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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.
| 1. |
In a class of 60 students, 40 opted for NCC, 30 opted for NSS and 20 opted for both NCC and NSS. If one of these students is selected at random, then the probability that the student selected has opted neither for NCC nor for NSS is |
| A. | \(\frac{1}{6}\) |
| B. | \(\frac{1}{3}\) |
| C. | \(\frac{2}{3}\) |
| D. | \(\frac{5}{6}\) |
| Answer» B. \(\frac{1}{3}\) | |
| 2. |
In a multiple-choice test, an examinee either knows the correct answer with probability p, or guesses with probability 1 - p. The probability of answering a question correctly is , if he or she merely guesses. If the examinee answers a question correctly, the probability that he or she really knows the answer is |
| A. | \(\frac{{{\rm{mp}}}}{{1 + {\rm{mp}}}}\) |
| B. | \(\frac{{{\rm{mp}}}}{{1 + \left( {{\rm{m}} - 1} \right){\rm{p}}}}\) |
| C. | \(\frac{{\left( {{\rm{m}} - 1} \right)}}{{1 + \left( {{\rm{m}} - 1} \right){\rm{p}}}}\) |
| D. | \(\frac{{\left( {{\rm{m}} - 1} \right){\rm{p}}}}{{1 + {\rm{mp}}}}\) |
| Answer» C. \(\frac{{\left( {{\rm{m}} - 1} \right)}}{{1 + \left( {{\rm{m}} - 1} \right){\rm{p}}}}\) | |
| 3. |
Eight coins are tossed 25,600 times. The average number of eight heads is |
| A. | 1000 |
| B. | 200 |
| C. | 300 |
| D. | 100 |
| Answer» E. | |
| 4. |
Consider the following statements:1) P(A̅ ∪ B) = P(A̅) + P (B) – P(A̅ ∩ B)2) P(A ∪ B̅ ) = P(B) – P(A ∩ B)3) P(A ∩ B) = P(B) P(A|B)Which of the above statements are correct? |
| A. | 1 and 2 only |
| B. | 1 and 3 only |
| C. | 2 and 3 only |
| D. | 1, 2, and 3 |
| Answer» C. 2 and 3 only | |
| 5. |
If x ∈ [0, 5], then what is the probability that x2 - 3x + 2 ≥ 0? |
| A. | \(\frac{4}{5}\) |
| B. | \(\frac{1}{5}\) |
| C. | \(\frac{2}{5}\) |
| D. | \(\frac{3}{5}\) |
| Answer» B. \(\frac{1}{5}\) | |
| 6. |
A random variable is known to have a cumulative distribution function \(F_X (x)=U(x)(1-\frac{x^2}{b})\). Its density function is: |
| A. | \(U(x) \frac{2x}{b}(1-e^{-x^2/b}) \) |
| B. | \(U(x)\frac{2x}{b} e^{-x^2/b}\) |
| C. | \(U(x)(1-\frac{x^2}{b})δ(x)\) |
| D. | \((1-\frac{x^2}{b})δ(x)+e^{-x^2/b}\) |
| Answer» C. \(U(x)(1-\frac{x^2}{b})δ(x)\) | |
| 7. |
A bag contains 4 blue, 3 green, 3 white and 5 black marbles. If four marbles are picked at random, what is the probability of at least one being blue? |
| A. | 69/91 |
| B. | 71/89 |
| C. | 43/51 |
| D. | 37/69 |
| E. | None of these |
| Answer» B. 71/89 | |
| 8. |
In a Binomial distribution, the mean is three times its variance. What is the probability of exactly 3 successes out of 5 trials? |
| A. | 80/243 |
| B. | 40/243 |
| C. | 20/243 |
| D. | 10/243 |
| Answer» B. 40/243 | |
| 9. |
If A and B are two events such that P(A) = 0.6, P(B) = 0.5 and P(A ∩ B) = 0.4, then consider the following statements:1. P(A̅ ∪ B) = 0.92. P(B̅ | A̅) = 0.6Which of the statements is / are correct? |
| A. | 1 only |
| B. | 2 only |
| C. | Both 1 and 2 |
| D. | Neither 1 nor 2 |
| Answer» E. | |
| 10. |
A bag contains X red balls and 5 green balls. 2 balls are picked up from the bag at random, one after the other, without replacement, the probability of both balls being red is 3/7. What will be the value of X? |
| A. | 10 |
| B. | 15 |
