MCQOPTIONS
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MCQOPTIONS
This section includes 43 Mcqs, each offering curated multiple-choice questions to sharpen your Mathematics knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
The probabilities of a student getting I, II and III division in an examination are respectively \[\frac{1}{10},\,\frac{3}{5}\] and \[\frac{1}{4}.\] The probability that the student fails in the examination is [MP PET 1997] |
| A. | \[\frac{197}{200}\] |
| B. | \[\frac{27}{100}\] |
| C. | \[\frac{83}{100}\] |
| D. | None of these |
| Answer» E. | |
| 2. |
If A and B are two events such that \[A\subseteq B,\] then \[P\,\left( \frac{B}{A} \right)=\] |
| A. | 0 |
| B. | 1 |
| C. | 44228 |
| D. | 44256 |
| Answer» C. 44228 | |
| 3. |
If \[4\,P(A)=6\,P\,(B)=10\,P\,(A\cap B)=1,\] then \[P\,\left( \frac{B}{A} \right)=\] [MP PET 2003] |
| A. | \[\frac{2}{5}\] |
| B. | \[\frac{3}{5}\] |
| C. | \[\frac{7}{10}\] |
| D. | \[\frac{19}{60}\] |
| Answer» B. \[\frac{3}{5}\] | |
| 4. |
A man make attempts to hit the target. The probability of hitting the target is \[\frac{3}{5}.\] Then the probability that A hit the target exactly 2 times in 5 attempts, is |
| A. | \[\frac{144}{625}\] |
| B. | \[\frac{72}{3125}\] |
| C. | \[\frac{216}{625}\] |
| D. | None of these |
| Answer» B. \[\frac{72}{3125}\] | |
| 5. |
Let A, B, C be three mutually independent events. Consider the two statements \[{{S}_{1}}\]and \[{{S}_{2}}\] \[{{S}_{1}}\,\,:\,\,A\] and \[B\cup C\] are independent \[{{S}_{2}}\,\,:\,\,A\] and \[B\cap C\] are independent Then [IIT 1994] |
| A. | Both \[{{S}_{1}}\] and \[{{S}_{2}}\] are true |
| B. | Only \[{{S}_{1}}\] is true |
| C. | Only \[{{S}_{2}}\] is true |
| D. | Neither \[{{S}_{1}}\] nor \[{{S}_{2}}\] is true |
| Answer» B. Only \[{{S}_{1}}\] is true | |
| 6. |
If\[P\,({{A}_{1}}\cup {{A}_{2}})=1-P(A_{1}^{c})\,P(A_{2}^{c})\] where c stands for complement, then the events \[{{A}_{1}}\] and \[{{A}_{2}}\] are [MP PET 1989] |
| A. | Mutually exclusive |
| B. | Independent |
| C. | Equally likely |
| D. | None of these |
| Answer» C. Equally likely | |
| 7. |
A bag contains 3 black and 4 white balls. Two balls are drawn one by one at random without replacement. The probability that the second drawn ball is white, is [MP PET 1995] |
| A. | \[\frac{4}{49}\] |
| B. | \[\frac{1}{7}\] |
| C. | \[\frac{4}{7}\] |
| D. | \[\frac{12}{49}\] |
| Answer» D. \[\frac{12}{49}\] | |
| 8. |
Seven chits are numbered 1 to 7. Three are drawn one by one with replacement. The probability that the least number on any selected chit is 5, is [EAMCET 1991] |
| A. | \[1-{{\left( \frac{2}{7} \right)}^{4}}\] |
| B. | \[4\,{{\left( \frac{2}{7} \right)}^{4}}\] |
| C. | \[{{\left( \frac{3}{7} \right)}^{3}}\] |
| D. | None of these |
| Answer» D. None of these | |
| 9. |
From a book containing 100 pages, one page is selected randomly. The probability that the sum of the digits of the page number of the selected page is 11, is |
| A. | \[\frac{2}{25}\] |
| B. | \[\frac{9}{100}\] |
| C. | \[\frac{11}{100}\] |
| D. | None of these |
| Answer» B. \[\frac{9}{100}\] | |
| 10. |
