MCQOPTIONS
Saved Bookmarks
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.
| 351. |
If two dice are thrown and at least one the dice show 5, then the probability that the sum is 10 or more is |
| A. | 1/6 |
| B. | 4/11 |
| C. | 3/11 |
| D. | 2/11 |
| Answer» D. 2/11 | |
| 352. |
Let the random variables X follow B (6, p) If \(16{\rm{\;P\;}}\left( {{\rm{X}} = 4} \right) = {\rm{P\;}}\left( {{\rm{X}} = 2} \right)\), then what is the value of p |
| A. | \(\frac{1}{3}\) |
| B. | \(\frac{1}{4}\) |
| C. | \(\frac{1}{5}\) |
| D. | \(\frac{1}{6}\) |
| Answer» D. \(\frac{1}{6}\) | |
| 353. |
Let x ∼ N(μ, σ2) If μ2 = σ2, (μ > 0), then the value of P(X < -μ | X |
| A. | [1 - P(Z ≤ 1)] |
| B. | [1 - P(Z ≤ 2)] |
| C. | 2[1 - P(Z ≤ 1)] |
| D. | 2[1 - P(Z ≤ 2)] |
| Answer» E. | |
| 354. |
Consider the following statements:1. If A and B are mutually exclusive events, then it is possible that P(A) = P(B) = 0.6.2. If A and B are any two events such that P(A|B) = 1, then P(B̅|A̅) = 1Which of the above statement is/are correct? |
| A. | 1 only |
| B. | 2 only |
| C. | Both 1 and 2 |
| D. | Neither 1 nor 2 |
| Answer» C. Both 1 and 2 | |
| 355. |
If A and B are two events such that P(A) = 0.5, P(B) = 0.6 and P(A ∩ B) = 0.4, then what is \(P\left( {\overline {A \cup B} } \right)\) equal to? |
| A. | 0.9 |
| B. | 0.7 |
| C. | 0.5 |
| D. | 0.3 |
| Answer» E. | |
| 356. |
A random variable X has the distribution law as given below:X123P(X = x)0.30.40.3The variance of the distribution is: |
| A. | 0.4 |
| B. | 0.6 |
| C. | 0.2 |
| D. | None of these |
| Answer» C. 0.2 | |
| 357. |
A bag has r red balls and b black balls. All balls are identical except for their colours. In a trial, a ball is randomly drawn from the bag, its colour is noted and the ball is placed back into the bag along with another ball of the same colour. Note that the number of balls in the bag will increase by one, after the trial. A sequence of four such trials is conducted. Which one of the following choices gives the probability of drawing a red ball in the fourth trial ? |
| A. | \(\frac{r}{r+b}\) |
| B. | \(\left(\frac{r}{r+b}\right)\left(\frac{r+1}{r+b+1}\right)\left(\frac{r+2}{r+b+2}\right)\left(\frac{r+3}{r+b+3}\right)\) |
| C. | \(\left(\frac{r+3}{r+b+3}\right)\) |
| D. | \(\left(\frac{r}{r+b+3}\right)\) |
| Answer» B. \(\left(\frac{r}{r+b}\right)\left(\frac{r+1}{r+b+1}\right)\left(\frac{r+2}{r+b+2}\right)\left(\frac{r+3}{r+b+3}\right)\) | |
| 358. |
In a random experiment, a fair die is rolled until two fours are obtained in succession. The probability that the experiment will end in the fifth throw of the die is equal to |
| A. | 175/65 |
| B. | 225/65 |
| C. | 200/65 |
| D. | 150/65 |
| Answer» B. 225/65 | |
| 359. |
For two mutually exclusive events A and B, P(A) = 0.2 and P (A̅ ∩ B) = 0.3. What is P (A|(A ∪ B)) equal to? |
| A. | \(\frac{1}{2}\) |
| B. | \(\frac{2}{5}\) |
| C. | \(\frac{2}{7}\) |
| D. | \(\frac{2}{3}\) |
| Answer» C. \(\frac{2}{7}\) | |
| 360. |
Probability is an attribute of |
| A. | An inductive argument |
| B. | A deductive argument |
