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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.
| 6051. |
A bag x contains 3 white balls and 2 black balls and another bag y contains 2 white balls and 4 black balls. A bag and a ball out of it are picked at random. The probability that the ball is white, is [IIT 1971] |
| A. | 3/5 |
| B. | 7/15 |
| C. | 1/2 |
| D. | None of these |
| Answer» C. 1/2 | |
| 6052. |
A bag contains 3 white and 2 black balls and another bag contains 2 white and 4 black balls. A ball is picked up randomly. The probability of its being black is [MP PET 1989] |
| A. | \[\frac{2}{5}\] |
| B. | \[\frac{8}{15}\] |
| C. | \[\frac{6}{11}\] |
| D. | \[\frac{2}{3}\] |
| Answer» C. \[\frac{6}{11}\] | |
| 6053. |
The probability that a leap year selected randomly will have 53 Sundays is [MP PET 1991, 93, 95; Pb. CET 2002] |
| A. | \[\frac{1}{7}\] |
| B. | \[\frac{2}{7}\] |
| C. | \[\frac{4}{53}\] |
| D. | \[\frac{4}{49}\] |
| Answer» C. \[\frac{4}{53}\] | |
| 6054. |
A bag contains 3 red and 7 black balls, two balls are taken out at random, without replacement. If the first ball taken out is red, then what is the probability that the second taken out ball is also red [Pb. CET 2000] |
| A. | \[\frac{1}{10}\] |
| B. | \[\frac{1}{15}\] |
| C. | \[\frac{3}{10}\] |
| D. | \[\frac{2}{21}\] |
| Answer» C. \[\frac{3}{10}\] | |
| 6055. |
The chance of throwing a total of 7 or 12 with 2 dice, is [Kurukshetra CEE 2002] |
| A. | \[\frac{2}{9}\] |
| B. | \[\frac{5}{9}\] |
| C. | \[\frac{5}{36}\] |
| D. | \[\frac{7}{36}\] |
| Answer» E. | |
| 6056. |
The chance of getting a doublet with 2 dice is [Kurukshetra CEE 2002] |
| A. | \[\frac{2}{3}\] |
| B. | \[\frac{1}{6}\] |
| C. | \[\frac{5}{6}\] |
| D. | \[\frac{5}{36}\] |
| Answer» C. \[\frac{5}{6}\] | |
| 6057. |
A problem in Mathematics is given to three students A, B, C and their respective probability of solving the problem is 1/2, 1/3 and 1/4. Probability that the problem is solved is [RPET 2001; AIEEE 2002] |
| A. | \[\frac{3}{4}\] |
| B. | \[\frac{1}{2}\] |
| C. | \[\frac{2}{3}\] |
| D. | \[\frac{1}{3}\] |
| Answer» B. \[\frac{1}{2}\] | |
| 6058. |
Two cards are drawn without replacement from a well-shuffled pack. Find the probability that one of them is an ace of heart [UPSEAT 2002] |
| A. | \[\frac{1}{25}\] |
| B. | \[\frac{1}{26}\] |
| C. | \[\frac{1}{52}\] |
| D. | None of these |
| Answer» C. \[\frac{1}{52}\] | |
| 6059. |
A coin is tossed and a dice is rolled. The probability that the coin shows the head and the dice shows 6 is [MP PET 1994; Pb. CET 2001] |
| A. | \[\frac{1}{8}\] |
| B. | \[\frac{1}{12}\] |
| C. | \[\frac{1}{2}\] |
| D. | 1 |
| Answer» C. \[\frac{1}{2}\] | |
| 6060. |
If a coin be tossed n times then probability that the head comes odd times is [RPET 2002] |
| A. | \[\frac{1}{2}\] |
| B. | \[\frac{1}{{{2}^{n}}}\] |
| C. | \[\frac{1}{{{2}^{n-1}}}\] |
| D. | None of these |
| Answer» B. \[\frac{1}{{{2}^{n}}}\] | |
| 6061. |
The probability that a leap year will have 53 Fridays or 53 Saturdays is [MP PET 2002] |
| A. | \[\frac{2}{7}\] |
| B. | \[\frac{3}{7}\] |
| C. | \[\frac{4}{7}\] |
| D. | \[\frac{1}{7}\] |
| Answer» C. \[\frac{4}{7}\] | |
| 6062. |
If two dice are thrown simultaneously then probability that 1 comes on first dice is [RPET 2002] |