A box contains 3 white and 2 red balls. A ball is drawn and another ball is drawn without replacing first ball, then the probability of second ball to be red is[Roorkee 1995] |
| A. | \[\frac{8}{25}\] |
| B. | \[\frac{2}{5}\] |
| C. | \[\frac{3}{5}\] |
| D. | \[\frac{21}{25}\] |
| Answer» C. \[\frac{3}{5}\] | |
| 11. |
A determinant is chosen at random. The set of all determinants of order 2 with elements 0 or 1 only. The probability that value of the determinant chosen is positive, is [IIT 1982] |
| A. | 42430 |
| B. | 44411 |
| C. | 44287 |
| D. | None of these |
| Answer» B. 44411 | |
| 12. |
In a single throw of two dice, the probability of obtaining a total of 7 or 9, is[AISSE 1979] |
| A. | \[\frac{5}{18}\] |
| B. | \[\frac{1}{6}\] |
| C. | \[\frac{1}{9}\] |
| D. | None of these |
| Answer» B. \[\frac{1}{6}\] | |
| 13. |
In a throw of three dice, the probability that at least one die shows up 1, is [DSSE 1981] |
| A. | \[\frac{5}{6}\] |
| B. | \[\frac{91}{216}\] |
| C. | \[\frac{1}{36}\] |
| D. | \[\frac{125}{216}\] |
| Answer» C. \[\frac{1}{36}\] | |
| 14. |
Two dice are thrown. If first shows 5, then the probability that the sum of the numbers appears on both is 8 or more than 8, is |
| A. | \[\frac{1}{12}\] |
| B. | \[\frac{11}{12}\] |
| C. | \[\frac{1}{3}\] |
| D. | \[\frac{2}{3}\] |
| Answer» E. | |
| 15. |
The probabilityof getting head and tail alternately in three throws of a coin (or a throw of three coins), is[RPET 1997] |
| A. | \[\frac{1}{8}\] |
| B. | \[\frac{1}{4}\] |
| C. | \[\frac{1}{3}\] |
| D. | \[\frac{3}{8}\] |
| Answer» C. \[\frac{1}{3}\] | |
| 16. |
Three persons work independently on a problem. If the respective probabilities that they will solve it are 1/3, 1/4 and 1/5, then the probability that none can solve it [MNR 1990; UPSEAT 2000] |
| A. | \[\frac{2}{5}\] |
| B. | \[\frac{3}{5}\] |
| C. | \[\frac{1}{3}\] |
| D. | None of these |
| Answer» B. \[\frac{3}{5}\] | |
| 17. |
The probability of getting a number greater than 2 in throwing a die is [MP PET 1988] |
| A. | \[\frac{1}{3}\] |
| B. | \[\frac{2}{3}\] |
| C. | \[\frac{1}{2}\] |
| D. | \[\frac{1}{6}\] |
| Answer» C. \[\frac{1}{2}\] | |
| 18. |
A and B toss a coin alternatively, the first to show a head being the winner. If A starts the game, the chance of his winning is[MP PET 1987] |
| A. | 44413 |
| B. | 44228 |
| C. | 44256 |
| D. | 44257 |
| Answer» E. | |
| 19. |
A card is drawn at random from a pack of 52 cards. The probability that the drawn card is a court card i.e. a jack, a queen or a king, is |
| A. | \[\frac{3}{52}\] |
| B. | \[\frac{3}{13}\] |
| C. | \[\frac{4}{13}\] |
| D. | None of these |
| Answer» C. \[\frac{4}{13}\] | |
| 20. |
From 10,000 lottery tickets numbered from 1 to 10,000, one ticket is drawn at random. What is the probability that the number marked on the drawn ticket is divisible by 20 |
| A. | \[\frac{1}{100}\] |
| B. | \[\frac{1}{50}\] |
| C. | \[\frac{1}{20}\] |
| D. | \[\frac{1}{10}\] |
| Answer» D. \[\frac{1}{10}\] | |
| 21. |
The probability of getting a total of 5 or 6 in a single throw of 2 dice is [MP PET 1988] |
| A. | \[\frac{1}{2}\] |
| B. | \[\frac{1}{4}\] |
| C. | \[\frac{1}{3}\] |
| D. | \[\frac{1}{6}\] |
| Answer» C. \[\frac{1}{3}\] | |
| 22. |
