( \frac{\overline{A}}{\overline{B}} \right)=\] |
| A. | \[1-P\left( \frac{A}{B} \right)\] |
| B. | \[1-P\left( \frac{\overline{A}}{B} \right)\] |
| C. | \[\frac{1-P(A\cup B)}{P(\overline{B})}\] |
| D. | \[\frac{P(\overline{A})}{P(\overline{B})}\] |
| Answer» D. \[\frac{P(\overline{A})}{P(\overline{B})}\] | |
| 7855. |
Given two independent events, if the probability that exactly one of them occurs is \[\frac{26}{49}\] and the probability that none of them occurs is \[\frac{15}{49},\] then the probability of more probable of the two events is: |
| A. | 44381 |
| B. | 44383 |
| C. | 44380 |
| D. | 44382 |
| Answer» B. 44383 | |
| 7856. |
There are n letters and n addressed envelopes, the probability that all the letters are not kept in the right envelope, is |
| A. | \[\frac{1}{n!}\] |
| B. | \[1-\frac{1}{n!}\] |
| C. | \[1-\frac{1}{n}\] |
| D. | None of these |
| Answer» C. \[1-\frac{1}{n}\] | |
| 7857. |
A boy is throwing stones at a target. The probability of hitting the target at any trial is \[\frac{1}{2}\]. The probability of hitting the target 5th time at the 10th throw is: |
| A. | \[\frac{5}{{{2}^{10}}}\] |
| B. | \[\frac{63}{{{2}^{9}}}\] |
| C. | \[\frac{^{10}{{C}_{5}}}{{{2}^{10}}}\] |
| D. | None of these |
| Answer» C. \[\frac{^{10}{{C}_{5}}}{{{2}^{10}}}\] | |
| 7858. |
If X follows a binomial distribution with parameter n=8 and \[p=\frac{1}{2}\], then \[P(\left| X-4 \right|\le 2)\] is |
| A. | \[\frac{119}{128}\] |
| B. | \[\frac{119}{228}\] |
| C. | \[\frac{19}{128}\] |
| D. | \[\frac{18}{128}\] |
| Answer» B. \[\frac{119}{228}\] | |
| 7859. |
If \[{{E}_{1}}\] and \[{{E}_{2}}\] are two events such that \[P({{E}_{1}})=1/4,P({{E}_{2}}/{{E}_{1}})=1/2\] and \[P({{E}_{1}}/{{E}_{2}})=1/4\], then choose the incorrect statement. |
| A. | \[{{E}_{1}}and{{E}_{2}}\] are independent |
| B. | \[{{E}_{1}}\] and \[{{E}_{2}}\] are exhaustive |
| C. | \[{{E}_{2}}\] is twice as likely to occur as \[{{E}_{1}}\] |
| D. | Probabilities of the events\[{{E}_{1}}\cap {{E}_{2}}\], \[{{E}_{1}}\] and \[{{E}_{2}}\] are in GP. |
| Answer» C. \[{{E}_{2}}\] is twice as likely to occur as \[{{E}_{1}}\] | |
| 7860. |
A man and a woman appear in an interview for two vacancies in the same post. The probability of man?s selection is ¼ and that of the woman?s selection is 1/3. Then the probability that none of them will be selected is. |
| A. | \[\frac{1}{2}\] |
| B. | \[\frac{3}{4}\] |
| C. | \[\frac{2}{3}\] |
| D. | \[\frac{2}{5}\] |
| Answer» B. \[\frac{3}{4}\] | |
| 7861. |
Three letters are written to three different persons and addresses on the three envelopes are also written. Without looking in the addresses, the letters are kept in these envelopes. The probability that all the letters are not placed into their right envelopes is |
| A. | \[\frac{1}{2}\] |
| B. | \[\frac{1}{3}\] |
| C. | \[\frac{1}{6}\] |
| D. | \[\frac{5}{6}\] |
| Answer» C. \[\frac{1}{6}\] | |
| 7862. |
A fair die is tossed eight times. The probability that a third six is observed on the eighth throw is |
| A. | \[^{7}{{C}_{2}}\frac{{{5}^{5}}}{{{6}^{8}}}\] |
