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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.
| 6001. |
Two dice are thrown. The probability that the sum of the points on two dice will be 7, is [IIT 1974; MNR 1981, 91; RPET 1995, 97, 2002; UPSEAT 2000] |
| A. | \[\frac{5}{36}\] |
| B. | \[\frac{6}{36}\] |
| C. | \[\frac{7}{36}\] |
| D. | \[\frac{8}{36}\] |
| Answer» C. \[\frac{7}{36}\] | |
| 6002. |
A coin is tossed until a head appears or until the coin has been tossed five times. If a head does not occur on the first two tosses, then the probability that the coin will be tossed 5 times is [CEE 1993] |
| A. | \[\frac{1}{2}\] |
| B. | \[\frac{3}{5}\] |
| C. | \[\frac{1}{4}\] |
| D. | \[\frac{1}{3}\] |
| Answer» D. \[\frac{1}{3}\] | |
| 6003. |
The probability of happening of an impossible event i.e. \[P\,(\varphi )\] is [MP PET 1993] |
| A. | 1 |
| B. | 0 |
| C. | 2 |
| D. | ?1 |
| Answer» C. 2 | |
| 6004. |
If two balanced dice are tossed once, the probability of the event, that the sum of the integers coming on the upper sides of the two dice is 9, is [MP PET 1987] |
| A. | \[\frac{7}{18}\] |
| B. | \[\frac{5}{36}\] |
| C. | \[\frac{1}{9}\] |
| D. | \[\frac{1}{6}\] |
| Answer» D. \[\frac{1}{6}\] | |
| 6005. |
Three dice are thrown simultaneously. What is the probability of obtaining a total of 17 or 18 [AI CBSE 1983] |
| A. | \[\frac{1}{9}\] |
| B. | \[\frac{1}{72}\] |
| C. | \[\frac{1}{54}\] |
| D. | None of these |
| Answer» D. None of these | |
| 6006. |
In a single throw of two dice what is the probability of getting a total 13 |
| A. | 0 |
| B. | 1 |
| C. | \[\frac{13}{36}\] |
| D. | \[\frac{25}{36}\] |
| Answer» B. 1 | |
| 6007. |
A card is drawn at random from a pack of cards. What is the probability that the drawn card is neither a heart nor a king |
| A. | \[\frac{4}{13}\] |
| B. | \[\frac{9}{13}\] |
| C. | \[\frac{1}{4}\] |
| D. | \[\frac{13}{26}\] |
| Answer» C. \[\frac{1}{4}\] | |
| 6008. |
A bag contains 4 white, 5 black and 6 red balls. If a ball is drawn at random, then what is the probability that the drawn ball is either white or red |
| A. | \[\frac{4}{15}\] |
| B. | \[\frac{1}{2}\] |
| C. | \[\frac{2}{5}\] |
| D. | \[\frac{2}{3}\] |
| Answer» E. | |
| 6009. |
A man and a woman appear in an interview for two vacancies in the same post. The probability of man's selection is 1/4 and that of the woman's selection is 1/3. What is the probability that none of them will be selected [MNR 1988] |
| A. | \[\frac{1}{2}\] |
| B. | \[\frac{1}{12}\] |
| C. | \[\frac{1}{4}\] |
| D. | None of these |
| Answer» B. \[\frac{1}{12}\] | |
| 6010. |
Two dice are thrown together. If the numbers appearing on the two dice are different, then what is the probability that the sum is 6 |
| A. | \[\frac{5}{36}\] |
| B. | \[\frac{1}{6}\] |
| C. | \[\frac{2}{15}\] |
| D. | None of these |
| Answer» D. None of these | |
| 6011. |
Two cards are drawn from a pack of 52 cards. What is the probability that one of them is a queen and the other is an ace |
| A. | \[\frac{2}{663}\] |
| B. | \[\frac{2}{13}\] |
| C. | \[\frac{4}{663}\] |
| D. | None of these |
| Answer» E. | |
| 6012. |
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. \[\frac{1}{2}\] | |
