Discrete Probability MCQ

Test your knowledge with important Discrete Probability MCQ and their applications. These MCQs are beneficial for competitive exams too. Explore 30 + more Discrete Probability MCQs at Bissoy

• Determine the radius of convergence and interval of convergence for the power series: ∞∑n=0 (x−7)n+1/nn.
  ক

  0, −1<x<1

  খ

  ∞, −∞<x<∞

  গ

  1, −2<x<2

  ঘ

  2, −1<x<1
• What is the radius of convergence and interval of convergence for the power series ∞∑n=0m!(2x-1)m?
  ক

  3, 12

  খ

  1, 0.87

  গ

  2, 5.4

  ঘ

  0, 1/2
• Find the power series representation for the function f(x)=x/4−x.
  ক

  ∞∑n=0xn+1/4n+1

  খ

  ∞∑n=0xn+14n

  গ

  ∞∑n=0xn4n

  ঘ

  ∞∑n=0xn+1
• An example of Maclaurin series is _______
  ক

  ∞∑n=0 (xn/n!)

  খ

  ∞∑n=0 (x/5+n!)

  গ

  ∞∑n=0 (xn+1/(n-1)!)

  ঘ

  (xn/n)
• Determine a power series representation for the function g(x)=ln(7−x).
  ক

  ∞∑n=0 xn+1/7n+1

  খ

  ln(14)∞∑n=0 xn+1/7n

  গ

  ln(7)∞∑n=0 xn+1/7n+1

  ঘ

  ln∞∑n=0 x/7n+1
• Determine the interval and radius of convergence for the power series: ∞∑n=17n/n(3x−1)n-1.
  ক

  (2x+1)/6

  খ

  7|3x−1|

  গ

  5|x+1|

  ঘ

  3!*|4x−9|
• sec(x) has a trigonometric series that is given by _______
  ক

  ∞∑n=0 ((-1)nE2n / (2n)!)*x2n

  খ

  ∞∑n=0 ((-1)nE2n)

  গ

  ((-1)nB2n / (2n)!)*x2n

  ঘ

  ∞∑n=0 ((2n)!)*x2n+1
• Which of the following series is called the “formal power series”?
  ক

  b0+b1x+b2x2+…+bnxn

  খ

  b1x+b2x2+…+bnxn

  গ

  1/2b0+1/3b1x+1/4b2x2+…+1/nbnxn

  ঘ

  n2(b0+b1x+b2x2+…+bnxn)
• The third term of a geometric progression with common ratio equal to half the initial term is 81. Determine the 12th term.
  ক

  312

  খ

  415

  গ

  68

  ঘ

  59
• The explicit formula for the geometric sequence 3, 15, 75, 375,… is _______
  ক

  2*6! * 3n-1

  খ

  3 * 5n-1

  গ

  3! * 8n-1

  ঘ

  7 * 4n-1
• Transform 54y = n+1 into equivalent a logarithmic expression.
  ক

  log12 (n+1)

  খ

  log41 (n2)

  গ

  log63 (n)

  ঘ

  log54 (n+1)
• Given: log4 z = B log2/3z, for all z > 0. Find the value of constant B.
  ক

  2/(3!*ln(2))

  খ

  1/ln(7)

  গ

  (4*ln(9))

  ঘ

  1/(2*ln(3))
• Solve for x the equation 2x + 3 = 5x + 2.
  ক

  ln (24/8)

  খ

  ln (25/8) / ln (2/5)

  গ

  ln (32/5) / ln (2/3)

  ঘ

  ln (3/25)
• Solve for x: log2(x2-3x)=log2(5x-15).
  ক

  2, 5

  খ

  7

  গ

  23

  ঘ

  3, 5
• Find the value of x: 3 x2 alogax = 348?
  ক

  7.1

  খ

  4.5

  গ

  6.2

  ঘ

  4.8
• Computation of the discrete logarithm is the basis of the cryptographic system _______
  ক

  Symmetric cryptography

  খ

  Asymmetric cryptography

  গ

  Diffie-Hellman key exchange

  ঘ

  Secret key cryptography
• There are 9 letters having different colors (red, orange, yellow, green, blue, indigo, violet) and 4 boxes each of different shapes (tetrahedron, cube, polyhedron, dodecahedron). How many ways are there to place these 9 letters into the 4 boxes such that each box contains at least 1 letter?
  ক