| B. | \[^{7}{{C}_{3}}\frac{{{5}^{3}}}{{{6}^{8}}}\] |
| C. | \[^{7}{{C}_{6}}\frac{{{5}^{6}}}{{{6}^{8}}}\] |
| D. | None of these |
| Answer» B. \[^{7}{{C}_{3}}\frac{{{5}^{3}}}{{{6}^{8}}}\] | |
| 7863. |
Probability that a man who is 40 year old, living till 75 years is 5/16, and another man who is 35 years old living till 70 years is 3/7 then what is the probability that at least one of them will be alive till 35 years hence? |
| A. | 47058 |
| B. | 19/28 |
| C. | 17/28 |
| D. | None of these |
| Answer» D. None of these | |
| 7864. |
A man is known to speak the truth 3 out of 4 times. He throws a die and reports that it is a six. The probability that it is actually a six is |
| A. | \[\frac{3}{8}\] |
| B. | \[\frac{1}{5}\] |
| C. | \[\frac{3}{4}\] |
| D. | \[\frac{1}{2}\] |
| Answer» B. \[\frac{1}{5}\] | |
| 7865. |
A father has 3 children with at least one boy. The probability that he has 2 boys and 1 girl is |
| A. | \[1/4\] |
| B. | \[1/3\] |
| C. | \[2/3\] |
| D. | None of these |
| Answer» C. \[2/3\] | |
| 7866. |
In a binomial distribution \[B\left( n,p=\frac{1}{4} \right)\], if the probability of at least one success is greater than or equal to \[\frac{9}{10}\], then n is greater than: |
| A. | \[\frac{1}{{{\log }_{10}}4+{{\log }_{10}}3}\] |
| B. | \[\frac{9}{{{\log }_{10}}4-{{\log }_{10}}3}\] |
| C. | \[\frac{4}{{{\log }_{10}}4-{{\log }_{10}}3}\] |
| D. | \[\frac{1}{{{\log }_{10}}4-{{\log }_{10}}3}\] |
| Answer» E. | |
| 7867. |
The mean and the variance of binomial distribution are 4 and 2 respectively. Then the probability of 2 successes is |
| A. | \[\frac{28}{256}\] |
| B. | \[\frac{219}{256}\] |
| C. | \[\frac{128}{256}\] |
| D. | \[\frac{37}{256}\] |
| Answer» B. \[\frac{219}{256}\] | |
| 7868. |
Let \[{{E}^{c}}\] denote the complement of an event E. let E, F, G be pairwise independent events with \[P(G)>0\] and \[P(E\cap F\cap G)=0\]. Then \[P({{E}^{c}}\cap {{F}^{c}}/G)\] equals |
| A. | \[P({{E}^{c}})+P({{F}^{c}})\] |
| B. | \[P({{E}^{c}})-P({{F}^{c}})\] |
| C. | \[P({{E}^{c}})-P(F)\] |
| D. | \[P(E)-P({{F}^{c}})\] |
| Answer» D. \[P(E)-P({{F}^{c}})\] | |
| 7869. |
The probability of a man hitting a target is 1/4. The number of times he must shoot so that the probability he hits target, at least once is more than 0.9, is [use \[\log 4=0.602\,\,and\,\,\log 3=0.477\]] |
| A. | 7 |
| B. | 8 |
| C. | 6 |
| D. | 5 |
| Answer» C. 6 | |
| 7870. |
Rahul has to write a project, probability that he will get a project copy is ?P?, probability that he will get a blue pen is ?q? and probability that he will get a black pen is 1/2, if he can complete the project either with blue or with black pen or with both and probability that he completed the project is 1/2 then \[P(1+q)\]is |
| A. | \[\frac{1}{2}\] |
| B. | 1 |
| C. | \[\frac{1}{4}\] |
| D. | 2 |
| Answer» C. \[\frac{1}{4}\] | |
| 7871. |
6 coins are tossed together 64 times, if throwing a hand is considered as a success then the ex-pected frequency of at least 3 successes is |
| A. | 64 |
| B. | 21 |
| C. | 32 |
| D. | 42 |
| Answer» E. | |
