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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.
| 101. |
For any two events A and B, the probability that at least one of them occur is 0.6. If A and B occur simultaneously with a probability 0.3, then P(A') + P(B') is |
| A. | 0.9 |
| B. | 1.15 |
| C. | 1.1 |
| D. | 1 |
| Answer» D. 1 | |
| 102. |
Let X1 and X2 be independent random variables each having geometric distribution qk p ; k = 0, 1, 2, …. Then the conditional distribution of X1 given X1 + X2 is |
| A. | Binomial |
| B. | Poisson |
| C. | Uniform |
| D. | Exponential |
| Answer» D. Exponential | |
| 103. |
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 |
| A. | 3 / 5 |
| B. | 1 / 5 |
| C. | 2 / 5 |
| D. | 4 / 5 |
| Answer» D. 4 / 5 | |
| 104. |
2 dices are thrown randomly. Find the probability that the sum would be 6. |
| A. | 11/36 |
| B. | 5/36 |
| C. | 25/36 |
| D. | 1/6 |
| E. | 1/18 |
| Answer» C. 25/36 | |
| 105. |
For two events, A and B, it is given that \({\rm{P}}\left( {\rm{A}} \right) = \frac{3}{5},{\rm{\;P}}\left( {\rm{B}} \right) = \frac{3}{{10}}\) and \({\rm{P}}\left( {{\rm{A|B}}} \right) = \frac{2}{3}\). If A̅ and B̅ are the complementary events of A and B, then what is P(A̅ | B̅) equal to? |
| A. | \(\frac{3}{7}\) |
| B. | \(\frac{3}{4}\) |
| C. | \(\frac{1}{3}\) |
| D. | \(\frac{4}{7}\) |
| Answer» B. \(\frac{3}{4}\) | |
| 106. |
A box contains 15 blue balls and 45 black balls. If 2 balls are selected randomly, without replacement, the probability of an outcome in which the first selected is a blue ball and the second selected is a black ball, is ______. |
| A. | \(\dfrac{45}{236}\) |
| B. | \(\dfrac{1}{4}\) |
| C. | \(\dfrac{3}{16}\) |
| D. | \(\dfrac{3}{4}\) |
| Answer» B. \(\dfrac{1}{4}\) | |
| 107. |
An unbiased die with faces marked 1, 2, 3, 4, 5 and 6 is rolled four times. Out of four face values obtained, the probability that the minimum face value is not less than 2 and the maximum face value is not greater than 5 is |
| A. | 16/81 |
| B. | 1/81 |
| C. | 80/81 |
| D. | 65/81 |
| Answer» B. 1/81 | |
| 108. |
Find the probability of getting exactly 9 heads if an unbiased coin is tossed 20 times ? |
| A. | 20C8 \(\rm \frac{1}{2}^{20}\) |
| B. | 20C9 \(\rm \frac{1}{2}^{20}\) |
| C. | 20C9 \(\rm \frac{1}{2}^{10}\) |
| D. | 20C9 \(\rm \frac{1}{2}^{40}\) |
| Answer» C. 20C9 \(\rm \frac{1}{2}^{10}\) | |
| 109. |
A dice is thrown. What is the probability of getting a number not greater than 5? |
| A. | \(\frac{6}{5}\) |
| B. | \(\frac{7}{5}\) |
| C. | \(\frac{5}{6}\) |
| D. | \(\frac{5}{7}\) |
| Answer» D. \(\frac{5}{7}\) | |
| 110. |
A die is thrown. The probability of getting a number greater than 6 is: |
| A. | \(\frac{1}{2}\) |
| B. | \(\frac{1}{6}\) |
| C. | 1 |
| D. | 0 |
| Answer» E. | |
| 111. |
A question is given to three students A, B and C whose chances of solving it are \(\frac{1}{2},\frac{1}{3}\) and \(\frac{1}{4}\) respectively. What is the probability that the question will be solved? |
