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MCQOPTIONS
This section includes 992 Mcqs, each offering curated multiple-choice questions to sharpen your General Aptitude knowledge and support exam preparation. Choose a topic below to get started.
| 51. |
If two fair dice are thrown, then what is the probability that the sum is neither 8 not 9? |
| A. | \(\frac{1}{6}\) |
| B. | \(\frac{1}{4}\) |
| C. | \(\frac{3}{4}\) |
| D. | \(\frac{5}{6}\) |
| Answer» D. \(\frac{5}{6}\) | |
| 52. |
A box contains 2 blue, 3 black and 4 red balls. Balls are drawn from the box at random one at a time without replacement. The probability of drawing 2 blue balls first followed by 3 black balls and subsequently 4 red balls is |
| A. | 2/350 |
| B. | 1/629 |
| C. | 1/1260 |
| D. | 1/24 |
| Answer» D. 1/24 | |
| 53. |
If A and B events such that \(P\;\left( {A \cup B} \right) = \frac{3}{4},\;P\;\left( {A \cap B} \right) = \frac{1}{4}\) and \(P\left( {\bar A} \right) = \frac{2}{3}\), then what is P(B) equal to? |
| A. | 1/3 |
| B. | 2/3 |
| C. | 1/8 |
| D. | 2/9 |
| Answer» C. 1/8 | |
| 54. |
In eight throws of a die, 5 or 6 is considered a success. The mean and standard deviation of total number of successes is respectively given by |
| A. | \(\frac{8}{3},\frac{{16}}{9}\) |
| B. | \(\frac{8}{3},\frac{4}{3}\) |
| C. | \(\frac{4}{3},\frac{4}{3}\) |
| D. | \(\frac{4}{3},\frac{{16}}{9}\) |
| Answer» C. \(\frac{4}{3},\frac{4}{3}\) | |
| 55. |
In an examination, a student can choose the order in which two questions (QuesA and QuesB) must be attempted.- If the first question is answered wrong, the student gets zero marks.- If the first question is answered correctly and the second question is not answered correctly, the student gets the marks only for the first question.- If both the questions are answered correctly, the student gets the sum of the marks of the two questions.The following table shows the probability of correctly answering a question and the marks of the question respectively. questionProbability of answering correctlymarksQuesA0.810QuesB0.520Assuming that the student always wants to maximize her expected marks in the examination, in which order should she attempt the questions and what is the expected marks for that order (assume that the questions are independent)? |
| A. | First QuesB and then QuesA. Expected marks 14 |
| B. | First QuesB and then QuesA. Expected marks 22 |
| C. | First QuesA and then QuesB. Expected marks 14. |
| D. | First QuesA and then QuesB. Expected marks 16. |
| Answer» E. | |
| 56. |
A committee of 3 is to be formed from a group of 2 boys and 2 girls. What is the probability that the committee consists of 2 boys and 1 girl? |
| A. | \(\dfrac{2}{3}\) |
| B. | \(\dfrac{1}{4}\) |
| C. | \(\dfrac{3}{4}\) |
| D. | \(\dfrac{1}{2}\) |
| Answer» E. | |
| 57. |
In a car showroom different models of car are on display. There are two models of 800 cc car and four models of 1500 cc car. What is the probability that a customer will choose am 800 cc car? |
| A. | 0.22 |
| B. | 0.67 |
| C. | 0.33 |
| D. | 0.5 |
| Answer» D. 0.5 | |
| 58. |