| C. | Disjunctive proposition |
| D. | Categorical proposition |
| Answer» B. A deductive argument | |
| 361. |
If E1 and E2 are two events associated with a random experiment such that P(E2) = 0.35, P(E1 or E2) = 0.85 and P(E1 and E2) = 0.15 then P(E1) is ? |
| A. | 0.25 |
| B. | 0.35 |
| C. | 0.65 |
| D. | 0.75 |
| Answer» D. 0.75 | |
| 362. |
A point is chosen at random inside a rectangle measuring 6 inches by 5 inches. What is the probability that the randomly selected point is at least one inch from the edge of the rectangle? |
| A. | \(\frac{2}{3}\) |
| B. | \(\frac{1}{3}\) |
| C. | \(\frac{1}{4}\) |
| D. | \(\frac{2}{5}\) |
| Answer» E. | |
| 363. |
Match the items of List I with those of List II and choose the correct code of combinationList IList IIa.\(P\left( {{H_i}/E} \right) = P\frac{{\left( {{H_i} \cap E} \right)}}{{P\left( E \right)}}\)i)Theorem of additionb.\(P\left( {{E_2}/{E_1}} \right) = P\frac{{\left( {{E_1} \cap {C_2}} \right)}}{{P\left( {{E_1}} \right)}}\)ii)Theorem of multiplicationc.P(E1 ∩ E2) = P(E1) × P(E2)iii) Conditional probabilityd. P(E1 ∪ E2) = P(E1) + P(E2)iv)Baye’s theorem |
| A. | a-i, b-iv, c-ii, d-iii |
| B. | a-iv, b-iii, c-ii, d-i |
| C. | a-iii, b-iv, c-ii, d-i |
| D. | a-iv, b-iii, c-i, d-ii |
| Answer» C. a-iii, b-iv, c-ii, d-i | |
| 364. |
Given below are two quantities named A & B. Based on the given information, you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose between the possible answers.A bucket has 4 Blue balloons, 6 Red balloons & 3 Green balloons. Five balloons are drawn from the bucket at random.Quantity A: Find the probability that out of 5 balloons: 2 are Blue, 2 are Red and 1 is Green.Quantity B: Find the probability that out of 5 balloons: 3 are Red, 1 is Blue and 1 is Green |
| A. | Quantity A > Quantity B |
| B. | Quantity A < Quantity B |
| C. | Quantity A ≥ Quantity B |
| D. | Quantity A ≤ Quantity B |
| E. | Quantity A = Quantity B or No relation. |
| Answer» B. Quantity A < Quantity B | |
| 365. |
A box contains 25 parts of which 10 are defective. Two parts are being drawn simultaneously in a random manner from the box. The probability of both the parts being good is |
| A. | 7/20 |
| B. | 42/125 |
| C. | 25/29 |
| D. | 5/9 |
| Answer» B. 42/125 | |
| 366. |
A box contains 4 green, 5 blue and 4 red balls. One ball is drawn at random. What is the probability that it is either green or red? |
| A. | 9/13 |
| B. | 7/13 |
| C. | 8/13 |
| D. | 1/13 |
| Answer» D. 1/13 | |
| 367. |
Himanshu received a coded message : CHANGTANGSANG, which he has to decipher by forming a single word. He knows the correct positions of all the A's.Find the probability that he is able to decode the message correctly? |
| A. | 0.50 |
| B. | (3! × 3!)/10! |
| C. | 1/31 |
| D. | 36/101 |
| Answer» C. 1/31 | |
| 368. |
A bag contains 5 black and 6 white balls; two balls are drawn at random. What is the probability that the balls drawn are white? |
| A. | 10/11 |
| B. | 4/11 |
| C. | 6/11 |
| D. | 3/11 |
| Answer» E. | |
| 369. |
For a standard normal probability distribution, the mean (μ) and the standard deviation (s) are : |