| 7872. |
If the random variable X takes the values \[{{x}_{1}},{{x}_{2}},{{x}_{3}}...{{x}_{10}}\] with probabilities \[P(X={{x}_{i}})=ki,\]then the value of k is equal to |
| A. | \[\frac{1}{10}\] |
| B. | \[\frac{1}{15}\] |
| C. | \[\frac{1}{55}\] |
| D. | 10 |
| Answer» D. 10 | |
| 7873. |
A die marked 1, 2, 3 in red and 4, 5, 6 in green is tossed. Let A be the event, "the number is even", and B be the event, "the number is red" then; |
| A. | \[P(A)P(B)=\frac{1}{6}\] |
| B. | A and B are independent |
| C. | A and B are dependent |
| D. | None of these |
| Answer» D. None of these | |
| 7874. |
Rajesh doesn't like to study. Probability that he will study is 1/3. If the studied then probability that he will fail is1/2 and if he didn?t study then probability that he will fail is 3/4 if in result Rajesh failed then what the probability that he didn't studies is. |
| A. | 44257 |
| B. | 44289 |
| C. | 44256 |
| D. | None of these |
| Answer» C. 44256 | |
| 7875. |
In a sequence of independent trials, the probability of success on each trial is ¼. The probability that the second success occurs on the fourth or later trial, if the trials continue up to the second success only, is |
| A. | \[\frac{5}{32}\] |
| B. | \[\frac{27}{32}\] |
| C. | \[\frac{23}{32}\] |
| D. | \[\frac{9}{32}\] |
| Answer» C. \[\frac{23}{32}\] | |
| 7876. |
If three vertices of a regular hexagon are chosen at random, then the chance that they form an equilateral triangle is: |
| A. | \[\frac{1}{3}\] |
| B. | \[\frac{1}{5}\] |
| C. | \[\frac{1}{10}\] |
| D. | \[\frac{1}{2}\] |
| Answer» D. \[\frac{1}{2}\] | |
| 7877. |
A cricket club has 15 members, of whom only 5 can bowl. If the name of 15 members are put into a box and 11 are drawn at random, then the probability of getting an eleven contain at least 3 bowlers is |
| A. | 41456 |
| B. | 41426 |
| C. | 42309 |
| D. | 41609 |
| Answer» E. | |
| 7878. |
In a relay race, there are six teams A, B, C, D, E and F. what is the probability that A, B, C finish first, second, third respectively? |
| A. | \[\frac{1}{2}\] |
| B. | \[\frac{1}{12}\] |
| C. | \[\frac{1}{60}\] |
| D. | \[\frac{1}{120}\] |
| Answer» E. | |
| 7879. |
A point is selected at random from the interior of a circle. The probability that the point is close to the centre, then the boundary of the circle, is |
| A. | \[\frac{3}{4}\] |
| B. | \[\frac{1}{2}\] |
| C. | \[\frac{1}{4}\] |
| D. | None of these |
| Answer» D. None of these | |
| 7880. |
An experiment consists of flipping a coin and then flipping it a second time if head occurs. If a tail occurs on the first flip, then a six-faced die is tossed once. Assuming that the outcomes are equally likely, what is the probability of getting one head and one tail? |
| A. | ¼ |
| B. | 13150 |
| C. | 44348 |
| D. | 44409 |
| Answer» B. 13150 | |
| 7881. |
It has been found that if A and B play a game 12 times. A wins 6 times, B wins 4 times and they draw twice. A and B take part in a series of 3 games. The probability that they with alternately, is: |
| A. | \[5/12\] |
| B. | \[5/36\] |