| A. | \[\frac{1}{36}\] |
| B. | \[\frac{5}{36}\] |
| C. | \[\frac{1}{6}\] |
| D. | None of these |
| Answer» D. None of these | |
| 6063. |
In a college, 25% of the boys and 10% of the girls offer Mathematics. The girls constitute 60% of the total number of students. If a student is selected at random and is found to be studying Mathematics, the probability that the student is a girl, is [MP PET 2001] |
| A. | \[\frac{1}{6}\] |
| B. | \[\frac{3}{8}\] |
| C. | \[\frac{5}{8}\] |
| D. | \[\frac{5}{6}\] |
| Answer» C. \[\frac{5}{8}\] | |
| 6064. |
A pair of a dice thrown, if 5 appears on at least one of the dice, then the probability that the sum is 10 or greater is [MP PET 2001] |
| A. | \[\frac{11}{36}\] |
| B. | \[\frac{2}{9}\] |
| C. | \[\frac{3}{11}\] |
| D. | \[\frac{1}{12}\] |
| Answer» E. | |
| 6065. |
Three coins are tossed together, then the probability of getting at least one head is [RPET 2001; MP PET 1989] |
| A. | \[\frac{1}{2}\] |
| B. | \[\frac{3}{4}\] |
| C. | \[\frac{1}{8}\] |
| D. | \[\frac{7}{8}\] |
| Answer» E. | |
| 6066. |
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. \[\frac{2}{21}\] | |
| 6067. |
What is the probability that when one die is thrown, the number appearing on top is even [AMU 2000] |
| A. | \[\frac{1}{6}\] |
| B. | \[\frac{1}{3}\] |
| C. | \[\frac{1}{2}\] |
| D. | None of these |
| Answer» D. None of these | |
| 6068. |
Suppose that a die (with faces marked 1 to 6) is loaded in such a manner that for K = 1, 2, 3?., 6, the probability of the face marked K turning up when die is tossed is proportional to K. The probability of the event that the outcome of a toss of the die will be an even number is equal to [AMU 2000] |
| A. | \[\frac{1}{2}\] |
| B. | \[\frac{4}{7}\] |
| C. | \[\frac{2}{5}\] |
| D. | \[\frac{1}{21}\] |
| Answer» B. \[\frac{4}{7}\] | |
| 6069. |
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. | |
| 6070. |
Two cards are drawn one by one at random from a pack of 52 cards. The probability that both of them are king, is [MP PET 1994] |
| A. | \[\frac{2}{13}\] |
| B. | \[\frac{1}{169}\] |
| C. | \[\frac{1}{221}\] |
| D. | \[\frac{30}{221}\] |
| Answer» D. \[\frac{30}{221}\] | |
| 6071. |
A coin is tossed 4 times. The probability that at least one head turns up is [MP PET 2000] |
| A. | \[\frac{1}{16}\] |
| B. | \[\frac{2}{16}\] |
| C. | \[\frac{14}{16}\] |
| D. | \[\frac{15}{16}\] |
| Answer» E. | |
| 6072. |
A binary number is made up of 16 bits. The probability of an incorrect bit appearing is p and the errors in different bits are independent of one another. The probability of forming an incorrect number is [AMU 1999] |
| A. | \[\frac{p}{16}\] |
| B. | \[{{p}^{16}}\] |
| C. | \[{}^{16}{{C}_{1}}{{p}^{16}}\] |
| D. | \[1-{{(1-p)}^{16}}\] |
| Answer» E. | |
| 6073. |
Two integers are chosen at random and multiplied. The probability that the product is an even integer is [AMU 1999] |
| A. | \[\frac{1}{2}\] |
| B. | \[\frac{2}{3}\] |
| C. | \[\frac{3}{4}\] |
| D. | \[\frac{4}{5}\] |
| Answer» C. \[\frac{3}{4}\] | |
| 6074. |
An integer is chosen at random and squared. The probability that the last digit of the square is 1 or 5 is [AMU 1999] |
| A. | \[\frac{2}{10}\] |
| B. | \[\frac{3}{10}\] |