| A. | μ = 0, s = 1 |
| B. | μ = 16, s = 4 |
| C. | μ = 25, s = 5 |
| D. | μ = 100, s = 10 |
| Answer» B. μ = 16, s = 4 | |
| 370. |
A coin is tossed 300 times with the frequencies of two outcomes: Head - 100, Tail - 200, probability of occurrence of these events will be? |
| A. | 1/3, 1/3 |
| B. | 1/2, 1/2 |
| C. | 1/3, 2/3 |
| D. | 1/2, 2/3 |
| Answer» D. 1/2, 2/3 | |
| 371. |
A can solve 90% of the problems given in a book and B can solve 70%. What is the probability that at least one of them will solve a problem, selected at random from the book? |
| A. | 0.16 |
| B. | 0.69 |
| C. | 0.97 |
| D. | 0.20 |
| Answer» D. 0.20 | |
| 372. |
Cycle tyres are supplied in lots of 10 and there is a chance of 1 in 500 tyres to be defective. Using Poisson distribution the approximate number of lots containing no defective tyres in a consignment of 10000 lots. (Note: e-0.02 = 0.9802) |
| A. | 9.802 |
| B. | 98.02 |
| C. | 9802 |
| D. | 9800 |
| Answer» D. 9800 | |
| 373. |
An unbiased coin is tossed an infinite number of times. The probability that the fourth head appears at the tenth toss is |
| A. | 0.067 |
| B. | 0.073 |
| C. | 0.082 |
| D. | 0.091 |
| Answer» D. 0.091 | |
| 374. |
A box contains 15 cards bearing number 1, 2, 3 ..........,15. A card is drawn at random from the box. What is the probability that number on the card is a prime number? |
| A. | 1/2 |
| B. | 3/5 |
| C. | 2/5 |
| D. | 1/3 |
| Answer» D. 1/3 | |
| 375. |
In an examination, the probability of a candidate solving a question is 1/2. out of given 5 questions in the examination, what is the probability that the candidate was able to solve at least 2 questions? |
| A. | 1/64 |
| B. | 3/16 |
| C. | 1/2 |
| D. | 13/16 |
| Answer» E. | |
| 376. |
Person A can hit a target 4 times in 5 attempts. Person B - 3 times in four attempts. Person C - 2 times in 3 attempts. They fire a volley. The probability that the target is hit atleast two times is |
| A. | 3/4 |
| B. | 1/2 |
| C. | 5/6 |
| D. | 1 |
| Answer» D. 1 | |
| 377. |
A bag contains 7 pink and 9 blue balls. Two balls are drawn in succession at random. What is the probability that one of them is pink and the other blue? |
| A. | 21/20 |
| B. | 21/40 |
| C. | 31/24 |
| D. | 31/40 |
| E. | None of these |
| Answer» C. 31/24 | |
| 378. |
A bag contains 4 white and 2 black balls and another bag contains 3 white and 5 black balls. If one ball is drawn from each bag, then the probability of one ball being white and the other ball being black is |
| A. | \(\frac{5}{{24}}\) |
| B. | \(\frac{13}{{24}}\) |
| C. | \(\frac{1}{{4}}\) |
| D. | \(\frac{2}{{3}}\) |
| Answer» C. \(\frac{1}{{4}}\) | |
| 379. |
If A, B, C are three events, then what is the probability that at least two of these events occur together? |
| A. | P(A ∩ B) + P(B ∩ C) + P(C ∩ A) |
| B. | P(A ∩ B) + P(B ∩ C) + P(C ∩ A) – P(A ∩ B ∩ C) |
| C. | P(A ∩ B) + P(B ∩ C) + P(C ∩ A) – 2P(A ∩ B ∩ C) |
| D. | P(A ∩ B) + P(B ∩ C) + P(C ∩ A) – 3P(A ∩ B ∩ C) |
| Answer» D. P(A ∩ B) + P(B ∩ C) + P(C ∩ A) – 3P(A ∩ B ∩ C) | |
| 380. |