| C. | 13 |
| D. | 20 |
| E. | None of the above |
| Answer» B. 15 | |
| 11. |
Given that \(\rm P (A) = \frac 1 3,\;P(B) = P\left( \frac A B \right) = \frac 1 6\) then the probability \(P \left( \frac B A \right)\) is equal to: |
| A. | 1 / 4 |
| B. | 3 / 4 |
| C. | 1 / 8 |
| D. | None of these |
| Answer» E. | |
| 12. |
A die is thrown once. Find the probability that its is even. |
| A. | 5/6 |
| B. | 1/2 |
| C. | 1/3 |
| D. | 2/3 |
| Answer» C. 1/3 | |
| 13. |
If \(\rm P(A \cup B)=\dfrac{5}{6}, P(A \cap B)=\dfrac{1}{3}\) and \(\rm P(not \ A)=\dfrac{1}{2}\), then which one of the following is not correct? |
| A. | \(\rm P(B) = \dfrac{2}{3}\) |
| B. | P(A ∩ B) = P(A) P(B) |
| C. | P(A ∪ B) > P(A) + P(B) |
| D. | P(not A and not B) = P(not A) P(not B) |
| Answer» D. P(not A and not B) = P(not A) P(not B) | |
| 14. |
Consider an unbiased cubic dice with opposite faces coloured identically and each face coloured red, blue or green such that each colour appears only two times on the dice. If the dice is thrown thrice, the probability of obtaining red colour on top face of the dice at least twice is _______ |
| A. | \({7 \over 27}\) |
| B. | \({10 \over 127}\) |
| C. | \({19 \over 27}\) |
| D. | \({1 \over 3}\) |
| Answer» B. \({10 \over 127}\) | |
| 15. |
If 3 coins are tossed simultaneously, what is the probability of getting at least 2 heads? |
| A. | 1/3 |
| B. | 1/2 |
| C. | 1/8 |
| D. | 7/8 |
| E. | 2/3 |
| Answer» C. 1/8 | |
| 16. |
A box has ten chits numbered 0, 1, 2, 3, ……., 9. First, one chit is drawn at random and kept aside. From the remaining, a second chit is drawn at random. What is the probability that the second chit drawn is “9”? |
| A. | 1/10 |
| B. | 1/9 |
| C. | 1/90 |
| D. | None of the above |
| Answer» B. 1/9 | |
| 17. |
From a cloth store, 15 customers bought an orange dress, 15 bought red dress, 20 bought a blue dress, 2 bought all the three colures and 8 bought at least two of these. How many bought at least one dress form the store? |
| A. | 25 |
| B. | 39 |
| C. | 40 |
| D. | 45 |
| Answer» D. 45 | |
| 18. |
Let A and B are two mutually exclusive events with \({\rm{P}}\left( {\rm{A}} \right) = \frac{1}{3}\) and \({\rm{P}}\left( {\rm{B}} \right) = \frac{1}{4}\). What is the value of \({\rm{P}}\left( {{\rm{\bar A}} \cap {\rm{\bar B}}} \right)?\) |
| A. | \(\frac{1}{6}\) |
| B. | \(\frac{1}{4}\) |
| C. | \(\frac{1}{3}\) |
| D. | \(\frac{5}{{12}}\) |
| Answer» E. | |
| 19. |
Choose the correct cod for the following statements being correct or incorrect.Statement I: If the value of \(\beta_2, i.e \frac{\mu_4}{\sigma_4}\), of a distribution gives the value more than 3, its curve is platykurtic.Statement II: In a moderately asymmetrical distribution, the standard deviation is 1.25 times of mean deviation. |
| A. | Both the statements I and II are correct |
| B. | Both the statements I and II are incorrect. |
| C. | Statement I is correct, but II is incorrect |
| D. | Statement II is correct, but I is incorrect |
| Answer» E. | |
| 20. |
In the figure shown above, PQRS is a square. The shaded portion is formed by the intersection of sectors of circles with radius equal to the side of the square and centrs at S and Q.The probability that any point picked randomly within the square falls in the shaded area is ________ |
