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MCQOPTIONS
This section includes 69 Mcqs, each offering curated multiple-choice questions to sharpen your SRMJEEE knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
An event has 4 possible outcomes with probabilities 1/2, 1/4, 1/8, 1/16. What will be the rate of information if there are approximately 24 outcomes/second possible? |
| A. | 78 bits/sec |
| B. | 3 bits/sec |
| C. | 39 bits/sec |
| D. | 6 bits/sec |
| Answer» D. 6 bits/sec | |
| 2. |
Consider the two statements.S1 : There exist random variables X and Y such that(E[X - E(X)) (Y - E(Y))])2 > Var[X] Var[Y]S2 : For all random variables X and Y,Cov[X, Y] = E [|X - E[X]| |Y - E[Y]|]Which one of the following choices is correct? |
| A. | S1 is false, but S2 is true. |
| B. | S1 is true, but S2 is false. |
| C. | Both S1 and S2 are true. |
| D. | Both S1 and S2 are false. |
| Answer» E. | |
| 3. |
A six-faced fair dice is rolled five times. The probability (in %) of obtaining “ONE” at least four times is |
| A. | 33.3 |
| B. | 3.33 |
| C. | 0.33 |
| D. | 0.0033 |
| Answer» D. 0.0033 | |
| 4. |
Consider a Poisson distribution for the tossing of a biased coin. The mean for this distribution is μ. The standard deviation for this distribution is given by |
| A. | √μ |
| B. | μ2 |
| C. | μ |
| D. | 1/μ |
| Answer» B. μ2 | |
| 5. |
In a group of 24 members, each member drinks either tea or coffee or both. If 15 of them drink tea and 18 drink coffee, find the probability that a person selected from the group drinks both tea and coffee. |
| A. | 1 / 8 |
| B. | 3 / 8 |
| C. | 5 / 24 |
| D. | None of the options |
| Answer» C. 5 / 24 | |
| 6. |
A box contains 5 red and 10 green balls. Eight (8) of them are placed in another box. The chances that the latter box contains 2 red and 6 green balls are ____ |
| A. | 240/429 |
| B. | 140/367 |
| C. | 140/429 |
| D. | 240/367 |
| Answer» D. 240/367 | |
| 7. |
Given a mean of 9 and a standard deviation of √6, determine the values of n and p in a binomial distribution. |
| A. | 81 and 1/9 respectively |
| B. | 72 and ½ respectively |
| C. | 27 and 1/3 respectively |
| D. | 18 and 1/6 respectively |
| Answer» D. 18 and 1/6 respectively | |
| 8. |
Consider a random process given by x(t) = A cos (2π fC t + θ), where A is a Rayleigh distributed random variable and θ is uniformly distributed in [0, 2π]. A and θ are independent. For any time t, the probability density function (PDF) of x(t) is: |
| A. | Gaussian |
| B. | Rayleigh |
| C. | Rician |
| D. | Uniform in [-A, A] |
| Answer» C. Rician | |
| 9. |
If P(X) = ¼, P(Y) = 1/3, and P(X ∩ Y) = 1/12, the value of P(Y/X) is |
| A. | ¼ |
| B. | 4/25 |
| C. | 1/3 |
| D. | 29/50 |
| Answer» D. 29/50 | |
| 10. |
For the function f(x) = a + bx, 0 ≤ x ≤ 1, to be a valid probability density function, which one of the following statements is correct? |
| A. | a = 1, b = 4 |
| B. | a = 0.5, b = 1 |
| C. | a = 0, b = 1 |
| D. | a = 1, b = -1 |
| Answer» C. a = 0, b = 1 | |
| 11. |
Four red balls, four green balls and four blue balls are put in a box. Three balls are pulled out of the box at random one after another without replacement. The probability that all the three balls are red is |
| A. | 1/72 |
| B. | 1/55 |
| C. | 1/36 |
| D. | 1/27 |
| Answer» C. 1/36 | |
| 12. |
A five-digit number is formed by the digits (0, 1, 2, 3, 4) without repetition. Find the probability that the number formed is divisible by 4. |
| A. | \(\frac{{16}}{5}\) |
| B. | \(\frac{{1}}{16}\) |
| C. | \(\frac{{5}}{16}\) |
| D. | \(\frac{{1}}{6}\) |
| Answer» D. \(\frac{{1}}{6}\) | |
| 13. |
Consider a sequence of tossing of a fair coin where the outcomes of tosses are independent. The probability of getting the head for the third time in the fifth toss is |