A bag contains 6 white and 4 black balls. Two balls are drawn at random. Find the probability that they are of the same color. |
| A. | 6/13 |
| B. | 7/15 |
| C. | 8/17 |
| D. | 9/20 |
| Answer» C. 8/17 | |
| 381. |
A box contains 6 black and 5 red balls. Two balls are drawn one after another from the box without replacement. The probability for both balls to be red is |
| A. | \(\frac3{11}\) |
| B. | \(\frac2{11}\) |
| C. | \(\frac5{11}\) |
| D. | \(\frac{25}{121}\) |
| Answer» C. \(\frac5{11}\) | |
| 382. |
From a pack of 52 playing cards, a card is drawn at random. What is the probability that the card is a spade or an ace? |
| A. | \(\dfrac{4}{13}\) |
| B. | \(\dfrac{6}{13}\) |
| C. | \(\dfrac{8}{13}\) |
| D. | \(\dfrac{2}{5}\) |
| Answer» B. \(\dfrac{6}{13}\) | |
| 383. |
An experiment has 10 equally likely outcomes. Let A and B be two non-empty events of the experiment. If A consists of 4 outcomes, the number of outcomes that B must have so that A and B are independent, is |
| A. | 2, 4 and 8 |
| B. | 3, 6 or 9 |
| C. | 4 or 8 |
| D. | 5 or 10 |
| Answer» E. | |
| 384. |
In a single throw of a die, what is the probability of getting a number greater than 1? |
| A. | \(\dfrac{5}{6}\) |
| B. | \(\dfrac{1}{3}\) |
| C. | \(\dfrac{1}{13}\) |
| D. | \(\dfrac{1}{5}\) |
| Answer» B. \(\dfrac{1}{3}\) | |
| 385. |
Let a die be loaded in such a way that even faces are twice likely to occur as the odd faces. What is the probability that a prime number will show up when the die is tossed? |
| A. | \(\frac{1}{3}\) |
| B. | \(\frac{2}{3}\) |
| C. | \(\frac{4}{9}\) |
| D. | \(\frac{5}{9}\) |
| Answer» D. \(\frac{5}{9}\) | |
| 386. |
if A = {6, 8, 23, 69, 80} and B = {4, 8, 69, 80, 82} and aggregate set U = {1, 2, 3, ...150}| then n(A ∪ B) ∶ {n(A ∩ B) + 10}...is. |
| A. | 11 ∶ 3 |
| B. | 13 ∶ 1 |
| C. | 11 ∶ 1 |
| D. | 7 ∶ 13 |
| Answer» E. | |
| 387. |
An unbiased coin is tossed five times. The outcome of each toss is either a head or a tail. The probability of getting at least one head is |
| A. | \(\frac{1}{{32}}\) |
| B. | \(\frac{{13}}{{32}}\) |
| C. | \(\frac{{16}}{{32}}\) |
| D. | \(\frac{{31}}{{32}}\) |
| Answer» E. | |
| 388. |
For two dependent events A and B, it is given that P(A) = 0.2 and P(B) = 0.5. If A ⊆ B, then the values of conditional probabilities P(A|B) and P(B|A) are respectively |
| A. | \(\frac{2}{5},\frac{3}{5}\) |
| B. | \(\frac{2}{5},\;1\) |
| C. | \(1,\frac{2}{5}\) |
| D. | Information is insufficient |
| Answer» C. \(1,\frac{2}{5}\) | |
| 389. |
A bag contains 19 red balls and 19 black balls. Two balls are removed at a time repeatedly and discarded if they are of the same colour, but if they are different, black ball is discarded and red ball is returned to the bag. The probability that this process will terminate with one red ball is |
| A. | 1 |
| B. | 1/21 |
| C. | 0 |
| D. | 0.5 |
| Answer» B. 1/21 | |
| 390. |
If the probability of hitting a target by a shooter, in any shot, is \(\frac{1}{3}\), then the minimum number of independent shots at the target required by him so that the probability of hitting the target at least once is greater than \(\frac{5}{6}\) is: |