| A. | \(\frac{1}{{24}}\) |
| B. | \(\frac{1}{4}\) |
| C. | \(\frac{3}{4}\) |
| D. | \(\frac{{23}}{{24}}\) |
| Answer» D. \(\frac{{23}}{{24}}\) | |
| 112. |
A problem in Mathematics is given to 3 students A, B and C. If the probability of A solving the problem is \(\dfrac{1}{2}\) and B not solving it is \(\dfrac{1}{4}\) and the whole probability of the problem being solved is \(\dfrac{63}{64}\), then what is the probability of solving it by C? |
| A. | \(\dfrac18\) |
| B. | \(\dfrac1{64}\) |
| C. | \(\dfrac78\) |
| D. | \(\dfrac12\) |
| Answer» D. \(\dfrac12\) | |
| 113. |
A bag has four cuboids and three cubes. What is probability of getting 1 cube ? |
| A. | 3/7 |
| B. | 4/7 |
| C. | 1 |
| D. | 2/7 |
| Answer» B. 4/7 | |
| 114. |
A card is drawn from a well-shuffled deck of 52 cards. What is the probability that it is queen of spade? |
| A. | \(\frac{1}{{52}}\) |
| B. | \(\frac{1}{{13}}\) |
| C. | \(\frac{1}{4}\) |
| D. | \(\frac{1}{8}\) |
| Answer» B. \(\frac{1}{{13}}\) | |
| 115. |
If {x} is a continuous, real valued random variable defined over the interval (− ∞, + ∞) and its occurrence is defined by the density function given as: \({\rm{ f}}\left( {\rm{x}} \right){\rm{ = }}\frac{{\rm{1}}}{{\sqrt {{\rm{2\pi }}\;} }{{\rm{\times b}}}}\times{{\rm{e}}^{{\rm{ - }}\frac{{\rm{1}}}{{\rm{2}}}{{\left( {\frac{{{\rm{x - a }}}}{{\rm{b }}}} \right)}^{\rm{2}}}}}\)where 'a' and 'b' are the statistical attributes of the random variable {x}. The value of the integral \( \mathop \smallint \limits_{-\infty}^a\frac{{\rm{1}}}{{\sqrt {{\rm{2\pi }}\;} }{{\rm{\times b}}}}\times{{\rm{e}}^{{\rm{ - }}\frac{{\rm{1}}}{{\rm{2}}}{{\left( {\frac{{{\rm{x - a }}}}{{\rm{b }}}} \right)}^{\rm{2}}}}}dx\) is |
| A. | 1 |
| B. | 0.5 |
| C. | π |
| D. | 2 π |
| Answer» C. π | |
| 116. |
In throwing of a dice, the probability of getting an even number is |
| A. | \(\frac{1}{2}\) |
| B. | \(\frac{1}{3}\) |
| C. | \(\frac{1}{6}\) |
| D. | \(\frac{1}{4}\) |
| Answer» B. \(\frac{1}{3}\) | |
| 117. |
A coin is tossed 5 times. The probability that tail appears an odd number of times, is |
| A. | \(\frac{1}{2}\) |
| B. | \(\frac{1}{3}\) |
| C. | \(\frac{2}{5}\) |
| D. | \(\frac{1}{5}\) |
| Answer» B. \(\frac{1}{3}\) | |
| 118. |
In how many ways all letters of word ASSERTION can be arranged? |
| A. | 5760 |
| B. | 362880 |
| C. | 181440 |
| D. | 6480 |
| Answer» D. 6480 | |
| 119. |
Person X can solve 80% of the ISRO question paper and Person Y can solve 60%. The probability that at least one of them will solve a problem from the question paper, selected at random is: |
| A. | 0.48 |
| B. | 0.7 |
| C. | 0.88 |
| D. | 0.92 |
| Answer» E. | |
| 120. |
A box contains 4 red balls, 5 green balls and 6 white balls. A ball is drawn at random from the box. What is the probability that the ball drawn is either red or green? |