| C. | \[19/27\] |
| D. | \[5/27\] |
| Answer» C. \[19/27\] | |
| 7882. |
In an examination, the probability of a candidate solving a question is \[\frac{1}{2}.\] Out of given 5 questions in the examination, what is the probability that the candidate was able to solve at least 2 questions? |
| A. | \[\frac{1}{64}\] |
| B. | \[\frac{3}{16}\] |
| C. | \[\frac{1}{2}\] |
| D. | \[\frac{13}{16}\] |
| Answer» E. | |
| 7883. |
If \[\frac{1+4p}{4},\frac{1-p}{2}\] and \[\frac{1-2p}{2}\] are the probabilities of three mutually exclusive events, then value of p is |
| A. | \[\frac{1}{2}\] |
| B. | \[\frac{1}{3}\] |
| C. | \[\frac{1}{4}\] |
| D. | \[\frac{2}{3}\] |
| Answer» B. \[\frac{1}{3}\] | |
| 7884. |
Let \[\omega \] be a complex cube root of unity with \[\omega \ne 1.\] A fair die is thrown three times. If \[r,{{r}_{2}}\] and \[{{r}_{3}}\] are the numbers obtained on the die, then the probability that \[{{\omega }^{{{r}_{1}}}}+{{\omega }^{{{r}_{2}}}}+{{\omega }^{{{r}_{3}}}}=0\] is |
| A. | 43101 |
| B. | 44440 |
| C. | 44441 |
| D. | 13150 |
| Answer» D. 13150 | |
| 7885. |
Three numbers are chosen at random without replacement from the set \[A=\{x|1\le x\le 10,x\in N\}\]. The prodigality that the minimum of the chosen numbers is 3 and maximum is 7, is |
| A. | \[\frac{1}{12}\] |
| B. | \[\frac{1}{15}\] |
| C. | \[\frac{1}{40}\] |
| D. | None of these |
| Answer» D. None of these | |
| 7886. |
The probability of choosing at random a number that is divisible by 6 or 8 from among 1 to 90 is equal to: |
| A. | \[\frac{1}{6}\] |
| B. | \[\frac{1}{30}\] |
| C. | \[\frac{11}{80}\] |
| D. | \[\frac{23}{90}\] |
| Answer» E. | |
| 7887. |
Seven people set themselves indiscriminately at round table. The probability that two distinguished person will be next to each is |
| A. | \[\frac{1}{3}\] |
| B. | \[\frac{1}{2}\] |
| C. | \[\frac{1}{4}\] |
| D. | \[\frac{2}{3}\] |
| Answer» B. \[\frac{1}{2}\] | |
| 7888. |
In a series of 3 one -day cricket matches between teams A and B of a collage, the probability of team A winning or drawing are 1/3 and 1/6 respectively. If a win, lose or draw gives 2, 0 and 1 point respectively, then what is the probability that team A will score 5 points in the series? |
| A. | \[\frac{17}{18}\] |
| B. | \[\frac{11}{12}\] |
| C. | \[\frac{1}{12}\] |
| D. | \[\frac{1}{18}\] |
| Answer» E. | |
| 7889. |
In a knock out chess tournament, eight players \[{{P}_{1}},\,\,{{P}_{2}},...{{P}_{8}}\] Participated. It is known that whenever the players \[{{P}_{i}}\] and \[{{P}_{j}}\] play, the player's \[{{P}_{i}}\] will win j if \[i |
| A. | 31/35 |
| B. | 12875 |
| C. | 12997 |
| D. | None of these |
| Answer» C. 12997 | |
| 7890. |
Amar, Bimal and Chetan are three contestants for an election, odds against Amar will win is 4 : 1 and odds against Bimal will win is 5 : 1 and odds in favor of Chetan will win 2 : 3 the what is probability that either Amar or Bimal or Chetan will win the election. |
| A. | \[23/20\] |
| B. | \[11/30\] |
| C. | \[7/10\] |
| D. | None of these |
| Answer» E. | |
| 7891. |