Find the probability that a leap year has 52 Sundays. |
| A. | 3/5 |
| B. | 1/3 |
| C. | 5/7 |
| D. | 1/2 |
| Answer» D. 1/2 | |
| 59. |
A dealer has a stock of 15 gold coins out of which 6 are counterfeits. A person randomly picks 4 of the 15 gold coins. What is the probability that all the coins picked will be counterfeits? |
| A. | \(\dfrac{1}{91}\) |
| B. | \(\dfrac{4}{91}\) |
| C. | \(\dfrac{6}{91}\) |
| D. | \(\dfrac{15}{91}\) |
| Answer» B. \(\dfrac{4}{91}\) | |
| 60. |
In a box there are 5 red balls, 3 blue balls and 2 green balls. If a ball is selected at random what is the probability that it is blue or green? |
| A. | \(\frac{2}{5}\) |
| B. | \(\frac{1}{3}\) |
| C. | \(\frac{9}{10}\) |
| D. | \(\frac{1}{2}\) |
| Answer» E. | |
| 61. |
In throwing of two dice, the number of exhaustive events that ‘5’ will never appear on any one of the dice is |
| A. | 5 |
| B. | 18 |
| C. | 25 |
| D. | 36 |
| Answer» D. 36 | |
| 62. |
A box contains 3 coins, one coin is fair, one coin is two headed and one coin is weighted, so that the probability of heads appearing is \(\dfrac{1}{3}\). A coin is selected at random and tossed, then the probability that head appears, is |
| A. | \(\dfrac{11}{18}\) |
| B. | \(\dfrac{7}{18}\) |
| C. | \(\dfrac{1}{8}\) |
| D. | \(\dfrac{1}{4}\) |
| Answer» B. \(\dfrac{7}{18}\) | |
| 63. |
If P(E) = 0.38 then probability of 'not E' is |
| A. | 0.72 |
| B. | 0.73 |
| C. | 0.62 |
| D. | 0.5 |
| Answer» D. 0.5 | |
| 64. |
A card is drawn at random from a well shuffled standard deck of 52 cards. What is the probability of getting either a heart or a diamond? |
| A. | \(\frac{{7}}{{16}}\) |
| B. | \(\frac{{1}}{{2}}\) |
| C. | \(\frac{{3}}{{13}}\) |
| D. | \(\frac{{1}}{{4}}\) |
| Answer» C. \(\frac{{3}}{{13}}\) | |
| 65. |
If P(E) = 0.73, then probability of 'not E' is |
| A. | 0.3 |
| B. | 0.27 |
| C. | 0.25 |
| D. | 0.37 |
| Answer» C. 0.25 | |
| 66. |
Dialing a telephone number, an old person forgets last three digits. Remembering only that these digits are different, he dialed at random. What is the chance that the number dialed is CORRECT? |
| A. | \(\frac{1}{1000}\) |
| B. | \(\frac{1}{720}\) |
| C. | \(\frac{9}{70}\) |
| D. | \(\frac{1}{7840}\) |
| Answer» C. \(\frac{9}{70}\) | |
| 67. |
For Bernoulli distribution with probability p of success and q of a failure, the relation between mean and variance is - |
| A. | Mean < Variance |
| B. | Mean > Variance |
| C. | Mean = Variance |
| D. | Mean ≤ Variance |
| Answer» C. Mean = Variance | |
| 68. |
How many elements are present only in B? |
| A. | 28 |
| B. | 18 |
| C. | 12 |
| D. | 10 |
| Answer» D. 10 | |
| 69. |
An urn contains 5 red and 2 green balls. A ball is drawn at random from the urn. If the drawn ball is green, then a red ball is added to the urn and if the drawn ball is red, then a green ball is added to the urn; the original ball is not returned to the urn. Now, a second ball is drawn at random from it. The probability that the second ball is red, is: |
| A. | 21/49 |
| B. | 27/49 |
| C. | 26/49 |
| D. | 32/49 |
| Answer» E. | |
| 70. |