| A. | \(\frac{1}{2}\) |
| B. | \(\frac{\pi }{2}\) |
| C. | \(4 - \frac{\pi }{2}\) |
| D. | \(\frac{\pi }{2} - 1\) |
| Answer» E. | |
| 21. |
If A ⊆ B, then which one of the following is not correct? |
| A. | \(P\;\left( {A \cap \bar B} \right) = 0\) |
| B. | \(P\;{\rm{(}}A{\rm{|}}B) = \frac{{P\left( A \right)}}{{P\left( B \right)}}\) |
| C. | \(P\;{\rm{(}}B{\rm{|}}A) = \frac{{P\left( B \right)}}{{P\left( A \right)}}\) |
| D. | \(P{\rm{(}}A{\rm{|}}\left( {A \cup B} \right)) = \frac{{P\left( A \right)}}{{P\left( B \right)}}\) |
| Answer» D. \(P{\rm{(}}A{\rm{|}}\left( {A \cup B} \right)) = \frac{{P\left( A \right)}}{{P\left( B \right)}}\) | |
| 22. |
Out of 2n + 1 tickets, which are consecutively numbered, three are drawn at random. Then the probability that the numbers on them are in the arithmetic progression is |
| A. | \(\dfrac{n^2}{4n^2 - 1}\) |
| B. | \(\dfrac{n}{4n^2 - 1}\) |
| C. | \(\dfrac{3n^2}{4n^2 - 1}\) |
| D. | \(\dfrac{3n}{4n^2 - 1}\) |
| Answer» E. | |
| 23. |
A fruit box contains 10 apples, 3 of which were defective. Two apples are picked randomly with replacement. The probability that none of the two apples was defective is approximately |
| A. | 0.49 |
| B. | 0.25 |
| C. | 0.65 |
| D. | 0.75 |
| Answer» B. 0.25 | |
| 24. |
Consider the following statements:1. Two events are mutually exclusive if the occurrence of one event prevents the occurrence of the other.2. The probability of the union of two mutually exclusive events is the sum of their individual probabilities.Which of the above statements is/are correct? |
| A. | 1 only |
| B. | 2 only |
| C. | Both 1 and 2 |
| D. | Neither 1 nor 2 |
| Answer» D. Neither 1 nor 2 | |
| 25. |
'ELISA' test is employed to diagnose:- |
| A. | Swine Flu |
| B. | Polio Virus |
| C. | AIDS antibodies |
| D. | Cancer |
| Answer» D. Cancer | |
| 26. |
Let two events A and B be such that P(A) = L and P(B) = M. Which one of the following is correct? |
| A. | \(P(A|B)<\dfrac{L+M-1}{M}\) |
| B. | \(P(A|B)>\dfrac{L+M-1}{M}\) |
| C. | \(P(A|B)\ge\dfrac{L+M-1}{M}\) |
| D. | \(P(A|B)=\dfrac{L+M-1}{M}\) |
| Answer» D. \(P(A|B)=\dfrac{L+M-1}{M}\) | |
| 27. |
A bag contains 4 red, 5 white and 6 black balls. Three balls are drawn WITHOUT replacement. What is the probability that the three drawn balls are black? |
| A. | \(\dfrac{4}{91}\) |
| B. | \(\dfrac{2}{5}\) |
| C. | \(\dfrac{1}{5}\) |
| D. | \(\dfrac{6}{91}\) |
| Answer» B. \(\dfrac{2}{5}\) | |
| 28. |
If A and B are two mutually exclusive events, then what is the probability of occurrence of either event A or event B? |
| A. | P(A) + P(B) |
| B. | P(A ∪ B') |
| C. | P(A ∩ B) |
| D. | P(A) P(B) |
| Answer» B. P(A ∪ B') | |
| 29. |
A coin is tossed 4 times. The probability of getting heads exactly 3 times will be: |
| A. | 0.75 |
| B. | 0.33 |
| C. | 0.5 |
| D. | 0.25 |
| Answer» E. | |
| 30. |
A certain type of missile hits the target with probability p = 0.3. What is the least number of missiles should be fired so that there is at least on 80% probability that the target is hit? |
| A. | 5 |
| B. | 6 |
| C. | 7 |
| D. | None of the above |
| Answer» B. 6 | |
| 31. |
Let U and V be two events of a sample space S and P(A) denote the probability of an event A. Which of the following statements is true? |