| A. | 2/5 |
| B. | 1/5 |
| C. | 3/5 |
| D. | 7/15 |
| Answer» D. 7/15 | |
| 121. |
Probabilities to solve a certain problem by Pragati and Tripti are respectively \(\frac{1}{3}\) and \(\frac{1}{2}\). The probability that the problem will be solved is: |
| A. | \(\frac{1}{2}\) |
| B. | \(\frac{1}{3}\) |
| C. | \(\frac{2}{3}\) |
| D. | \(\frac{1}{6}\) |
| Answer» D. \(\frac{1}{6}\) | |
| 122. |
Let us consider ∪ as a combined set of 70 elements. If A, B are subsets of ∪ such that n(A) = 20, n(B) = 30 and n(A ∩ B) = 10 then n (A '∩ B') = |
| A. | 40 |
| B. | 60 |
| C. | 30 |
| D. | None of these |
| Answer» D. None of these | |
| 123. |
A bag contains 4 red, 5 black and 6 white balls. If a ball is drawn from the bag, then what is the probability that it is black ? |
| A. | \(\frac{1}{3}\) |
| B. | \(\frac{4}{15}\) |
| C. | \(\frac{2}{5}\) |
| D. | \(\frac{2}{15}\) |
| Answer» B. \(\frac{4}{15}\) | |
| 124. |
If A and B are two events such that \(\rm P(A\cup B) = \dfrac{5}{6}\), \(\rm P(A\cap B) = \dfrac{1}{3}\) and \(\rm P(\bar{B}) = \dfrac{1}{2}\), then the events A and B are: |
| A. | Dependent. |
| B. | Independent. |
| C. | Mutually exclusive. |
| D. | None of these. |
| Answer» C. Mutually exclusive. | |
| 125. |
A special dice with numbers 1, -1, 2, -2, 0 and 3 is thrown thrice. What is the probability that the sum of the numbers occurring on the upper face is zero? |
| A. | 1/72 |
| B. | 1/8 |
| C. | 7/72 |
| D. | 25/216 |
| Answer» E. | |
| 126. |
If we throw two coins in the air, then the probability of getting both tails will be: |
| A. | 1/2 |
| B. | 1/4 |
| C. | 2 |
| D. | 4 |
| Answer» C. 2 | |
| 127. |
Match List I with List II.Let A and B be events with P(A) = \(\frac{2}{3}\), P(B) = \(\frac{1}{2}\) and P (A ∩ B) = \(\frac{1}{3}\)List- IList - IIProbability of an event Value(A) P (A ∩ Bc)(I) \(\frac{2}{3}\)(B) P (A ∪ Bc)(II) \(\frac{1}{3}\)(C) P (Ac ∩ Bc)(III) \(\frac{5}{6}\)(D) P (Ac ∪ Bc)(IV) \(\frac{1}{6}\)(Here c stands for complement)Choose the correct answer from the options given below: |
| A. | (A)-(II), (B)-(III), (C)-(IV), (D)-(I) |
| B. | (A)-(IV), (B)-(III), (C)-(II), (D)-(I) |
| C. | (A)-(I), (B)-(III), (C)-(IV), (D)-(II) |
| D. | (A)-(II), (B)-(IV), (C)-(III), (D)-(I) |
| Answer» B. (A)-(IV), (B)-(III), (C)-(II), (D)-(I) | |
| 128. |
A medicine is known to be 75% effective to cure a patient. If the medicine is given to 5 patients, what is the probability that at least one patient is cured by this medicine? |
| A. | \(\frac{1}{{1024}}\) |
| B. | \(\frac{{243}}{{1024}}\) |
| C. | \(\frac{{1023}}{{1024}}\) |
| D. | \(\frac{{781}}{{1024}}\) |
| Answer» D. \(\frac{{781}}{{1024}}\) | |
| 129. |
Among the four normal distributions with probability density functions as shown below, which one has the lowest variance? |
| A. | I |
| B. | II |
| C. | III |
| D. | IV |
| Answer» E. | |
| 130. |
If 1 card is taken out of a group of cards, then the probability of that card is not ace is - |