| 6013. |
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. | 5/8 |
| B. | 1/2 |
| C. | 1/3 |
| D. | 2/3 |
| Answer» E. | |
| 6014. |
Two dice are thrown together. The probability that sum of the two numbers will be a multiple of 4 is [MP PET 1990] |
| A. | \[\frac{1}{9}\] |
| B. | \[\frac{1}{3}\] |
| C. | \[\frac{1}{4}\] |
| D. | \[\frac{5}{9}\] |
| Answer» D. \[\frac{5}{9}\] | |
| 6015. |
If in a lottary there are 5 prizes and 20 blanks, then the probability of getting a prize is |
| A. | \[\frac{1}{5}\] |
| B. | \[\frac{2}{5}\] |
| C. | \[\frac{4}{5}\] |
| D. | None of these |
| Answer» B. \[\frac{2}{5}\] | |
| 6016. |
Two dice are thrown simultaneously. What is the probability of obtaining sum of the numbers less than 11 |
| A. | \[\frac{17}{18}\] |
| B. | \[\frac{1}{12}\] |
| C. | \[\frac{11}{12}\] |
| D. | None of these |
| Answer» D. None of these | |
| 6017. |
In a throw of a die, what is the probability of getting a number less than 7 |
| A. | 0 |
| B. | 1 |
| C. | \[\frac{1}{2}\] |
| D. | None of these |
| Answer» C. \[\frac{1}{2}\] | |
| 6018. |
In a simultaneous throw of three coins, what is the probability of getting at least 2 tails |
| A. | \[\frac{1}{8}\] |
| B. | \[\frac{1}{4}\] |
| C. | \[\frac{1}{2}\] |
| D. | None of these |
| Answer» D. None of these | |
| 6019. |
A card is drawn from a well shuffled pack of cards. The probability of getting a queen of club or king of heart is [MP PET 1988] |
| A. | \[\frac{1}{52}\] |
| B. | \[\frac{1}{26}\] |
| C. | \[\frac{1}{18}\] |
| D. | None of these |
| Answer» C. \[\frac{1}{18}\] | |
| 6020. |
A problem of mathematics is given to three students whose chances of solving the problem are 1/3, 1/4 and 1/5 respectively. The probability that the question will be solved is [BIT Ranchi 1991; MP PET 1990] |
| A. | \[\frac{2}{3}\] |
| B. | \[\frac{3}{4}\] |
| C. | \[\frac{4}{5}\] |
| D. | \[\frac{3}{5}\] |
| Answer» E. | |
| 6021. |
The probability of drawing a white ball from a bag containing 3 black balls and 4 white balls, is |
| A. | \[\frac{4}{7}\] |
| B. | \[\frac{3}{7}\] |
| C. | \[\frac{1}{7}\] |
| D. | None of these |
| Answer» B. \[\frac{3}{7}\] | |
| 6022. |
Two dice are thrown simultaneously. What is the probability of obtaining a multiple of 2 on one of them and a multiple of 3 on the other [AI CBSE 1981] |
| A. | \[\frac{5}{36}\] |
| B. | \[\frac{11}{36}\] |
| C. | \[\frac{1}{6}\] |
| D. | \[\frac{1}{3}\] |
| Answer» C. \[\frac{1}{6}\] | |
| 6023. |
In a single throw of two dice the probability of obtaining an odd number is |
| A. | \[\frac{1}{6}\] |
| B. | \[\frac{1}{2}\] |
| C. | \[\frac{1}{3}\] |
| D. | None of these |
| Answer» C. \[\frac{1}{3}\] | |
| 6024. |
The probability of happening an event A in one trial is 0.4. The probability that the event A happens at least once in three independent trials is [IIT 1980; Kurukshetra CEE 1998; DCE 2001] |
| A. | 0.936 |
| B. | 0.784 |
| C. | 0.904 |
| D. | 0.216 |
| Answer» C. 0.904 | |
| 6025. |
The probability of a sure event is [MP PET 1988] |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | \[\frac{1}{2}\] |
| Answer» C. 2 | |
| 6026. |