Let the sample space consist of non-negative integers up to 50, X denote the numbers which are multiples of 3 and Y denote the odd numbers. Which of the following is/are correct?1. \({\rm{P}}\left( {\rm{X}} \right) = \frac{8}{{25}}\)2. \({\rm{P}}\left( {\rm{Y}} \right) = \frac{1}{2}\)Select the correct answer using the code given below. |
| A. | 1 only |
| B. | 2 only |
| C. | Both 1 and 2 |
| D. | Neither 1 nor 2 |
| Answer» E. | |
| 71. |
If three unbiased coins are tossed, then the probabilities of getting at least two tails and at most two tails are |
| A. | \(\frac{1}{2}\;and\;\frac{5}{8}\) |
| B. | \(\frac{1}{2}\;and\;\frac{3}{8}\) |
| C. | \(\frac{1}{2}\;and\;\frac{7}{8}\) |
| D. | \(\frac{7}{8}\;and\;\frac{1}{2}\) |
| Answer» D. \(\frac{7}{8}\;and\;\frac{1}{2}\) | |
| 72. |
If a box contains 3 white cushions, 4 red cushions and 5 blue cushions, what is the probability of selecting a white or blue cushion?A. 2/3B. 3/4C. 1/4D. 1/9 |
| A. | A |
| B. | D |
| C. | B |
| D. | C |
| Answer» B. D | |
| 73. |
In a leap year, the probability of getting 53 Sundays is |
| A. | 4/7 |
| B. | 3/7 |
| C. | 1/7 |
| D. | 2/7 |
| Answer» E. | |
| 74. |
Out of 264 pens in a box, 33 are defective. If one pen is selected at random what is the probability that it is NOT a defective one? |
| A. | 1/4 |
| B. | 3/4 |
| C. | 7/8 |
| D. | 1/8 |
| Answer» D. 1/8 | |
| 75. |
If a coin is tossed till the first head appears, then what will be the sample space? |
| A. | {H} |
| B. | {TH} |
| C. | {T, HT, HHT, HHHT, ………} |
| D. | {H, TH, TTH, TTTH, ……….} |
| Answer» E. | |
| 76. |
If \(P(A \cap B)=\dfrac{1}{2}, P(\bar A \cap \bar B)= \dfrac{1}{2} \) and 2 P(A) = P(B) = p, then the value of p is given by: |
| A. | 1 / 3 |
| B. | 1 / 4 |
| C. | 2 / 3 |
| D. | 1 / 2 |
| Answer» D. 1 / 2 | |
| 77. |
A fair coin is tossed and an unbiased dice is rolled together. What is the probability of getting a 2 or 4 or 6 along with head? |
| A. | \(\frac{1}{2}\) |
| B. | \(\frac{1}{3}\) |
| C. | \(\frac{1}{4}\) |
| D. | \(\frac{1}{6}\) |
| Answer» D. \(\frac{1}{6}\) | |
| 78. |
In a bolt factory, machines X, Y, Z manufacture bolts that are respectively 25% 35%, and 40% of the factory’s total output. The machines X, Y, Z respectively produce 2%, 4% and 5% defective bolts. A bolt is drawn at random from the product and is found to be defective. What is the probability that it was manufactured by machine X? |
| A. | 5/39 |
| B. | 14/39 |
| C. | 20/39 |
| D. | 34/39 |
| Answer» B. 14/39 | |
| 79. |
If three dice are rolled under the condition that no two dice show the same face, then what is the probability that one of the faces is having the number 6? |
| A. | \(\dfrac{5}{6}\) |
| B. | \(\dfrac{5}{9}\) |
| C. | \(\dfrac{1}{2}\) |
| D. | \(\dfrac{5}{12}\) |
| Answer» D. \(\dfrac{5}{12}\) | |
| 80. |
A knitting wool sample card has 4 red, 1 black, 2 pink and 5 blue samples. If one sample is picked at random what is the probability that it is pink? |
| A. | \(\dfrac{1}{3}\) |
| B. | \(\dfrac{1}{4}\) |
| C. | \(\dfrac{1}{6}\) |
| D. | \(\dfrac{2}{4}\) |
| Answer» D. \(\dfrac{2}{4}\) | |
| 81. |