| A. | 12/13 |
| B. | 1/13 |
| C. | 2/13 |
| D. | 3/13 |
| Answer» B. 1/13 | |
| 131. |
A coin is tossed. What is the probability of getting a head? |
| A. | 1/2 |
| B. | 1/4 |
| C. | 1/3 |
| D. | 1/5 |
| Answer» B. 1/4 | |
| 132. |
An unbiased coin is tossed. If the outcome is a head then a pair of unbiased dice is rolled and the sum of the numbers obtained on them is noted. If the toss of the coin results in tail then a card from a well-shuffled pack of nine cards numbered 1, 2, 3, …., 9 is randomly picked and the number on the card is noted. The probability that the noted number is either 7 or 8 is: |
| A. | 13/36 |
| B. | 15/72 |
| C. | 19/72 |
| D. | 19/36 |
| Answer» D. 19/36 | |
| 133. |
In a class there are 15 boys and 10 girls. Three students are selected at random. What is the probability that all are boys? |
| A. | 91/460 |
| B. | 95/460 |
| C. | 97/460 |
| D. | 99/460 |
| Answer» B. 95/460 | |
| 134. |
If a card is drawn at random from a well shuffled pack of 52 playing cards, then the probability of getting a red coloured face card is |
| A. | \(\frac{2}{{13}}\) |
| B. | \(\frac{1}{{13}}\) |
| C. | \(\frac{3}{{26}}\) |
| D. | \(\frac{3}{{52}}\) |
| Answer» D. \(\frac{3}{{52}}\) | |
| 135. |
A chain of video stores sells three different brands of DVD players. Of its DVD player sales, 50% are brand 1, 30% are brand 2 and 20% are brand 3. Each manufacturer offers one year warranty on parts and labor. It is known that 25% of brand 1 DVD players require warranty repair work whereas the corresponding percentage for brands 2 and 3 are 20% and 10% respectively. The probability that a randomly selected purchaser has a DVD player that will need repair while under warranty, is: |
| A. | 0.795 |
| B. | 0.205 |
| C. | 0.125 |
| D. | 0.06 |
| Answer» C. 0.125 | |
| 136. |
A person wanted to visit four places Chennai, Bangalore, Delhi and Mumbai on one trip. Find the probability of the person visiting Chennai just before Mumbai. |
| A. | 1/2 |
| B. | 1/12 |
| C. | 1/4 |
| D. | 1/6 |
| Answer» D. 1/6 | |
| 137. |
Minimum number of times a fair coin must be tossed so that the probability of getting at least one head is more than 99% is: |
| A. | 5 |
| B. | 6 |
| C. | 8 |
| D. | 7 |
| Answer» E. | |
| 138. |
A dice is thrown, what is the probability getting prime number? |
| A. | 1/2 |
| B. | 2/3 |
| C. | 1/3 |
| D. | 4/5 |
| Answer» B. 2/3 | |
| 139. |
Consider the following in respect of two events A and B:1) P(A occurs but not B) = P(A) – P(B) if B ⊂ A2) P(A alone or B alone occurs) = P(A) + P(B) – P(A ∩ B)3) P(A ∪ B) = P(A) + P(B) if A and B are mutually exclusiveWhich of the above is/are correct? |
| A. | 1 only |
| B. | 1 and 3 only |
| C. | 2 and 3 only |
| D. | 1 and 2 only |
| Answer» C. 2 and 3 only | |
| 140. |
A coin is tossed 10 times and the outcomes are observed as : H, T, H, T, T, H, H, T, H, H (H is Head; T is Tail)What is the probability of getting Head? |