From a pack of 52 cards two are drawn with replacement. The probability, that the first is a diamond and the second is a king, is[MNR 1979] |
| A. | \[\frac{1}{26}\] |
| B. | \[\frac{17}{2704}\] |
| C. | \[\frac{1}{52}\] |
| D. | None of these |
| Answer» D. None of these | |
| 23. |
The probability of choosing at random a number that is divisible by 6 or 8 from among 1 to 90 is equal to [Pb. CET 2002] |
| A. | \[\frac{1}{6}\] |
| B. | \[\frac{1}{30}\] |
| C. | \[\frac{11}{80}\] |
| D. | \[\frac{23}{90}\] |
| Answer» E. | |
| 24. |
Four coins are tossed. The probability that at least one head turns up, is[DSSE 1981] |
| A. | 42370 |
| B. | 44287 |
| C. | 15/16 |
| D. | None of these |
| Answer» D. None of these | |
| 25. |
There are 10 pairs of shoes in a cupboard from which 4 shoes are picked at random. The probability that there is at least one pair, is |
| A. | \[\frac{99}{323}\] |
| B. | \[\frac{224}{323}\] |
| C. | \[\frac{100}{323}\] |
| D. | None of these |
| Answer» B. \[\frac{224}{323}\] | |
| 26. |
Find the probability that the two digit number formed by digits 1, 2, 3, 4, 5 is divisible by 4 (while repetition of digit is allowed) [UPSEAT 2002] |
| A. | \[\frac{1}{30}\] |
| B. | \[\frac{1}{20}\] |
| C. | \[\frac{1}{40}\] |
| D. | None of these |
| Answer» E. | |
| 27. |
If any four numbers are selected and they are multiplied, then the probability that the last digit will be 1, 3, 5 or 7 is [RPET 2002] |
| A. | \[\frac{4}{625}\] |
| B. | \[\frac{18}{625}\] |
| C. | \[\frac{16}{625}\] |
| D. | None of these |
| Answer» D. None of these | |
| 28. |
From a pack of 52 cards two cards are drawn in succession one by one without replacement. The probability that both are aces is [RPET 2001] |
| A. | \[\frac{2}{13}\] |
| B. | \[\frac{1}{51}\] |
| C. | \[\frac{1}{221}\] |
| D. | \[\frac{2}{21}\] |
| Answer» D. \[\frac{2}{21}\] | |
| 29. |
The probability that in a year of the 22nd century chosen at random there will be 53 Sundays is [Orissa JEE 2003] |
| A. | \[\frac{3}{28}\] |
| B. | \[\frac{2}{28}\] |
| C. | \[\frac{7}{28}\] |
| D. | \[\frac{5}{28}\] |
| Answer» E. | |
| 30. |
The corners of regular tetrahedrons are numbered 1, 2, 3, 4. Three tetrahedrons are tossed.The probability that the sum of upward corners will be 5 is [AMU 1999] |
| A. | \[\frac{5}{24}\] |
| B. | \[\frac{5}{64}\] |
| C. | \[\frac{3}{32}\] |
| D. | \[\frac{3}{16}\] |
| Answer» D. \[\frac{3}{16}\] | |
| 31. |
The chances of throwing a total of 3 or 5 or 11 with two dice is [Kurukshetra CEE 1996] |
| A. | \[\frac{5}{36}\] |
| B. | \[\frac{1}{9}\] |
| C. | \[\frac{2}{9}\] |
| D. | \[\frac{19}{36}\] |
| Answer» D. \[\frac{19}{36}\] | |
| 32. |
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. | None of these |
| Answer» B. \[\frac{1}{5}\] | |
| 33. |
In an entrance test there are multiple choice questions. There are four possible answers to each question of which one is correct. The probability that a student knows the answer to a question is 90%. If he gets the correct answer to a question, then the probability that he was guessing, is |
| A. | \[\frac{37}{40}\] |
| B. | \[\frac{1}{37}\] |
| C. | \[\frac{36}{37}\] |
| D. | \[\frac{1}{9}\] |
| Answer» C. \[\frac{36}{37}\] | |