| A. | \(\frac{5}{{16}}\) |
| B. | \(\frac{3}{{16}}\) |
| C. | \(\frac{3}{5}\) |
| D. | \(\frac{9}{{16}}\) |
| Answer» C. \(\frac{3}{5}\) | |
| 14. |
For a symmetrical distribution the coefficient of skewness is |
| A. | 1 |
| B. | -1 |
| C. | 3 |
| D. | zero |
| Answer» E. | |
| 15. |
A sample of 15 data is as follows: 17, 18, 17, 17, 13, 18, 5, 5, 6, 7, 8, 9, 20, 17, 3. the mode of the data is |
| A. | 4 |
| B. | 13 |
| C. | 17 |
| D. | 20 |
| Answer» D. 20 | |
| 16. |
A die is tossed three times, What is the probability of getting an odd number at least once ? |
| A. | 7/16 |
| B. | 7/8 |
| C. | 3/16 |
| D. | 7/5 |
| Answer» C. 3/16 | |
| 17. |
A continuous random variable X has the distribution functionF(x) = 0 if x < 1= k (x - 1)4 if 1 < x < 3= 1 if x > 3The value of k is |
| A. | \(\frac{1}{{16}}\) |
| B. | \(\frac{1}{{4}}\) |
| C. | \(\frac{1}{{8}}\) |
| D. | \(\frac{1}{{2}}\) |
| Answer» B. \(\frac{1}{{4}}\) | |
| 18. |
Determine the correlation coefficient between the pulses x(t) and y(t) shown in the fig. below: |
| A. | 1 |
| B. | -1 |
| C. | 0 |
| D. | 2π |
| Answer» D. 2π | |
| 19. |
If X ∼ N (0, 1) and Y = X2 then the correlation coefficient r (X, Y) is |
| A. | one |
| B. | zero |
| C. | infinity |
| D. | two |
| Answer» C. infinity | |
| 20. |
A deck of five cards (each carrying a distinct number from 1 to 5) is shuffled thoroughly. Two cards are then removed from the deck, one at a time. What is the probability that the two cards are selected with the number of the first card being one higher than the number on the second card? |
| A. | \(\frac{1}{5}\) |
| B. | \(\frac{4}{{25}}\) |
| C. | \(\frac{1}{4}\) |
| D. | \(\frac{1}{2}\) |
| Answer» E. | |
| 21. |
If the probability of a bad reaction from a certain injection is 0.001, the chance that out of 2000 individuals, more than two will suffer of a bad reaction is |
| A. | 0.72 |
| B. | 0.54 |
| C. | 0.32 |
| D. | 0.14 |
| Answer» D. 0.14 | |
| 22. |
A class of 30 students occupy a classroom containing 5 rows of seats, with 8 seats in each row. If the student seat themselves at random, the probability that the sixth seat in the fifth row will be empty is |
| A. | 1/5 |
| B. | 1/3 |
| C. | 1/4 |
| D. | 2/5 |
| Answer» D. 2/5 | |
| 23. |
For a random variable x having the PDF shown in the figure given below the mean and variance are, respectively |
| A. | 0.5 and 0.66 |
| B. | 2.0 and 1.33 |
| C. | 1.0 and 0.66 |
| D. | 1.0 and 1.33 |
| Answer» E. | |
| 24. |
A box contains 2 washers, 3 nuts and 4 bolts. Items are drawn from the box at random one at a time without replacement. The probability of drawing 2 washers first followed by 3 nuts and subsequently the 4 bolts is |
| A. | 2/315 |
| B. | 1/630 |
| C. | 1/1260 |
| D. | 1/2520 |
| Answer» D. 1/2520 | |
| 25. |
Let X1, X2 be two independent normal random variables with means μ1, μ2 and standard deviations σ1, σ2, respectively. Consider Y = X1 – X2; μ1 = μ2 =1, σ1 = 1, σ2 = 2. Then, |
| A. | Y is normally distributed with mean 0 and variance 1 |
| B. | Y is normally distributed with mean 0 and variance 5 |
| C. | Y has mean 0 and variance 5, but is NOT normally distributed |
| D. | Y has mean 0 and variance 1, but is NOT normally distributed |
| Answer» C. Y has mean 0 and variance 5, but is NOT normally distributed | |
| 26. |
If three coins are tossed simultaneously, the probability of getting at least one head |
| A. | 1/8 |
| B. | 3/8 |
| C. | 1/2 |
| D. | 7/8 |
| Answer» E. | |
| 27. |
Events A, Band C are mutually exclusive events such that \(P(A) = \dfrac{3x + 1}{3}, P(B) = \dfrac{1-x}{4}\)and \(P(C) = \dfrac{1-2x}{4}\)The set of possible values of x are in the interval |