| A. | 3 |
| B. | 6 |
| C. | 5 |
| D. | 4 |
| Answer» D. 4 | |
| 391. |
If A and B are two events and \(P(A\cup B)=\dfrac{5}{6}, P(A\cap B)=\dfrac{1}{2}\), P(A) = 2/3 then A and B are two events which are |
| A. | Dependent |
| B. | Independent |
| C. | Mutually exclusive |
| D. | Equally likely |
| Answer» E. | |
| 392. |
Let X be a continuous random variable denoting the temperature measured. The range of temperature is [0, 100] degree Celsius and let the probability density function of X be f(x) = 0.01 for 0 ≤ X ≤ 100.The mean of X is ______ |
| A. | 5.0 |
| B. | 2.5 |
| C. | 25.0 |
| D. | 50.0 |
| Answer» E. | |
| 393. |
If 5 of a Company’s 10 delivery tracks do not meet emission standards and 3 of them are chosen for inspection, then what is the probability that none of the trucks chosen will meet emission standards? |
| A. | \(\frac{1}{8}\) |
| B. | \(\frac{3}{8}\) |
| C. | \(\frac{1}{{12}}\) |
| D. | \(\frac{1}{4}\) |
| Answer» D. \(\frac{1}{4}\) | |
| 394. |
For a random variable, X, let \(\bar{X}\) be the sample average. The sample size is n. The mean and the standard deviation of X are μ and σ, respectively. The standard deviation of \(\bar{X}\) is |
| A. | nσ |
| B. | σ |
| C. | \(\sigma \over n\) |
| D. | \(\sigma \over \sqrt{n} \) |
| Answer» E. | |
| 395. |
For two events R and S, let P(R) = 0.4, P(S) = p and P(R ∪ S) = 0.6. Then p equals |
| A. | 0.2, when R and S are independent |
| B. | 0.2, when R and S are mutually disjoint |
| C. | Not determined in any case |
| D. | 0.2, when R and S are dependent |
| Answer» C. Not determined in any case | |
| 396. |
In throwing of a dice, what is the probability of getting more than 4? |
| A. | 1/2 |
| B. | 1/4 |
| C. | 1/3 |
| D. | 1/6 |
| Answer» D. 1/6 | |
| 397. |
A bag contains 5 black and 6 white balls; one balls are drawn at random. What is the probability that the balls drawn are black? |
| A. | 6/11 |
| B. | 5/6 |
| C. | 5/11 |
| D. | 2/5 |
| Answer» D. 2/5 | |
| 398. |
A speaks truth in 75% cases and B in 80% of cases. In what percentage of cases are they likely to contradict each other, narrating the same incident? |
| A. | 35% |
| B. | 45% |
| C. | 15% |
| D. | 5% |
| Answer» B. 45% | |
| 399. |
A problem is given to 4 students A, B, C and D in a class. If the probability that they can solve the problem is \(\dfrac{1}{3}, \dfrac{1}{4}, \dfrac{1}{5}\) and \(\dfrac{1}{6}\) respectively, what is the probability that problem will be solved? |
| A. | \(\dfrac{2}{5}\) |
| B. | \(\dfrac{3}{5}\) |
| C. | \(\dfrac{2}{3}\) |
| D. | \(\dfrac{1}{3}\) |
| Answer» D. \(\dfrac{1}{3}\) | |
| 400. |
In a series of 3 one-day cricket matches between teams A and B of a college, the probability of team A winning or drawing are 1/3 and 1/6 respectively. If a win, loss or draw gives 2, 0 and 1 point respectively, then what is the probability that team A will score 5 points in the series? |
| A. | \(\frac{{17}}{{18}}\) |
| B. | \(\frac{{11}}{{12}}\) |
| C. | \(\frac{1}{{12}}\) |
| D. | \(\frac{1}{{18}}\) |
| Answer» E. | |