From a deck of cards, cards are taken out with replacement. What is the probability that the fourteenth card taken out is an ace? |
| A. | \(\frac{1}{{51}}\) |
| B. | \(\frac{4}{{51}}\) |
| C. | \(\frac{1}{{52}}\) |
| D. | \(\frac{1}{{13}}\) |
| Answer» E. | |
| 82. |
Probability density function of a random variable X is given below\(f\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {0.25}&{if\;1 \le x \le 5}\\ 0&{otherwise} \end{array}} \right.\)P (X ≤ 4) is |
| A. | 3/4 |
| B. | 1/2 |
| C. | 1/4 |
| D. | 1/8 |
| Answer» B. 1/2 | |
| 83. |
If A and B are two events such that 2P(A) = 3P(B), where 0 < P(A) < P(B) < 1, then which one of the following is correct? |
| A. | P(A|B) < P(B|A) < P(A ∩ B) |
| B. | P(A ∩ B) < P(B|A) < P(A|B) |
| C. | P(B|A) < P(A|B) < P(A ∩ B) |
| D. | P(A ∩ B) < P(A|B) < P(B|A) |
| Answer» C. P(B|A) < P(A|B) < P(A ∩ B) | |
| 84. |
A and B are independent witnesses in a case, the chance that A speaks truth is x and B speaks truth is y, If A and B agree on certain statements, the probability that the statement is true is |
| A. | \(\rm \dfrac{xy}{xy+(1-x)(1-y)}\) |
| B. | \(\rm \dfrac{xy}{(1-x)(1-y)}\) |
| C. | \(\rm \dfrac{(1-x)(1-y)}{xy+(1-x)(1-y)}\) |
| D. | \(\rm \dfrac{x+y}{xy+(1-x)(1-y)}\) |
| Answer» B. \(\rm \dfrac{xy}{(1-x)(1-y)}\) | |
| 85. |
In city there are 50 squares (including dead ends). Among these squares, m squares are there each of which is adjacent to odd number of roads. Then which of the following is impossible for the value of m? |
| A. | 10 |
| B. | 2 |
| C. | 0 |
| D. | 15 |
| Answer» E. | |
| 86. |
If A and B be two arbitrary events, then |
| A. | \(P(A∩B)=P(A)P(B)\) |
| B. | \(P(A∪B)=P(A)+P(B)\) |
| C. | \(P(A/B)=P(A∩B)P(B)\) |
| D. | \(P(A∪B)≤P(A)+P(B)\) |
| Answer» E. | |
| 87. |
Match List I with List II List I List IIA. Bayes' Theorem I. P(E̅) = 1 - P(E) B. Conditional Probability II. \(P(E_1 \cup E_2) = P(E_1) + P(E_2)\)C. Theorem of complementary eventsIII. \(P(E_2/E_1)=\dfrac{P(E_1 \cap E_2)}{P(E_1)}\)D. Theorem of additionIV. \(P(H_i/E)=\dfrac{P(H_i \cap E)}{P(E)}\) Choose the correct answer from the options given below: |
| A. | A - I, B - IV, C - III, D - II |
| B. | A - III, B - IV, C - II, D - I |
| C. | A - III, B - IV, C - I, D - II |
| D. | A - IV, B - III, C - I, D - II |
| Answer» E. | |
| 88. |
If two dice are thrown, then the probability that at least one of the dice shows a number less than 5 is: |
| A. | 7 / 9 |
| B. | 8 / 9 |
| C. | 1 / 3 |
| D. | 2 / 3 |
| Answer» C. 1 / 3 | |
| 89. |
If two dice are thrown, then what is the probability that the sum on the two faces is greater than or equal to 4? |
| A. | \(\frac{{13}}{{18}}\) |
| B. | \(\frac{5}{6}\) |
| C. | \(\frac{{11}}{{12}}\) |
| D. | \(\frac{{35}}{{36}}\) |
| Answer» D. \(\frac{{35}}{{36}}\) | |
| 90. |
If the truth value of the statement p → (~q ∨ r) is false (F), then the truth values of the statements p, q, and r are respectively: |
| A. | T, T, F |
| B. | T, F, F |
| C. | T, F, T |
| D. | F, T, T |
| Answer» B. T, F, F | |
| 91. |
In a single throw of a die, what is the probability of getting a number greater than 4? |
| A. | \(\frac{1}{3}\) |
| B. | \(\frac{1}{2}\) |