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. \[\frac{1}{3}\] | |
| 6027. |
Three letters are to be sent to different persons and addresses on the three envelopes are also written. Without looking at the addresses, the probability that the letters go into the right envelope is equal to [MNR 1982; MP PET 1990; Orissa JEE 2004] |
| A. | \[\frac{1}{27}\] |
| B. | \[\frac{1}{9}\] |
| C. | \[\frac{4}{27}\] |
| D. | \[\frac{1}{6}\] |
| Answer» E. | |
| 6028. |
The probability of getting at least one tail in 4 throws of a coin is [MNR 1983; Kurukshetra CEE 1998] |
| A. | \[\frac{15}{16}\] |
| B. | \[\frac{1}{16}\] |
| C. | \[\frac{1}{4}\] |
| D. | None of these |
| Answer» B. \[\frac{1}{16}\] | |
| 6029. |
A box contains 6 nails and 10 nuts. Half of the nails and half of the nuts are rusted. If one item is chosen at random, what is the probability that it is rusted or is a nail [MP PET 1992, 2000] |
| A. | \[\frac{3}{16}\] |
| B. | \[\frac{5}{16}\] |
| C. | \[\frac{11}{16}\] |
| D. | \[\frac{14}{16}\] |
| Answer» D. \[\frac{14}{16}\] | |
| 6030. |
In a single throw of two dice, the probability of getting more than 7 is [MP PET 1991] |
| A. | \[\frac{7}{36}\] |
| B. | \[\frac{7}{12}\] |
| C. | \[\frac{5}{12}\] |
| D. | \[\frac{5}{36}\] |
| Answer» D. \[\frac{5}{36}\] | |
| 6031. |
One card is drawn from each of two ordinary packs of 52 cards. The probability that at least one of them is an ace of heart, is |
| A. | \[\frac{103}{2704}\] |
| B. | \[\frac{1}{2704}\] |
| C. | \[\frac{2}{52}\] |
| D. | \[\frac{2601}{2704}\] |
| Answer» B. \[\frac{1}{2704}\] | |
| 6032. |
Two cards are drawn from a pack of 52 cards. What is the probability that at least one of the cards drawn is an ace |
| A. | \[\frac{33}{221}\] |
| B. | \[\frac{188}{221}\] |
| C. | \[\frac{1}{26}\] |
| D. | \[\frac{21}{221}\] |
| Answer» B. \[\frac{188}{221}\] | |
| 6033. |
A dice is thrown twice. The probability of getting 4, 5 or 6 in the first throw and 1, 2, 3 or 4 in the second throw is |
| A. | 1 |
| B. | \[\frac{1}{3}\] |
| C. | \[\frac{7}{36}\] |
| D. | None of these |
| Answer» C. \[\frac{7}{36}\] | |
| 6034. |
Two dice are thrown simultaneously. The probability of getting the sum 2 or 8 or 12 is |
| A. | \[\frac{5}{18}\] |
| B. | \[\frac{7}{36}\] |
| C. | \[\frac{7}{18}\] |
| D. | \[\frac{5}{36}\] |
| Answer» C. \[\frac{7}{18}\] | |
| 6035. |
Consider the circuit, If the probability that each switch is closed is p, then find the probability of current flowing through AB [DCE 2005] |
| A. | \[{{p}^{2}}+p\] |
| B. | \[{{p}^{3}}+p-1\] |
| C. | \[{{p}^{3}}+p\] |
| D. | \[{{p}^{2}}+p+1\] |
| Answer» B. \[{{p}^{3}}+p-1\] | |
| 6036. |
A and B are two independent events such that \[P(A)=1/2\]and\[P(B)=1/3\]. Then P (neither A nor B) is equal to [J & K 2005] |
| A. | 2/3 |
| B. | 1/6 |
| C. | 5/6 |
| D. | 1/3 |
| Answer» E. | |
| 6037. |
In a throw of a dice the probability of getting one in even number of throw is [IIT Screening 2005] |
| A. | \[\frac{5}{36}\] |
| B. | \[\frac{5}{11}\] |
| C. | \[\frac{6}{11}\] |
| D. | \[\frac{1}{6}\] |
| Answer» C. \[\frac{6}{11}\] | |
| 6038. |
Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting others. The probability that all the three apply for the same house is [AIEEE 2005] |