| C. | \[\frac{4}{10}\] |
| D. | \[\frac{9}{25}\] |
| Answer» C. \[\frac{4}{10}\] | |
| 6075. |
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. \[\frac{3}{16}\] | |
| 6076. |
The sum of two positive numbers is 100. The probability that their product is greater than 1000 is [RPET 1999] |
| A. | \[\frac{7}{9}\] |
| B. | \[\frac{7}{10}\] |
| C. | \[\frac{2}{5}\] |
| D. | None of these |
| Answer» B. \[\frac{7}{10}\] | |
| 6077. |
A coin is tossed 3 times by 2 persons. What is the probability that both get equal number of heads [DCE 1999] |
| A. | \[\frac{3}{8}\] |
| B. | \[\frac{1}{9}\] |
| C. | \[\frac{5}{16}\] |
| D. | None of these |
| Answer» D. None of these | |
| 6078. |
A fair coin is tossed repeatedly. If tail appears on first four tosses then the probability of head appearing on fifth toss equals [IIT 1998] |
| A. | \[\frac{1}{2}\] |
| B. | \[\frac{1}{32}\] |
| C. | \[\frac{31}{32}\] |
| D. | \[\frac{1}{5}\] |
| Answer» B. \[\frac{1}{32}\] | |
| 6079. |
A person can kill a bird with probability 3/4. He tries 5 times. What is the probability that he may not kill the bird [RPET 1997] |
| A. | \[\frac{243}{1024}\] |
| B. | \[\frac{781}{1024}\] |
| C. | \[\frac{1}{1024}\] |
| D. | \[\frac{1023}{1024}\] |
| Answer» D. \[\frac{1023}{1024}\] | |
| 6080. |
If a dice is thrown twice, then the probability of getting 1 in the first throw only is |
| A. | \[\frac{1}{36}\] |
| B. | \[\frac{3}{36}\] |
| C. | \[\frac{5}{36}\] |
| D. | \[\frac{1}{6}\] |
| Answer» D. \[\frac{1}{6}\] | |
| 6081. |
A bag contains 30 balls numbered from 1 to 30, one ball is drawn randomly. The probability that number on the ball is multiple of 5 or 7 is [RPET 1997] |
| A. | \[\frac{1}{2}\] |
| B. | \[\frac{1}{3}\] |
| C. | \[\frac{2}{3}\] |
| D. | \[\frac{1}{4}\] |
| Answer» C. \[\frac{2}{3}\] | |
| 6082. |
Two dice are thrown together. The probability that at least one will show its digit 6 is [RPET 1996] |
| A. | \[\frac{11}{36}\] |
| B. | \[\frac{36}{11}\] |
| C. | \[\frac{5}{11}\] |
| D. | \[\frac{1}{6}\] |
| Answer» B. \[\frac{36}{11}\] | |
| 6083. |
An unbiased die is tossed until a number greater than 4 appears. The probability that an even number of tosses is needed is [IIT 1994] |
| A. | \[\frac{1}{2}\] |
| B. | \[\frac{2}{5}\] |
| C. | \[\frac{1}{5}\] |
| D. | \[\frac{2}{3}\] |
| Answer» C. \[\frac{1}{5}\] | |
| 6084. |
From a pack of 52 cards, two cards are drawn one by one without replacement. The probability that first drawn card is a king and second is a queen, is [MP PET 1997] |
| A. | \[\frac{2}{13}\] |
| B. | \[\frac{8}{663}\] |
| C. | \[\frac{4}{663}\] |
| D. | \[\frac{103}{663}\] |
| Answer» D. \[\frac{103}{663}\] | |
| 6085. |
From a pack of 52 cards one card is drawn at random, the probability that it is either a king or a queen is |
| A. | \[\frac{1}{13}\] |
| B. | \[\frac{2}{13}\] |
| C. | \[\frac{3}{13}\] |
| D. | \[\frac{4}{13}\] |
| Answer» C. \[\frac{3}{13}\] | |
| 6086. |
The chance of India winning toss is 3/4. If it wins the toss, then its chance of victory is 4/5 otherwise it is only 1/2. Then chance of India's victory is [Kurukshetra CEE 1998] |
| A. | \[\frac{1}{5}\] |
| B. | \[\frac{3}{5}\] |
| C. | \[\frac{3}{40}\] |
| D. | \[\frac{29}{40}\] |
| Answer» E. | |
| 6087. |