  260100

  খ

  878760

  গ

  437102

  ঘ

  256850
• In class, students want to join sports. 15 people will join football, 24 people will join basketball, and 7 people will join both. How many people are there in the class?
  ক

  19

  খ

  82

  গ

  64

  ঘ

  30
• In a renowned software development company of 240 computer programmers 102 employees are proficient in Java, 86 in C#, 126 in Python, 41 in C# and Java, 37 in Java and Python, 23 in C# and Python, and just 10 programmers are proficient in all three languages. How many computer programmers are there those are not proficient in any of these three languages?
  ক

  138

  খ

  17

  গ

  65

  ঘ

  49
• At a software company, skilled workers have been hired for a project. Out of 75 candidates, 48 of them were software engineer; 35 of them were hardware engineer; 42 of them were network engineer; 18 of them had skills in all three jobs and all of them had skills in at least one of these jobs. How many candidates were hired who were skilled in exactly 2 jobs?
  ক

  69

  খ

  14

  গ

  32

  ঘ

  8
• There are 70 patients admitted in a hospital in which 29 are diagnosed with typhoid, 32 with malaria, and 14 with both typhoid and malaria. Find the number of patients diagnosed with typhoid or malaria or both.
  ক

  39

  খ

  17

  গ

  47

  ঘ

  53
• Find the sequence generated by 1/1−x2−x4.,assume that 1, 1, 2, 3, 5, 8,… has generating function 1/1−x−x2.
  ক

  0, 0, 1, 1, 2, 3, 5, 8,…

  খ

  0, 1, 2, 3, 5, 8,…

  গ

  1, 1, 2, 2, 4, 6, 8,…

  ঘ

  1, 4, 3, 5, 7,…
• Suppose G is the generating function for the sequence 4, 7, 10, 13, 16, 19,…, the find a generating function (in terms of G) for the sequence of differences between terms.
  ক

  (1−x)G−4/x

  খ

  (1−x)G−4/x3

  গ

  (1−x)G+6/x

  ঘ

  (1−x)G−x2
• What is the generating function for the sequence with closed formula an=4(7n)+6(−2)n?
  ক

  (4/1−7x)+6!

  খ

  (3/1−8x)

  গ

  (4/1−7x)+(6/1+2x)

  ঘ

  (6/1-2x)+8
• What will be the sequence generated by the generating function 4x/(1-x)2?
  ক

  12, 16, 20, 24,…

  খ

  1, 3, 5, 7, 9,…

  গ

  0, 4, 8, 12, 16, 20,…

  ঘ

  0, 1, 1, 3, 5, 8, 13,…
• What is multiplication of the sequence 1, 2, 3, 4,… by the sequence 1, 3, 5, 7, 11,….?
  ক

  1, 5, 14, 30,…

  খ

  2, 8, 16, 35,…

  গ

  1, 4, 7, 9, 13,…

  ঘ

  4, 8, 9, 14, 28,…
• What is the recurrence relation for the sequence 1, 3, 7, 15, 31, 63,…?
  ক

  an = 3an-1−2an+2

  খ

  an = 3an-1−2an-2

  গ

  an = 3an-1−2an-1

  ঘ

  an = 3an-1−2an-3
• What is the generating function for the generating sequence A = 1, 9, 25, 49,…?
  ক

  1+(A-x2)

  খ

  (1-A)-1/x

  গ

  (1-A)+1/x2

  ঘ

  (A-x)/x3
• What is the sequence depicted by the generating series 4 + 15x2 + 10x3 + 25x5 + 16x6+⋯?
  ক

  10, 4, 0, 16, 25, …

  খ

  0, 4, 15, 10, 16, 25,…

  গ

  4, 0, 15, 10, 25, 16,…

  ঘ

  4, 10, 15, 25,…
• Naina receives emails that consists of 18% spam of those emails. The spam filter is 93% reliable i.e., 93% of the mails it marks as spam are actually a spam and 93% of spam mails are correctly labelled as spam. If a mail marked spam by her spam filter, determine the probability that it is really spam.
  ক

  50%

  খ

  84%

  গ

  39%

  ঘ

  63%