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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.
| 5951. |
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 | |
| 5952. |
If \[P(A)=2/3\], \[P(B)=1/2\] and \[\text{ }P(A\cup B)=5/6\] then events A and B are [Kerala (Engg.) 2002] |
| A. | Mutually exclusive |
| B. | Independent as well as mutually exhaustive |
| C. | Independent |
| D. | Dependent only on A |
| Answer» B. Independent as well as mutually exhaustive | |
| 5953. |
If A and B are two independent events, then A and \[\bar{B}\] are |
| A. | Not independent |
| B. | Also independent |
| C. | Mutually exclusive |
| D. | None of these |
| Answer» C. Mutually exclusive | |
| 5954. |
Two fair dice are tossed. Let A be the event that the first die shows an even number and B be the event that the second die shows an odd number. The two event A and B are [IIT 1979] |
| A. | Mutually exclusive |
| B. | Independent and mutually exclusive |
| C. | Dependent |
| D. | None of these |
| Answer» E. | |
| 5955. |
A card is drawn from a pack of 52 cards. If A = card is of diamond, B = card is an ace and \[A\cap B=\]card is ace of diamond, then events A and B are |
| A. | Independent |
| B. | Mutually exclusive |
| C. | Dependent |
| D. | Equally likely |
| Answer» D. Equally likely | |
| 5956. |
Cards are drawn one by one without replacement from a pack of 52 cards. The probability that 10 cards will precede the first ace is |
| A. | \[\frac{241}{1456}\] |
| B. | \[\frac{164}{4165}\] |
| C. | \[\frac{451}{884}\] |
| D. | None of these |
| Answer» C. \[\frac{451}{884}\] | |
| 5957. |
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 | |
| 5958. |
A dice is rolled three times, the probability of getting a larger number than the previous number each time is |
| A. | \[\frac{15}{216}\] |
| B. | \[\frac{5}{54}\] |
| C. | \[\frac{13}{216}\] |
| D. | \[\frac{1}{18}\] |
| Answer» C. \[\frac{13}{216}\] | |
| 5959. |
A box contains 2 black, 4 white and 3 red balls. One ball is drawn at random from the box and kept aside. From the remaining balls in the box, another ball is drawn at random and kept aside the first. This process is repeated till all the balls are drawn from the box. The probability that the balls drawn are in the sequence of 2 black, 4 white and 3 red is |
| A. | \[\frac{1}{1260}\] |
| B. | \[\frac{1}{7560}\] |
| C. | \[\frac{1}{126}\] |
| D. | None of these |
| Answer» B. \[\frac{1}{7560}\] | |
| 5960. |
?A? draws two cards with replacement from a pack of 52 cards and ?B' throws a pair of dice what is the chance that ?A? gets both cards of same suit and ?B? gets total of 6 [MNR 1989] |
| A. | \[\frac{1}{144}\] |
| B. | \[\frac{1}{4}\] |
| C. | \[\frac{5}{144}\] |
| D. | \[\frac{7}{144}\] |
| Answer» D. \[\frac{7}{144}\] | |
| 5961. |
In order to get at least once a head with probability \[\ge 0.9,\] the number of times a coin needs to be tossed is [Roorkee 1989] |
| A. | 3 |
| B. | 4 |
| C. | 5 |
| D. | None of these |
| Answer» C. 5 | |
| 5962. |
For independent events \[{{A}_{1}},\,{{A}_{2}},\,..........,{{A}_{n}},\] \[P({{A}_{i}})=\frac{1}{i+1},\]\[i=1,\,\,2,\,......,\,\,n.\] Then the probability that none of the event will occur, is |
| A. | \[\frac{n}{n+1}\] |