A six faced dice is so biased that it is twice as likely to show an even number as an odd number when thrown. It is thrown twice. The probability that the sum of two numbers thrown is even, is [Kurukshetra CEE 1996] |
| A. | \[\frac{1}{12}\] |
| B. | \[\frac{1}{6}\] |
| C. | \[\frac{1}{3}\] |
| D. | \[\frac{2}{3}\] |
| Answer» E. | |
| 6088. |
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. \[\frac{19}{36}\] | |
| 6089. |
The probability that a teacher will give an unannounced test during any class meeting is 1/5. If a student is absent twice, then the probability that the student will miss at least one test is |
| A. | \[\frac{4}{5}\] |
| B. | \[\frac{2}{5}\] |
| C. | \[\frac{7}{5}\] |
| D. | \[\frac{9}{25}\] |
| Answer» E. | |
| 6090. |
Two card are drawn successively with replacement from a pack of 52 cards. The probability of drawing two aces is [MNR 1988; UPSEAT 2000] |
| A. | \[\frac{1}{169}\] |
| B. | \[\frac{1}{221}\] |
| C. | \[\frac{1}{2652}\] |
| D. | \[\frac{4}{663}\] |
| Answer» B. \[\frac{1}{221}\] | |
| 6091. |
If \[{}^{n}{{P}_{4}}\ :\ {}^{n}{{P}_{5}}=1:2\], then \[n=\] [MP PET 1987; RPET 1996] |
| A. | 4 |
| B. | 5 |
| C. | 6 |
| D. | 7 |
| Answer» D. 7 | |
| 6092. |
How many words comprising of any three letters of the word UNIVERSAL can be formed |
| A. | 504 |
| B. | 405 |
| C. | 540 |
| D. | 450 |
| Answer» B. 405 | |
| 6093. |
How many numbers lying between 999 and 10000 can be formed with the help of the digit 0,2,3,6,7,8 when the digits are not to be repeated [AMU 2005] |
| A. | 100 |
| B. | 200 |
| C. | 300 |
| D. | 400 |
| Answer» D. 400 | |
| 6094. |
Let the eleven letters \[A,B\].....,K denote an arbitrary permutation of the integers (1, 2,.....11), then \[(A-1)(B-2)(C-3).....(K-11)\] [Orissa JEE 2005] |
| A. | Necessarily zero |
| B. | Always odd |
| C. | Always even |
| D. | None of these |
| Answer» D. None of these | |
| 6095. |
If the letters of the word SACHIN arranged in all possible ways and these words are written out as in dictionary, then the word SACHIN appears at serial number [AIEEE 2005] |
| A. | 603 |
| B. | 602 |
| C. | 601 |
| D. | 600 |
| Answer» D. 600 | |
| 6096. |
If a man and his wife enter in a bus, in which five seats are vacant, then the number of different ways in which they can be seated is [Pb. CET 2004] |
| A. | 2 |
| B. | 5 |
| C. | 20 |
| D. | 40 |
| Answer» D. 40 | |
| 6097. |
The number of ways in which 9 persons can be divided into three equal groups is [Orissa JEE 2003] |
| A. | 1680 |
| B. | 840 |
| C. | 560 |
| D. | 280 |
| Answer» B. 840 | |
| 6098. |
If \[{}^{n}{{P}_{5}}=20.\ {}^{n}{{P}_{3}}\], then \[n=\] |
| A. | 4 |
| B. | 8 |
| C. | 6 |
| D. | 7 |
| Answer» C. 6 | |
| 6099. |
The number of words that can be formed out of the letters of the word ARTICLE so that the vowels occupy even places is [Karnataka CET 2003] |
| A. | 36 |
| B. | 574 |
| C. | 144 |
| D. | 754 |
| Answer» D. 754 | |
| 6100. |
Eleven books consisting of 5 Mathematics, 4 Physics and 2 Chemistry are placed on a shelf. The number of possible ways of arranging them on the assumption that the books of the same subject are all together is [AMU 2002] |
| A. | 4! 2! |
| B. | 11! |
| C. | 5! 4! 3! 2! |
| D. | None of these |
| Answer» D. None of these | |