| C. | \(\frac{2}{3}\) |
| D. | \(\frac{1}{4}\) |
| Answer» B. \(\frac{1}{2}\) | |
| 92. |
A card is drawn from a well shuffled pack of 52 cards. A gambler bets that it is either a heart or an ace. What are odds against his winning this bet? |
| A. | 9 ∶ 4 |
| B. | 4 ∶ 9 |
| C. | 35 ∶ 52 |
| D. | 1 ∶ 3 |
| Answer» B. 4 ∶ 9 | |
| 93. |
A box contains 4 red balls and 6 black balls. Three balls are selected randomly from the box one after another without replacement. The probability that the selected set contains one red ball and two black balls is |
| A. | 1/20 |
| B. | 1/12 |
| C. | 3/10 |
| D. | 1/2 |
| Answer» E. | |
| 94. |
A card is drawn from a well shuffled pack of playing cards. Find the probability that it is either a diamond or a king. |
| A. | 4/13 |
| B. | 1/13 |
| C. | 13/4 |
| D. | 5/13 |
| Answer» B. 1/13 | |
| 95. |
If the probability of A to fail in an examination is 0.2 and that for B is 0.3, then, the probability that either A or B fails is: |
| A. | 0.5 |
| B. | 0.38 |
| C. | 0.8 |
| D. | 0.25 |
| Answer» C. 0.8 | |
| 96. |
In a game, a man wins Rs. 100 if he gets 5 or 6 on a throw of a fair die and loses Rs. 50 for getting any other number on the die. If he decides to throw the die either till he gets five or a six or to a maximum of three throws, then his expected gain/loss (in rupees) is |
| A. | \(\frac{{400}}{3}{\rm{\;loss}}\) |
| B. | \({\rm{\;}}\frac{{400}}{9}{\rm{\;loss}}\) |
| C. | 0 |
| D. | \({\rm{\;}}\frac{{400}}{3}{\rm{\;gain}}\) |
| Answer» D. \({\rm{\;}}\frac{{400}}{3}{\rm{\;gain}}\) | |
| 97. |
A coin is biased so that heads comes up thrice as likely as tails. For three independent tosses of a coin, what is the probability of getting at most two tails? |
| A. | 0.16 |
| B. | 0.48 |
| C. | 0.58 |
| D. | 0.98 |
| Answer» E. | |
| 98. |
Consider the following statements:Statement I:Median can be computed even when the end intervals of a frequency distribution are open.Statement II:Median is a positional average.Which one of the following is correct in respect of the above statements? |
| A. | Both Statement I and Statement II are true and Statement II is the correct explanation of Statement I |
| B. | Both Statement I and Statement II are true and Statement II is not the correct explanation of Statement I |
| C. | Statement I is true but Statement II is false |
| D. | Statement I is false but Statement II is true |
| Answer» B. Both Statement I and Statement II are true and Statement II is not the correct explanation of Statement I | |
| 99. |
Consider a binomial random variable X. If X1, X2,...Xn are independent and identically distributed samples from the distribution of X with sum \(Y = \mathop \sum \limits_{i = 1}^n {X_i}\) then the distribution of Y as n → ∞ can be approximated as |
| A. | Exponential |
| B. | Bernoulli |
| C. | Binomial |
| D. | Normal |
| Answer» D. Normal | |
| 100. |
A coin is tossed five times. What is the probability that heads are observed more than three times? |
| A. | \(\frac{3}{{16}}\) |
| B. | \(\frac{5}{{16}}\) |
| C. | \(\frac{1}{{2}}\) |
| D. | \(\frac{3}{{32}}\) |
| Answer» B. \(\frac{5}{{16}}\) | |