| A. | \(\dfrac{3}{5}\) |
| B. | \(\dfrac{4}{5}\) |
| C. | \(\dfrac{2}{5}\) |
| D. | \(\dfrac{1}{5}\) |
| Answer» B. \(\dfrac{4}{5}\) | |
| 141. |
If \(P\left( B \right) = \frac{3}{4},\;P\left( {A \cap B \cap {C^c}} \right) = \frac{1}{3}\) and \(P\;\left( {{A^c}\; \cap \;B\; \cap \;{C^c}} \right) = \frac{1}{3},\) then what is P (B ∩ C) equal to? |
| A. | \(\frac{1}{{12}}\) |
| B. | \(\frac{3}{{4}}\) |
| C. | \(\frac{1}{{15}}\) |
| D. | \(\frac{1}{{9}}\) |
| Answer» B. \(\frac{3}{{4}}\) | |
| 142. |
A person throws two fair dice. He wins Rs. 15 for throwing a doublet (same numbers on the two dice), wins Rs. 12 when the throw results in the sum of 9, and loses Rs. 6 for any other outcome on the throw. Then the expected gain/loss (in Rupees) of the person is: |
| A. | \(\frac{1}{2}\) gain |
| B. | \(\frac{1}{4}\) loss |
| C. | \(\frac{1}{2}\) loss |
| D. | 2 gain |
| Answer» D. 2 gain | |
| 143. |
In a class of 125 students 70 passed in Maths 55 in statistics and 30 in both. probability that a student selected at random from the class has passed only in one subject is |
| A. | 13/25 |
| B. | 3/25 |
| C. | 17/25 |
| D. | 8/25 |
| Answer» B. 3/25 | |
| 144. |
An experiment succeeds twice as often as it fails. The probability that in the next six trials there will be at least four successes, is: |
| A. | \(\rm \dfrac{240}{729}\) |
| B. | \(\rm \dfrac{496}{729}\) |
| C. | \(\rm \dfrac{220}{729}\) |
| D. | \(\rm \dfrac{233}{729}\) |
| Answer» C. \(\rm \dfrac{220}{729}\) | |
| 145. |
If two fair dice are rolled then what is the conditional probability that the first dice lands on 6 given that the sum of numbers on the dice is 8? |
| A. | \(\frac{1}{3}\) |
| B. | \(\frac{1}{4}\) |
| C. | \(\frac{1}{5}\) |
| D. | \(\frac{1}{6}\) |
| Answer» D. \(\frac{1}{6}\) | |
| 146. |
If two dice are thrown in the air, the probability of getting sum as 3 will be |
| A. | 2/18 |
| B. | 3/18 |
| C. | 1/18 |
| D. | 1/36 |
| Answer» D. 1/36 | |
| 147. |
In throwing of two dice, what is the probability of getting an odd sum? |
| A. | 1/3 |
| B. | 1/2 |
| C. | 1/4 |
| D. | 1/6 |
| Answer» C. 1/4 | |
| 148. |
A bag has 5 white marbles, 8 red marbles and 4 purple marbles. If we take a marble randomly, then what is the probability of not getting purple marble? (approx.) |
| A. | 0.5 |
| B. | 0.66 |
| C. | 0.08 |
| D. | 0.77 |
| Answer» E. | |
| 149. |
If a fair die is rolled 4 times, then what is the probability that there are exactly 2 sixes? |
| A. | \(\frac{5}{{216}}\) |
| B. | \(\frac{{25}}{{216}}\) |
| C. | \(\frac{{125}}{{216}}\) |
| D. | \(\frac{{175}}{{216}}\) |
| Answer» C. \(\frac{{125}}{{216}}\) | |
| 150. |
If 'Head' appears consecutively in the first three tosses of a fair/unbiased coin, what is the probability of 'Head' appearing in the fourth toss also? |
| A. | 1 / 8 |
| B. | 7 / 8 |
| C. | 1 / 16 |
| D. | 1 / 2 |
| Answer» E. | |