Explore topic-wise MCQs in SRMJEEE .

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.

51.

Let X be a nominal variable with mean 1 and variance 4. The probability P (X < 0) is

A. 0.5
B. Greater than zero and less than 0.5
C. Greater than 0.5 and less than 1
D. 1.0
Answer» C. Greater than 0.5 and less than 1
Discussion
52.

For any discrete random variable X, with probability mass function P(X = j) = pj, pj ≥ 0, j ∈ {0,….,N}, and \(\mathop \sum \limits_{j = 0}^N {p_j} = 1\), define the polynomial function \({g_x}\left( z \right) = \;\mathop \sum \limits_{j = 0}^N {p_j}{z^j}\). For a certain discrete random variable Y, there exists a scalar β ∈ [0, 1] such that gγ (z) = (1 - β + β z)N. The expectation of Y is

A. Nβ (1 – β)
B. Nβ
C. N (1 - β)
D. Not expressible in terms of N and β alone
Answer» C. N (1 - β)
Discussion
53.

A continuous random variable X has a density function given by f(x) = kx (1-x), 0 ≤ x ≤ 1. The value of k is

A. 2
B. 3
C. 5
D. 6
Answer» E.
Discussion
54.

A probability distribution with right skew is shown in the figureThe correct statement for the probability distribution is

A. Mean is equal to mode
B. Mean is greater than median but less than mode
C. Mean is greater than median and mode
D. Mode is greater than median
Answer» D. Mode is greater than median
Discussion
55.

A random variable X has the probability density function given by \(f(x) = \frac{1}{4}\), -2 < x < 2. The moment generating function of X is given by

A. \(\frac{e^{2t}+e^{-2t}}{4t}\)
B. \(\frac{e^{2t}-e^{-2t}}{4t}\)
C. \(\frac{e^{2t}+e^{-2t}}{t}\)
D. \(\frac{e^{2t}-e^{-2t}}{t}\)
Answer» C. \(\frac{e^{2t}+e^{-2t}}{t}\)
Discussion
56.

Consider a continuous random variable with probability density functionF(t) = 1 + t for -1 ≤ t ≤ 0 = 1 – t for 0 ≤ t ≤ 1The standard deviation of the random variable is:

A. \(\frac{1}{{\sqrt 3 }}\)
B. \(\frac{1}{{\sqrt 6 }}\)
C. \(\frac{1}{3}\)
D. \(\frac{1}{6}\)
Answer» C. \(\frac{1}{3}\)
Discussion
57.

A continuous random variable X has uncountable many values in the interval [a, b]. If C is a values in the interval [a, b], then P{ X = C }

A. is zero
B. is strictly non-zero
C. depends on the limits {a, b}
D. is less than one, but non-zero
Answer» B. is strictly non-zero
Discussion
58.

Let E and F be any two events with P(EUF) = 0.8, P(E) = 0.4 and P(E/F) = 0.3. Then P(F) is

A. 3/7
B. 4/7
C. 3/5
D. 2/5
Answer» C. 3/5
Discussion
59.

"Mathematical Expectation of the product of two random variables is equal to the product of their expectations" is true for

A. any two random variables
B. if the random variables are independent
C. if the covariance between the random variables is nonzero
D. if the variance of the random variables is equal
Answer» C. if the covariance between the random variables is nonzero
Discussion
60.

Find the number of permutations of all the letters of the word.“committee”.

A. \(\frac{{9!}}{{ 8}}\)
B. \(\frac{{8}}{{ 9!}}\)
C. \(\frac{{8!}}{{ 2}}\)
D. \(\frac{{9!}}{{ 2}}\)
Answer» B. \(\frac{{8}}{{ 9!}}\)
Discussion
61.

Find the mode of the following data:Age0-66-1212-1818-2424-3030-3636-42 Frequency 611253518126

A. 20.22
B. 19.47
C. 21.12
D. 20.14
Answer» B. 19.47
Discussion
62.

Given the equation of line of regression of x on y, determine its regression coefficient.\(x - \bar x = \frac{{r{\sigma _x}}}{{{\sigma _y}}}\left( {y - \bar y} \right)\;\)

A. 1
B. \(\frac{{r{\sigma _y}}}{{{\sigma _x}}}\)
C. (y – x̅)
D. \(\frac{{r{\sigma _x}}}{{{\sigma _y}}}\)
Answer» E.
Discussion
63.

Let X and Y be two independent random variables. Which one of the relations between expectation (E), variance (Var) and covariance (Cov) given below is FALSE?

A. E(XY) = E(X) E(Y)
B. Cov(X, Y) = 0
C. Var (X + Y) = Var (X) + Var(Y)
D. E(X2Y2) = (E(X))2 (E(Y))2
Answer» E.
Discussion
64.

If the probability of a defective bolt is 0.1, then the mean and standard deviation for the distribution of bolts in a total of 400 are

A. 30, 3
B. 40, 5
C. 30, 4
D. 40, 6
Answer» E.
Discussion
65.

An automobile plant contracted to buy shock absorbers from two suppliers X and Y. X supplies 60% and Y supplies 40% of the shod absorbers. All shock absorbers are subjected to a quality test. The ones that pass the quality test are considered reliable Of X's shock absorbers, 96% are reliable. Of Y's shock absorbers, 72% are reliable. The probability that a randomly chosen shock absorber, which is found to be reliable is made by Y is

A. 0.288
B. 0.334
C. 0.667
D. 0.720
Answer» C. 0.667
Discussion
66.

For the regression equationsy = 0.516x + 33.73andx = 0.512 y + 32.52the means of x and y are nearly

A. 67.6 and 68.6
B. 68.6 and 68.6
C. 67.6 and 58.6
D. 68.6 and 58.6
Answer» B. 68.6 and 68.6
Discussion
67.

For a given process control chart, there are four rules for determining out- of-control state of the process which are being used simultaneously. The probability of Type-I error for the four rules are 0.005, 0.02, 0.03, and 0.05. Assuming independence of the rules, the probability of overall Type-I error when all the four rules are used simultaneously is

A. 0.101
B. 0.201
C. 0.001
D. 0.301
Answer» B. 0.201
Discussion
68.

Let the probability density function of a random variable, \(X\), be given as:\(fx\left( x \right) = \frac{3}{2}{e^{ - 3x}}u\left( x \right) + a{e^{4x}}u\left( { - x} \right)\)Where \(u\left( x \right)\) is the unit step function.Then the value of 'a' and \(Prob\left\{ {X \le 0} \right\}\;\) respectively, are

A. \(2,\frac{1}{2}\)
B. \(4,\frac{1}{2}\)
C. \(2,\frac{1}{4}\)
D. \(4\;,\frac{1}{4}\)
Answer» B. \(4,\frac{1}{2}\)
Discussion
69.

A person decides to toss a fair coin repeatedly until he gets a head. He will make at most 3 tosses. Let the random variable Y denote the number of heads. The value of var {Y}, where var{.} denotes the variance, equals.

A. \(\frac{7}{8}\)
B. \(\frac{{49}}{{64}}\)
C. \(\frac{7}{{64}}\)
D. \(\frac{{105}}{{64}}\)
Answer» D. \(\frac{{105}}{{64}}\)
Discussion