| 34. |
A dice is thrown two times. If getting the odd number is considered as success, then the probability of two successes is |
| A. | \[\frac{1}{2}\] |
| B. | \[\frac{3}{4}\] |
| C. | \[\frac{2}{3}\] |
| D. | \[\frac{1}{4}\] |
| Answer» E. | |
| 35. |
In a binomial distribution the probability of getting a success is 1/4 and standard deviation is 3, thenits mean is [EAMCET 2002] |
| A. | 6 |
| B. | 8 |
| C. | 12 |
| D. | 10 |
| Answer» D. 10 | |
| 36. |
A bag contains 2 white and 4 black balls. A ball is drawn 5 times with replacement. The probability that at least 4 of the balls drawn are white is [AMU 2001] |
| A. | \[\frac{8}{141}\] |
| B. | \[\frac{10}{243}\] |
| C. | \[\frac{11}{243}\] |
| D. | \[\frac{8}{41}\] |
| Answer» D. \[\frac{8}{41}\] | |
| 37. |
In a box of 10 electric bulbs, two are defective. Two bulbs are selected at random one after the other from the box. The first bulb after selection being put back in the box before making the second selection. The probability that both the bulbs are without defect is[MP PET 1987] |
| A. | \[\frac{9}{25}\] |
| B. | \[\frac{16}{25}\] |
| C. | \[\frac{4}{5}\] |
| D. | \[\frac{8}{25}\] |
| Answer» C. \[\frac{4}{5}\] | |
| 38. |
An experiment succeeds twice as often as it fails. Find the probability that in 4 trials there will be at least three success [AMU 1999] |
| A. | \[\frac{4}{27}\] |
| B. | \[\frac{8}{27}\] |
| C. | \[\frac{16}{27}\] |
| D. | \[\frac{24}{27}\] |
| Answer» D. \[\frac{24}{27}\] | |
| 39. |
The probability that a bulb produced by a factory will fuse after 150 days of use is 0.05. What is the probability that out of 5 such bulbs none will fuse after 150 days of use |
| A. | \[1-{{\left( \frac{19}{20} \right)}^{5}}\] |
| B. | \[{{\left( \frac{19}{20} \right)}^{5}}\] |
| C. | \[{{\left( \frac{3}{4} \right)}^{5}}\] |
| D. | \[90\,{{\left( \frac{1}{4} \right)}^{5}}\] |
| Answer» C. \[{{\left( \frac{3}{4} \right)}^{5}}\] | |
| 40. |
A die is thrown three times. Getting a 3 or a 6 is considered success. Then the probability of at least two successes is [DSSE 1981] |
| A. | \[\frac{2}{9}\] |
| B. | \[\frac{7}{27}\] |
| C. | \[\frac{1}{27}\] |
| D. | None of these |
| Answer» C. \[\frac{1}{27}\] | |
| 41. |
A fair coin is tossed a fixed number of times. If the probability of getting 7 heads is equal to that of getting 9 heads, then the probability of getting 3 heads is |
| A. | \[\frac{35}{{{2}^{12}}}\] |
| B. | \[\frac{35}{{{2}^{14}}}\] |
| C. | \[\frac{7}{{{2}^{12}}}\] |
| D. | None of these |
| Answer» B. \[\frac{35}{{{2}^{14}}}\] | |
| 42. |
If X follows a binomial distribution with parameters \[n=6\]and p. If\[9P\,(X=4)=P\,(X=2),\] then \[p=\] |
| A. | \[\frac{1}{3}\] |
| B. | \[\frac{1}{2}\] |
| C. | \[\frac{1}{4}\] |
| D. | 1 |
| Answer» D. 1 | |
| 43. |
A dice is thrown ten times. If getting even number is considered as a success, then the probability of four successes is |
| A. | \[^{10}{{C}_{4}}{{\left( \frac{1}{2} \right)}^{4}}\] |
| B. | \[^{10}{{C}_{4}}{{\left( \frac{1}{2} \right)}^{6}}\] |
| C. | \[^{10}{{C}_{4}}{{\left( \frac{1}{2} \right)}^{8}}\] |
| D. | \[^{10}{{C}_{6}}{{\left( \frac{1}{2} \right)}^{10}}\] |
| Answer» E. | |