| A. | If P(U) = P(V), then U = V. |
| B. | If P(U) = 0, then Uc = S. |
| C. | If U ∩ V = ϕ, then U and V are independent. |
| D. | If U and V are independent, then so are Uc and Vc. |
| Answer» C. If U ∩ V = ϕ, then U and V are independent. | |
| 32. |
Let A and B be two events such that \(P(\overline{A \cup B}) = \dfrac{1}{6}\), P(A ∩ B) = \(\dfrac{1}{4}\)and P(A̅) = \(\dfrac{1}{4}\), where A̅ stands for complement of event A. Then, events A and B are: |
| A. | Equally likely but not independent |
| B. | Mutually exclusive and independent |
| C. | Independent but not equally likely |
| D. | Equally likely and mutually exclusive |
| Answer» D. Equally likely and mutually exclusive | |
| 33. |
In April, If some males and some females were joined in office P such that the probability of choosing females is increased by \(4\frac{1}{6}\% \). Now, one candidate is selected at random and a selected candidate is a male,find the probability that it is selected from office P. |
| A. | 7/12 |
| B. | 26/69 |
| C. | 35/59 |
| D. | 43/79 |
| E. | 13/17 |
| Answer» D. 43/79 | |
| 34. |
A box contains 25 balls bearing numbers 1 , 2 , 3 , 4 _________ 25. If a ball is picked at random from the box, then the probability that the number on the ball is divisible by 5 or 7 is: |
| A. | 6/25 |
| B. | 2/25 |
| C. | 8/25 |
| D. | 0 |
| Answer» D. 0 | |
| 35. |
In a lottery of 10 tickets numbered 1 to 10, two tickets are drawn simultaneously. What is the probability that both the tickets drawn have prime numbers? |
| A. | \(\dfrac{1}{15}\) |
| B. | \(\dfrac{1}{2}\) |
| C. | \(\dfrac{2}{15}\) |
| D. | \(\dfrac{1}{5}\) |
| Answer» D. \(\dfrac{1}{5}\) | |
| 36. |
Let A and B be two non-null events such that A ⊂ B, then which of the following statements is always correct? |
| A. | P(A|B) = P(B) – P(A) |
| B. | P(A|B) ≥ P(A) |
| C. | P(A|B) ≤ P(A) |
| D. | P(A|B) = 1 |
| Answer» C. P(A|B) ≤ P(A) | |
| 37. |
Consider three boxes, each containing 10 balls labelled 1, 2… 10. Suppose one ball is randomly drawn from each of the boxes. Denote by ni, the label of the ball drawn from the ith box, (I = 1, 2, 3). Then, the number of ways in which the balls can be chosen such that n1 < n2 < n3 is |
| A. | 82 |
| B. | 120 |
| C. | 240 |
| D. | 164 |
| Answer» C. 240 | |
| 38. |
For an initial screening of an admission test, a candidate is given fifty problems to solve. If the probability that the candidate can solve any problem is \(\frac{4}{5}\), then the probability that he is unable to solve less than two problems is: |
| A. | \(\frac{{201}}{5}{\left( {\frac{1}{5}} \right)^{49}}\) |
| B. | \(\frac{{316}}{{25}}{\left( {\frac{4}{5}} \right)^{48}}\) |
| C. | \(\frac{{54}}{5}{\left( {\frac{4}{5}} \right)^{49}}\) |
| D. | \(\frac{{164}}{{25}}{\left( {\frac{1}{5}} \right)^{48}}\) |
| Answer» D. \(\frac{{164}}{{25}}{\left( {\frac{1}{5}} \right)^{48}}\) | |
| 39. |
In a toy factory, machines A, B, and C manufacture 30%, 40%, 30% of the output respectively. Out of their total output, 2%, 3%, 1% are defective. A toy is taken from the factory and is found to be defective. The probability that it was taken from machine B is: |
| A. | 4 / 5 |
| B. | 2 / 9 |
| C. | 3 / 4 |
| D. | 4 / 7 |
| Answer» E. | |
| 40. |
For Binomial distribution, n = 10 and p = 0.6, E(X2) (second moment about origin) is: |