| B. | \[\frac{n-1}{n+1}\] |
| C. | \[\frac{1}{n+1}\] |
| D. | None of these |
| Answer» D. None of these | |
| 5963. |
For any two independent events \[{{E}_{1}}\] and \[{{E}_{2}},\] \[P\,\{({{E}_{1}}\cup {{E}_{2}})\cap ({{\bar{E}}_{1}}\cap {{\bar{E}}_{2}})\}\] is [IIT 1991; Pb. CET 2003] |
| A. | \[<\frac{1}{4}\] |
| B. | \[>\frac{1}{4}\] |
| C. | \[\ge \frac{1}{2}\] |
| D. | None of these |
| Answer» B. \[>\frac{1}{4}\] | |
| 5964. |
If \[P(A)=0.65,\,\,P(B)=0.15,\] then \[P(\bar{A})+P(\bar{B})=\] [Pb. CET 1989; EAMCET 1988] |
| A. | 1.5 |
| B. | 1.2 |
| C. | 0.8 |
| D. | None of these |
| Answer» C. 0.8 | |
| 5965. |
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 | |
| 5966. |
A card is drawn at random from a pack of 100 cards numbered 1 to 100. The probability of drawing a number which is a square is [EAMCET 1989] |
| A. | \[\frac{1}{5}\] |
| B. | \[\frac{2}{5}\] |
| C. | \[\frac{1}{10}\] |
| D. | None of these |
| Answer» D. None of these | |
| 5967. |
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. \[\frac{3}{5}\] | |
| 5968. |
The probability of India winning a test match against West Indies is \[\frac{1}{2}\]. Assuming independence from match to match, the probability that in a 5 match series India's second win occurs at the third test, is [IIT 1995; Pb. CET 2003] |
| A. | \[\frac{2}{3}\] |
| B. | \[\frac{1}{2}\] |
| C. | \[\frac{1}{4}\] |
| D. | \[\frac{1}{8}\] |
| Answer» D. \[\frac{1}{8}\] | |
| 5969. |
For any event A [RPET 1995] |
| A. | \[P(A)+P(\bar{A})=0\] |
| B. | \[P(A)+P(\bar{A})=1\] |
| C. | \[P(A)>1\] |
| D. | \[P(\bar{A})<1\] |
| Answer» C. \[P(A)>1\] | |
| 5970. |
The probability of obtaining sum ?8? in a single throw of two dice [RPET 1995] |
| A. | \[\frac{1}{36}\] |
| B. | \[\frac{5}{36}\] |
| C. | \[\frac{4}{36}\] |
| D. | \[\frac{6}{36}\] |
| Answer» C. \[\frac{4}{36}\] | |
| 5971. |
A bag contains 3 white, 3 black and 2 red balls. One by one three balls are drawn without replacing them. The probability that the third ball is red, is [MNR 1994] |
| A. | \[\frac{1}{2}\] |
| B. | \[\frac{1}{3}\] |
| C. | \[\frac{2}{3}\] |
| D. | \[\frac{1}{4}\] |
| Answer» E. | |
| 5972. |
One card is drawn from a pack of 52 cards. The probability that it is a king or diamond is [MP PET 1990, 1994; RPET 1996] |
| A. | \[\frac{1}{26}\] |
| B. | \[\frac{3}{26}\] |
| C. | \[\frac{4}{13}\] |
| D. | \[\frac{3}{13}\] |
| Answer» D. \[\frac{3}{13}\] | |
| 5973. |
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. | 3/16 |
| B. | 3/8 |
| C. | 1/4 |
| D. | None of these |
| Answer» B. 3/8 | |
| 5974. |
The probability of hitting a target by three marksmen are \[\frac{1}{2},\,\frac{1}{3}\] and \[\frac{1}{4}\] respectively. The probability that one and only one of them will hit the target when they fire simultaneously, is [AI CBSE 1982] |
| A. | \[\frac{11}{24}\] |
| B. | \[\frac{1}{12}\] |
| C. | \[\frac{1}{8}\] |
| D. | None of these |
| Answer» B. \[\frac{1}{12}\] | |
| 5975. |
A bag contains 19 tickets numbered from 1 to 19. A ticket is drawn and then another ticket is drawn without replacement. The probability that both the tickets will show even number, is [AI CBSE 1986] |
| A. | \[\frac{9}{19}\] |
| B. | \[\frac{8}{18}\] |
| C. | \[\frac{9}{18}\] |