A coin is tossed three times. Consider the following events: A: No head appears B: Exactly one head appears C: At least two heads appear Which one of the following is correct? |
| A. | \[(A\cup B)\cap (A\cup C)=B\cup C\] |
| B. | \[(A\cap B')\cup (A\cap C')=B'\cup C'\] |
| C. | \[A\cap (B'\cup C')=A\cup B\cup C\] |
| D. | \[A\cap (B'\cup C')=B'\cap C'\] |
| Answer» E. | |
| 7892. |
If A, B, C are events such that \[P(A)=0.3,P(B)=0.4,P(C)=0.8,P(A\cap B)\]\[=0.08,P(A\cap C)=0.28\] \[P(A\cap B\cap C)=0.09\]. If \[P(A\cup B\cup C)\ge 0.75\] then find the range of \[x=P(B\cap C)\] lies in the interval |
| A. | \[0.23\le x\le 0.48\] |
| B. | \[0.23\le x\le 0.47\] |
| C. | \[0.22\le x\le 0.48\] |
| D. | None of these |
| Answer» B. \[0.23\le x\le 0.47\] | |
| 7893. |
Four persons are selected at random out of 3 men, 2 women and 4 children. Find the probability that there exactly 2 children in the selection. |
| A. | \[\frac{11}{21}\] |
| B. | \[\frac{8}{21}\] |
| C. | \[\frac{10}{21}\] |
| D. | \[\frac{7}{21}\] |
| Answer» D. \[\frac{7}{21}\] | |
| 7894. |
Let A and B are two events and \[P({A}')=0.3\], \[P(B)=0.4,\,P(A\cap {B}')=0.5\], then \[P(A\cup {B}')\] is [Orissa JEE 2005] |
| A. | 0.5 |
| B. | 0.8 |
| C. | 1 |
| D. | 0.1 |
| Answer» C. 1 | |
| 7895. |
A card is drawn from a pack of cards. Find the probability that the card will be a queen or a heart [RPET 2003] |
| A. | \[\frac{4}{3}\] |
| B. | \[\frac{16}{3}\] |
| C. | \[\frac{4}{13}\] |
| D. | \[\frac{5}{3}\] |
| Answer» D. \[\frac{5}{3}\] | |
| 7896. |
If A and B are events such that \[P(A\cup B)=3/4,\] \[P(A\cap B)=1/4,\] \[P(\bar{A})=2/3,\] then \[P(\bar{A}\cap B)\] is [AIEEE 2002] |
| A. | \[\frac{5}{12}\] |
| B. | \[\frac{3}{8}\] |
| C. | \[\frac{5}{8}\] |
| D. | \[\frac{1}{4}\] |
| Answer» B. \[\frac{3}{8}\] | |
| 7897. |
In a horse race the odds in favour of three horses are \[1:2\], \[1:3\] and \[1:4\]. The probability that one of the horse will win the race is |
| A. | \[\frac{37}{60}\] |
| B. | \[\frac{47}{60}\] |
| C. | \[\frac{1}{4}\] |
| D. | \[\frac{3}{4}\] |
| Answer» C. \[\frac{1}{4}\] | |
| 7898. |
The probability of solving a question by three students are \[\frac{1}{2},\,\,\frac{1}{4},\,\,\frac{1}{6}\] respectively. Probability of question is being solved will be [UPSEAT 1999] |
| A. | \[\frac{33}{48}\] |
| B. | \[\frac{35}{48}\] |
| C. | \[\frac{31}{48}\] |
| D. | \[\frac{37}{48}\] |
| Answer» B. \[\frac{35}{48}\] | |
| 7899. |
If \[P(A)=\frac{1}{2},\,\,P(B)=\frac{1}{3}\] and \[P(A\cap B)=\frac{7}{12},\] then the value of \[P\,({A}'\cap {B}')\] is |
| A. | \[\frac{7}{12}\] |
| B. | \[\frac{3}{4}\] |
| C. | \[\frac{1}{4}\] |
| D. | \[\frac{1}{6}\] |
| Answer» C. \[\frac{1}{4}\] | |
| 7900. |
If A and B are any two events, then the probability that exactly one of them occur is [BIT Ranchi 1990; IIT 1984; RPET 1995, 2002; MP PET 2004] |
| A. | \[P\,(A)+P\,(B)-P\,(A\cap B)\] |
| B. | \[P\,(A)+P\,(B)-2P\,(A\cap B)\] |
| C. | \[P\,(A)+P\,(B)-P\,(A\cup B)\] |
| D. | \[P\,(A)+P\,(B)-2P\,(A\cup B)\] |
| Answer» C. \[P\,(A)+P\,(B)-P\,(A\cup B)\] | |