| A. | \(\left[ \dfrac{1}{3}, \dfrac{1}{2} \right]\) |
| B. | \(\left[ \dfrac{1}{3}, \dfrac{2}{3} \right]\) |
| C. | \([0, 1]\) |
| D. | \(\left[ \dfrac{1}{3}, \dfrac{13}{3} \right]\) |
| Answer» C. \([0, 1]\) | |
| 28. |
Given P(A) = 1/4, P(B) = 1/3 and P(AUB) = 1/2. Value of P(A/B) is |
| A. | 1/4 |
| B. | 1/3 |
| C. | 1/6 |
| D. | 1/7 |
| Answer» B. 1/3 | |
| 29. |
A purse contains 4 copper coins and 3 silver coins. A second purse contains 6 copper coins and 4 silver coins. A purse is chosen randomly and a coin is taken out of it. What is the probability that it is a copper coin? |
| A. | 70/82 |
| B. | 35/70 |
| C. | 41/82 |
| D. | 41/70 |
| Answer» E. | |
| 30. |
If 37 and 43 are the means of two samples of size 13 and 17 respectively, then the mean of their combined sample will be: |
| A. | 38.9 |
| B. | 40.4 |
| C. | 39.7 |
| D. | 41.2 |
| Answer» C. 39.7 | |
| 31. |
A committee of 4 is to be formed from among 4 girls and 5 boys. What is the probability that the committee will have number of boys less than number of girls? |
| A. | \(\dfrac{2}{9}\) |
| B. | \(\dfrac{4}{9}\) |
| C. | \(\dfrac{4}{5}\) |
| D. | \(\dfrac{1}{6}\) |
| Answer» E. | |
| 32. |
A machine produces 0, 1 or 2 defective pieces in a day with an associated probability of \(\frac{{1}}{{6}}\), \(\frac{{2}}{{3}}\) and \(\frac{{1}}{{6}}\) respectively. The mean value and the variance of the number of defective pieces produced by the machine in a day, respectively, are |
| A. | 1 and \(\frac{{1}}{{3}}\) |
| B. | \(\frac{{1}}{{3}}\) and 1 |
| C. | 1 and \(\frac{{4}}{{3}}\) |
| D. | \(\frac{{1}}{{3}}\) and \(\frac{{4}}{{3}}\) |
| Answer» B. \(\frac{{1}}{{3}}\) and 1 | |
| 33. |
A box has 8 red balls and 8 green balls. Two balls are drawn randomly is succession from the box without replacement. The probability that the first ball drawn is red and the second ball drawn is green is |
| A. | 4/15 |
| B. | 7/16 |
| C. | 1/2 |
| D. | 8/15 |
| Answer» B. 7/16 | |
| 34. |
In the following table, x is a discrete random variable and p(x) is the probability density. The standard deviation of x isX123P(x)0.30.60.1 |
| A. | 0.18 |
| B. | 0.36 |
| C. | 0.54 |
| D. | 0.6 |
| Answer» E. | |
| 35. |
A box contains the following three coins.I. A fair coin with head on one face and tail on the other face.II. A coin with heads on both the faces.III. A coin with tails on both the faces.A coin is picked randomly from the box and tossed. Out of the two remaining coins in the box, one coin is then picked randomly and tossed. If the first toss results in a head, the probability of getting a head in the second toss is |
| A. | \(\frac{2}{5}\) |
| B. | \(\frac{1}{3}\) |
| C. | \(\frac{2}{3}\) |
| D. | \(\frac{1}{2}\) |
| Answer» C. \(\frac{2}{3}\) | |
| 36. |
A box contains 20 defective items and 80 non-defective items. If two items are selected at random without replacement, what will be the probability that both items are defective.? |
| A. | \(\frac{1}{5}\) |
| B. | \(\frac{1}{{25}}\) |
| C. | \(\frac{{20}}{{99}}\) |
| D. | \(\frac{{19}}{{495}}\) |
| Answer» E. | |
| 37. |
If the probability of an event E is denoted by P(E) and P(X) = 1 and P(Y) = 0.5, then the values of P(X/Y) and P(Y/X), respectively, are: |
| A. | 1 and 0.5 |
| B. | 0.5 and 1 |
| C. | 1 and1 |
| D. | 0.5 and 0.5 |
| Answer» B. 0.5 and 1 | |
| 38. |
A fair coin is tossed \(n\) times. The probability that the difference between the number of heads and tails is \(\left( {n - 3} \right)\) is |
| A. | \({2^{ - n}}\) |
| B. | 0 |
| C. | \({}_\;^n{C_{n - 3}}{2^{ - n}}\) |
| D. | \({2^{ - n + 3}}\) |
| Answer» C. \({}_\;^n{C_{n - 3}}{2^{ - n}}\) | |
| 39. |