| D. | \[\frac{4}{19}\] |
| Answer» E. | |
| 5976. |
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. \[\frac{1}{6}\] | |
| 5977. |
A bag contains 5 white, 7 red and 8 black balls. If four balls are drawn one by one without replacement, what is the probability that all are white [AISSE 1987] |
| A. | \[\frac{1}{969}\] |
| B. | \[\frac{1}{380}\] |
| C. | \[\frac{5}{20}\] |
| D. | None of these |
| Answer» B. \[\frac{1}{380}\] | |
| 5978. |
The probability of A, B, C solving a problem are \[\frac{1}{3},\,\frac{2}{7},\,\frac{3}{8}\]respectively. If all the three try to solve the problem simultaneously, the probability that exactly one of them will solve it, is [DSSE 1987] |
| A. | \[\frac{25}{168}\] |
| B. | \[\frac{25}{56}\] |
| C. | \[\frac{20}{168}\] |
| D. | \[\frac{30}{168}\] |
| Answer» C. \[\frac{20}{168}\] | |
| 5979. |
A man and his wife appear for an interview for two posts. The probability of the husband's selection is \[\frac{1}{7}\] and that of the wife's selection is \[\frac{1}{5}\]. What is the probability that only one of them will be selected [AISSE 1987; DSSE 1979, 81, 84] |
| A. | \[\frac{1}{7}\] |
| B. | \[\frac{2}{7}\] |
| C. | \[\frac{3}{7}\] |
| D. | None of these |
| Answer» C. \[\frac{3}{7}\] | |
| 5980. |
A card is drawn at random from a well shuffled pack of 52 cards. The probability of getting a two of heart or diamond is [DSSE 1979] |
| A. | \[\frac{1}{26}\] |
| B. | \[\frac{1}{52}\] |
| C. | \[\frac{1}{13}\] |
| D. | None of these |
| Answer» B. \[\frac{1}{52}\] | |
| 5981. |
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. \[\frac{1}{36}\] | |
| 5982. |
A locker can be opened by dialing a fixed three digit code (between 000 and 999). A stranger who does not know the code tries to open the locker by dialing three digits at random. The probability that the stranger succeeds at the \[{{k}^{th}}\]trial is |
| A. | \[\frac{k}{999}\] |
| B. | \[\frac{k}{1000}\] |
| C. | \[\frac{k-1}{1000}\] |
| D. | None of these |
| Answer» C. \[\frac{k-1}{1000}\] | |
| 5983. |
The event A is independent of itself if and only if \[P(A)=\] |
| A. | 0 |
| B. | 1 |
| C. | 0, 1 |
| D. | None of these |
| Answer» D. None of these | |
| 5984. |
A determinant is chosen at random from the set of all determinants of order 2 with elements 0 or 1 only. The probability that the determinant chosen is non-zero is |
| A. | \[\frac{3}{16}\] |
| B. | \[\frac{3}{8}\] |
| C. | \[\frac{1}{4}\] |
| D. | None of these |
| Answer» C. \[\frac{1}{4}\] | |
| 5985. |
If the probabilities of boy and girl to be born are same, then in a 4 children family the probability of being at least one girl, is |
| A. | \[\frac{14}{16}\] |
| B. | \[\frac{15}{16}\] |
| C. | \[\frac{1}{8}\] |
| D. | \[\frac{3}{8}\] |
| Answer» C. \[\frac{1}{8}\] | |
| 5986. |
A single letter is selected at random from the word ?PROBABILITY?. The probability that the selected letter is a vowel is [MNR 1986; UPSEAT 2000] |
| A. | \[\frac{2}{11}\] |
| B. | \[\frac{3}{11}\] |
| C. | \[\frac{4}{11}\] |
| D. | 0 |
| Answer» D. 0 | |
| 5987. |
There are 4 envelopes with addresses and 4 concerning letters. The probability that letter does not go into concerning proper envelope, is or There are four letters and four addressed envelopes. The chance that all letters are not despatched in the right envelope is [RPET 1997; MP PET 1999; DCE 1999] |