| A. | \[\frac{8}{9}\] |
| B. | \[\frac{7}{9}\] |
| C. | \[\frac{2}{9}\] |
| D. | \[\frac{1}{9}\] |
| Answer» E. | |
| 6039. |
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 | |
| 6040. |
The probabilities of a problem being solved by two students are \[\frac{1}{2},\frac{1}{3}\]. Then the probability of the problem being solved is [Pb. CET 2001] |
| A. | \[\frac{2}{3}\] |
| B. | \[\frac{4}{3}\] |
| C. | \[\frac{1}{3}\] |
| D. | 1 |
| Answer» B. \[\frac{4}{3}\] | |
| 6041. |
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. | |
| 6042. |
The probability that A speaks truth is \[\frac{4}{5}\], while this probability for B is \[\frac{3}{4}\]. The probability that they contradict each other when asked to speak on a fact [AIEEE 2004; MP PET 1997, 2002; IIT 1975; MNR 1987] |
| A. | \[\frac{4}{5}\] |
| B. | \[\frac{1}{5}\] |
| C. | \[\frac{7}{20}\] |
| D. | \[\frac{3}{20}\] |
| Answer» D. \[\frac{3}{20}\] | |
| 6043. |
Probability of throwing 16 in one throw with three dice is [UPSEAT 2004] |
| A. | \[\frac{1}{36}\] |
| B. | \[\frac{1}{18}\] |
| C. | \[\frac{1}{72}\] |
| D. | \[\frac{1}{9}\] |
| Answer» B. \[\frac{1}{18}\] | |
| 6044. |
?X? speaks truth in 60% and ?Y? in 50% of the cases. The probability that they contradict each other narrating the same incident is [UPSEAT 2004] |
| A. | \[\frac{1}{4}\] |
| B. | \[\frac{1}{3}\] |
| C. | \[\frac{1}{2}\] |
| D. | \[\frac{2}{3}\] |
| Answer» D. \[\frac{2}{3}\] | |
| 6045. |
Five horses are in a race. Mr. A selects two of the horses at random and bets on them. The probability that Mr. A selected the winning horse is [AIEEE 2003] |
| A. | \[\frac{4}{5}\] |
| B. | \[\frac{3}{5}\] |
| C. | \[\frac{1}{5}\] |
| D. | \[\frac{2}{5}\] |
| Answer» E. | |
| 6046. |
Four coins are tossed. The probability that at least one head turns up, is [DSSE 1981] |
| A. | 1/16 |
| B. | 1/4 |
| C. | 15/16 |
| D. | None of these |
| Answer» D. None of these | |
| 6047. |
The probability that a marksman will hit a target is given as 1/5. Then his probability of at least one hit in 10 shots, is |
| A. | \[1-{{\left( \frac{4}{5} \right)}^{10}}\] |
| B. | \[\frac{1}{{{5}^{10}}}\] |
| C. | \[1-\frac{1}{{{5}^{10}}}\] |
| D. | None of these |
| Answer» B. \[\frac{1}{{{5}^{10}}}\] | |
| 6048. |
A bag contains 3 red and 5 black balls and a second bag contains 6 red and 4 black balls. A ball is drawn from each bag. The probability that one is red and other is black, is [AISSE 1986] |
| A. | \[\frac{3}{20}\] |
| B. | \[\frac{21}{40}\] |
| C. | \[\frac{3}{8}\] |
| D. | None of these |
| Answer» C. \[\frac{3}{8}\] | |
| 6049. |
A box containing 4 white pens and 2 black pens. Another box containing 3 white pens and 5 black pens. If one pen is selected from each box, then the probability that both the pens are white is equal to [Pb.CET 2002] |
| A. | \[\frac{1}{2}\] |
| B. | \[\frac{1}{3}\] |
| C. | \[\frac{1}{4}\] |
| D. | \[\frac{1}{5}\] |
| Answer» D. \[\frac{1}{5}\] | |
| 6050. |
A coin is tossed twice. The probability of getting head both the times is [MNR 1978] |
| A. | \[\frac{1}{2}\] |
| B. | \[\frac{1}{4}\] |
| C. | \[\frac{3}{4}\] |
| D. | 1 |
| Answer» C. \[\frac{3}{4}\] | |