| A. | 30 |
| B. | 38.4 |
| C. | 8 |
| D. | 38 |
| Answer» C. 8 | |
| 41. |
A problem is given to three students A, B and C whose probabilities of solving the problem are \(\frac{1}{2},\frac{3}{4}\) and \(\frac{1}{4}\) respectively. What is the probability that the problem will be solved if they all solve the problem independently? |
| A. | \(\frac{{29}}{{32}}\) |
| B. | \(\frac{{27}}{{32}}\) |
| C. | \(\frac{{25}}{{32}}\) |
| D. | \(\frac{{23}}{{32}}\) |
| Answer» B. \(\frac{{27}}{{32}}\) | |
| 42. |
For two events A and B, let \({\rm{P}}\left( {\rm{A}} \right) = \frac{1}{2},{\rm{\;P}}\left( {{\rm{A}} \cup {\rm{B}}} \right) = \frac{2}{3}\) and \({\rm{P}}\left( {{\rm{A}} \cap {\rm{B}}} \right) = \frac{1}{6}\). What is the P(A̅ ∩ B) equal to? |
| A. | \(\frac{1}{6}\) |
| B. | \(\frac{1}{4}\) |
| C. | \(\frac{1}{3}\) |
| D. | \(\frac{1}{2}\) |
| Answer» B. \(\frac{1}{4}\) | |
| 43. |
A card is drawn from a pack of 100 cards numbered 1 to 100. What is the probability that a square number is drawn? |
| A. | 1/5 |
| B. | 2/5 |
| C. | 1/10 |
| D. | 3/10 |
| Answer» D. 3/10 | |
| 44. |
A and B play a game where each is asked to select a number from 1 to 25. If the two numbers match, both of them win a prize. The probability that they will not win a prize in a single trial, is: |
| A. | \(\frac{1}{25}\) |
| B. | \(\frac{24}{25}\) |
| C. | \(\frac{2}{25}\) |
| D. | None of these. |
| Answer» C. \(\frac{2}{25}\) | |
| 45. |
A coin is tossed three times. What is the probability of getting head and tail alternately? |
| A. | \(\frac{1}{8}\) |
| B. | \(\frac{1}{4}\) |
| C. | \(\frac{1}{2}\) |
| D. | \(\frac{3}{4}\) |
| Answer» C. \(\frac{1}{2}\) | |
| 46. |
For the distributions given below: Which of the following is correct for the above distributions? |
| A. | Standard deviation of A is significantly lower than standard deviation of B |
| B. | Standard deviation of A is slightly lower than standard deviation of B |
| C. | Standard deviation of A is same as standard deviation of B |
| D. | Standard deviation of A is significantly higher than standard deviation of B |
| Answer» D. Standard deviation of A is significantly higher than standard deviation of B | |
| 47. |
A test has 5 multiple-choice questions. Each question has 4 answer options (A, B, C, D).What is the probability that a student will choose "B" for at least three questions if he/she leaves no questions blank? |
| A. | 1/1024 |
| B. | 1/64 |
| C. | 53/512 |
| D. | 29/128 |
| Answer» D. 29/128 | |
| 48. |
If a man purchases a raffle ticket, he can win a first prize of Rs. 5,000 or a second prize of Rs. 2,000 with probabilities 0.001 and 0.003 respectively. What should be a fair price to pay for the ticket? |
| A. | Rs. 11 |
| B. | Rs. 15 |
| C. | Rs. 2,000 |
| D. | None of these |
| Answer» B. Rs. 15 | |
| 49. |
Find the total number of balls in the bag |
| A. | 91 |
| B. | 84 |
| C. | 63 |
| D. | none of these |
| E. | cannot be determined |
| Answer» D. none of these | |
| 50. |
If on an average, 2 customers arrive at shopping mall per minute, what is the probability that in a given minute, exactly 3 customers will arrive? (e-2 = 0.1353) |
| A. | 0.1804 |
| B. | 0.3532 |
| C. | 0.2352 |
| D. | 0.1404 |
| Answer» B. 0.3532 | |