| A. | \[\frac{19}{24}\] |
| B. | \[\frac{21}{23}\] |
| C. | \[\frac{23}{24}\] |
| D. | \[\frac{1}{24}\] |
| Answer» D. \[\frac{1}{24}\] | |
| 5988. |
There are n letters and n addressed envelops. The probability that each letter takes place in right envelop is |
| A. | \[\frac{1}{n\,!}\] |
| B. | \[\frac{1}{(n-1)\,!}\] |
| C. | \[1-\frac{1}{n\,!}\] |
| D. | None of these |
| Answer» B. \[\frac{1}{(n-1)\,!}\] | |
| 5989. |
A card is drawn randomly from a pack of playing cards. Then the probability that it is neither ace nor king, is |
| A. | \[\frac{11}{13}\] |
| B. | \[\frac{8}{13}\] |
| C. | \[\frac{10}{13}\] |
| D. | \[\frac{12}{13}\] |
| Answer» B. \[\frac{8}{13}\] | |
| 5990. |
. A number is chosen from first 100 natural numbers. The probability that the number is even or divisible by 5, is |
| A. | \[\frac{3}{4}\] |
| B. | \[\frac{2}{3}\] |
| C. | \[\frac{4}{5}\] |
| D. | \[\frac{3}{5}\] |
| Answer» E. | |
| 5991. |
A number is chosen at random from first ten natural numbers. The probability that number is odd and perfect square is |
| A. | \[\frac{2}{9}\] |
| B. | \[\frac{2}{5}\] |
| C. | \[\frac{3}{7}\] |
| D. | \[\frac{1}{5}\] |
| Answer» E. | |
| 5992. |
If A is a sure event, then the value of P (A not ) is |
| A. | 0 |
| B. | ?1 |
| C. | 1 |
| D. | None of these |
| Answer» B. ?1 | |
| 5993. |
If A and B are mutually exclusive events, then the value of P (A or B) is |
| A. | 0 |
| B. | ?1 |
| C. | 1 |
| D. | None of these |
| Answer» D. None of these | |
| 5994. |
The probability of 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. \[\frac{1}{3}\] | |
| 5995. |
The probabilities of winning the race by two athletes A and B are \[\frac{1}{5}\]and \[\frac{1}{4}.\] The probability of winning by neither of them, is |
| A. | \[\frac{3}{5}\] |
| B. | \[\frac{3}{4}\] |
| C. | \[\frac{2}{5}\] |
| D. | \[\frac{4}{5}\] |
| Answer» B. \[\frac{3}{4}\] | |
| 5996. |
For the two events A and B, \[P(A)=0.38,\,\] \[P(B)=0.41,\] then the value of \[P(A\]not) is |
| A. | 0.41 |
| B. | 0.62 |
| C. | 0.59 |
| D. | 0.21 |
| Answer» C. 0.59 | |
| 5997. |
From a well shuffled pack of cards one card is drawn at random. The probability that the card drawn is an ace is |
| A. | \[\frac{1}{13}\] |
| B. | \[\frac{4}{13}\] |
| C. | \[\frac{3}{52}\] |
| D. | None of these |
| Answer» B. \[\frac{4}{13}\] | |
| 5998. |
Three identical dice are rolled. The probability that same number will appear on each of them will be [SCRA 1991; MP PET 1989; IIT 1984; RPET 2000, 02; DCE 2001] |
| A. | \[\frac{1}{6}\] |
| B. | \[\frac{1}{36}\] |
| C. | \[\frac{1}{18}\] |
| D. | \[\frac{3}{28}\] |
| Answer» C. \[\frac{1}{18}\] | |
| 5999. |
The chance of throwing at least 9 in a single throw with two dice, is [SCRA 1980] |
| A. | \[\frac{1}{18}\] |
| B. | \[\frac{5}{18}\] |
| C. | \[\frac{7}{18}\] |
| D. | \[\frac{11}{18}\] |
| Answer» C. \[\frac{7}{18}\] | |
| 6000. |
The probability that an event will fail to happen is 0.05. The probability that the event will take place on 4 consecutive occasions is [Roorkee 1990] |
| A. | 0.00000625 |
| B. | 0.18543125 |
| C. | 0.00001875 |
| D. | 0.81450625 |
| Answer» E. | |