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12th Standard Maths Probability Distributions Equations English Medium Free Online Test One Mark Questions with Answer Key 2020 - 2021

12th Standard

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Maths

Time : 00:10:00 Hrs
Total Marks : 10

    Answer all the questions

    10 x 1 = 10
  1. A rod of length 2l is broken into two pieces at random. The probability density function of the shorter of the two pieces is
    \(f(x)=\left\{\begin{array}{ll} \frac{1}{l} & 0<x<l \\\ 0 & l \leq x<2 l \end{array}\right.\)
    The mean and variance of the shorter of the two pieces are respectively

    (a)

    \(\cfrac { l }{ 2 } ,\cfrac { { l }^{ 2 } }{ 3 } \)

    (b)

    \(\\ \cfrac { l }{ 2 } ,\cfrac { { l }^{ 2 } }{ 6 } \)

    (c)

    \(l,\cfrac { { l }^{ 2 } }{ 12 } \)

    (d)

    \(\cfrac { l }{ 2 } ,\cfrac { { l }^{ 2 } }{ 12 } \)

  2. Let X represent the difference between the number of heads and the number of tails obtained when a coin is tossed n times. Then the possible values of X are

    (a)

    i + 2n, i = 0,1,2... n

    (b)

    2i- n, i = 0,1,2... n

    (c)

    n - i, i = 0,1,2... n

    (d)

    2i + 2n, i = 0, 1, 2...n

  3. Four buses carrying 160 students from the same school arrive at a football stadium. The buses carry, respectively, 42, 36, 34, and 48 students. One of the students is randomly selected. Let X denote the number of students that were on the bus carrying the randomly selected student. One of the 4 bus drivers is also randomly selected. Let Y denote the number of students on that bus.
    Then E(X) and E(Y) respectively are

    (a)

    50,40

    (b)

    40,50

    (c)

    40.75,40

    (d)

    41,41

  4. On a multiple-choice exam with 3 possible destructives for each of the 5 questions, the probability that a student will get 4 or more correct answers just by guessing is

    (a)

    \(\cfrac { 11 }{ 243 } \)

    (b)

    \(\cfrac { 3 }{ 8 } \)

    (c)

    \(\cfrac { 1 }{ 243 } \)

    (d)

    \(\cfrac { 5 }{ 243 } \)

  5. If X is a binomial randam variable with expected value 6 and variance 2.4, then P(X=5) is 

    (a)

    \(\left( \cfrac { 10 }{ 5 } \right) \left( \cfrac { 3 }{ 5 } \right) ^{ 6 }\left( \cfrac { 2 }{ 5 } \right) ^{ 4 }\) 

    (b)

    \(\left( \cfrac { 10 }{ 5 } \right) \left( \cfrac { 3 }{ 5 } \right) ^{ 10 }\)

    (c)

    \(\left( \cfrac { 10 }{ 5 } \right) { \left( \cfrac { 3 }{ 5 } \right) }^{ 4 }\left( \cfrac { 2 }{ 5 } \right) ^{ 6 }\)

    (d)

    \(\left( \cfrac { 10 }{ 5 } \right) \left( \cfrac { 3 }{ 5 } \right) ^{ 5 }\left( \cfrac { 2 }{ 5 } \right) ^{ 5 }\)

  6. Suppose that X takes on one of the values 0, 1, and 2. If for some constant k, P(X = i) = k P(X = i-I) i = 1, 2 and P(X = 0) =\(\cfrac { 1 }{ 7 } \) then the value of k is

    (a)

    1

    (b)

    2

    (c)

    3

    (d)

    4

  7. If \(f(x)=\left\{\begin{array}{ll} 2 x & 0 \leq x \leq a \\ 0 & \text { otherwise } \end{array}\right.\) is a probability density function of a random variable, then the value of a is

    (a)

    1

    (b)

    2

    (c)

    3

    (d)

    4

  8. A computer salesperson knows from his past experience that he sells computers to one in every twenty customers who enter the showroom. What is the probability that he will sell a computer to exactly two of the next three customers?

    (a)

    \(\cfrac { 57 }{ { 20 }^{ 3 } } \)

    (b)

    \(\cfrac { 57 }{ { 20 }^{ 2 } } \)

    (c)

    \(\cfrac { { 19 }^{ 3 } }{ { 20 }^{ 3 } } \)

    (d)

    \(\cfrac { 57 }{ 20 } \)

  9. IfF(x) is the probability distribution function, then \(F\left( -\infty \right) \) is 

    (a)

    1

    (b)

    2

    (c)

    \(\infty \)

    (d)

    0

  10. If \(f(x)={ Cx }^{ 2 }={ cx }^{ 2 },0<x<2\) is the p.d.f, of x then c is

    (a)

    \(\cfrac { 1 }{ 3 } \)

    (b)

    \(\cfrac { 4 }{ 3 } \)

    (c)

    \(\cfrac { 8 }{ 3 } \)

    (d)

    \(\cfrac { 3 }{ 8 } \)

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