A fair (unbiased) coin was tossed four times in succession and resulted in the following outcomes: (i) Head (ii) Head (iii) Head (iv) Head. The probability of getting a ‘Tail’ when the coin is tossed again is |
| A. | 0 |
| B. | 1/2 |
| C. | 4/5 |
| D. | 1/5 |
| Answer» C. 4/5 | |
| 40. |
Given r12 = 0.6, r13 = 0.5 and r23 = 0.8, the value of r12.3 is : |
| A. | 0.47 |
| B. | 0.4 |
| C. | 0.74 |
| D. | 0.64 |
| Answer» C. 0.74 | |
| 41. |
Let X1, ... X50 be independent random variables following N(0, 1) distribution. Let \(Y=\displaystyle\sum_{i=1}^{50} X_i^2\), and E(Y) = a and Var(Y) = b.Then, the ordered pair (a, b) is : |
| A. | (50, 100) |
| B. | (50, 50) |
| C. | (25, 50) |
| D. | (25, 100) |
| Answer» B. (50, 50) | |
| 42. |
A problem is given to three students X, Y and Z, whose chances of solving it are respectively 1/3, 1/4 and 2/5. The probability that the problem is solved, is |
| A. | \(\frac{5}{{10}}\) |
| B. | \(\frac{7}{{10}}\) |
| C. | \(\frac{8}{{10}}\) |
| D. | \(\frac{2}{{10}}\) |
| Answer» C. \(\frac{8}{{10}}\) | |
| 43. |
Let X and Y be a bivariate random variable with correlation coefficient 1/2, and standard deviation 2 and 3 respectively, then Cov (X,Y) is |
| A. | 1/3 |
| B. | 3 |
| C. | 6 |
| D. | 1/6 |
| Answer» C. 6 | |
| 44. |
If x is a random variable with the expected value of 5 and the variance of 1, then the expected value of x2 is |
| A. | 24 |
| B. | 25 |
| C. | 26 |
| D. | 36 |
| Answer» D. 36 | |
| 45. |
As the value of one variable X increases , the value of other variable also increases, this is: |
| A. | Zero correlation |
| B. | Negative correlation |
| C. | Positive correlation |
| D. | Correlation coefficient |
| Answer» D. Correlation coefficient | |
| 46. |
Consider a discrete-random variable z assuming finitely many values. The cumulative distribution function, Fz(z) has the following properties:1. \(\mathop \smallint \limits_{ - \infty }^{ + \infty } {F_z}\left( z \right)dz = 1\) 2. Fz(z) is non-decreasing with finitely many jump-discontinuities3. Fz(z) is negative and non-decreasingWhich of the above properties is/are correct? |
| A. | 1 only |
| B. | 2 only |
| C. | 3 only |
| D. | 2 and 3 |
| Answer» C. 3 only | |
| 47. |
Let X1 and X2 be two independent exponentially distributed random variables with means 0.5 and 0.25, respectively. Then Y = min (X1, X2) is |
| A. | exponentially distributed with mean 1⁄6 |
| B. | exponentially distributed with mean 2 |
| C. | normally distributed with mean 3⁄4 |
| D. | normally distributed with mean 1⁄6 |
| Answer» B. exponentially distributed with mean 2 | |
| 48. |
An urn contains 5 red and 7green balls. A ball is drawn at random and its colour is noted. The ball is placed back into the urn along with another ball of the same colour. The probability of getting a red ball in the next draw is |
| A. | \(\frac{{65}}{{156}}\) |
| B. | \(\frac{{67}}{{156}}\) |
| C. | \(\frac{{79}}{{156}}\) |
| D. | \(\frac{{89}}{{156}}\) |
| Answer» B. \(\frac{{67}}{{156}}\) | |
| 49. |
A person on a trip has a choice between private car and public transport. The probability of using a private car is 0.45. While using public transport, further choice available re bus and metro. Out of which the probability of commuting by a bus is 0.55. In such a situation, the probability (rounded upto two decimals) of using a car, bus and metro respectively would be |
| A. | 0.45, 0.30 and 0.25 |
| B. | 0.45, 0.25 and 0.30 |
| C. | 0.45, 0.55 and 0 |
| D. | 0.45, 0.35 and 0.20 |
| Answer» B. 0.45, 0.25 and 0.30 | |
| 50. |
Let X be a normal random variable with mean zero and variance 9. If a = P(X ≥ 3) then P(|X| ≤ 3) equals: |
| A. | 1- 2a |
| B. | 1 - a |
| C. | 2a |
| D. | a |
| Answer» B. 1 - a | |