Question 1 |

A remote village has exactly 1000 vehicles with sequential registration numbers starting from 1000 . Out of the total vehicles, 30 \% are without pollution clearance certificate. Further, even- and oddnumbered vehicles are operated on even- and oddnumbered dates, respectively.

If 100 vehicles are chosen at random on an evennumbered date, the number of vehicles expected without pollution clearance certificate is.

If 100 vehicles are chosen at random on an evennumbered date, the number of vehicles expected without pollution clearance certificate is.

15 | |

30 | |

50 | |

70 |

Question 1 Explanation:

Since 30 \% of the total vehicles are without pollution clearance certificate.

Out of the 100 chosen vehicle, 30 \% i.e. 100 \times 0.3=30 vehicle are expected to be without pollution clearance certificate.

Out of the 100 chosen vehicle, 30 \% i.e. 100 \times 0.3=30 vehicle are expected to be without pollution clearance certificate.

Question 2 |

Which of the following probability distribution functions (PDFs) has the mean greater than the median?

Function 1 | |

Function 2 | |

Function 3 | |

Function 4 |

Question 2 Explanation:

Option (B) is correct.

Question 3 |

The probabilities of occurrences of two independent events A and B are 0.5 and 0.8, respectively. What is the probability of occurrence of at least A or B (rounded off to one decimal place)?

0.4 | |

0.2 | |

0.9 | |

0.7 |

Question 3 Explanation:

\begin{aligned}
& P(A)=0.5 \\
& P(B)=0.8
\end{aligned}

Probability of occurence of atleast A or B= \mathrm{P}(\mathrm{A} \cap \mathrm{B})

\begin{aligned} P(A \cap B) & =P(A)+P(B)-P(A \cap B) \\ & =0.5+0.8-P(A) \times P(B) \\ & =0.5+0.8-0.5 \times 0.8 \\ & =1.3-0.4 \\ & =0.9 \end{aligned}

Probability of occurence of atleast A or B= \mathrm{P}(\mathrm{A} \cap \mathrm{B})

\begin{aligned} P(A \cap B) & =P(A)+P(B)-P(A \cap B) \\ & =0.5+0.8-P(A) \times P(B) \\ & =0.5+0.8-0.5 \times 0.8 \\ & =1.3-0.4 \\ & =0.9 \end{aligned}

Question 4 |

A pair of six-faced dice is rolled thrice. The probability that the sum of the
outcomes in each roll equals 4 in exactly two of the three attempts is ______.
(round off to three decimal places)

0.045 | |

0.078 | |

0.018 | |

0.025 |

Question 4 Explanation:

Event, E = {(1, 3)(3, 1)(2, 2)}

n(E) = 3

n(S) = 36

p=P(E)=\frac{3}{36}=\frac{1}{12}

q=P(\bar{E})=1-\frac{1}{12}=\frac{11}{12}

P(x)=3C_2(p^2)(q^1)=3 \times \left (\frac{1}{12} \right )^2\left (\frac{11}{12} \right )=0.02

n(E) = 3

n(S) = 36

p=P(E)=\frac{3}{36}=\frac{1}{12}

q=P(\bar{E})=1-\frac{1}{12}=\frac{11}{12}

P(x)=3C_2(p^2)(q^1)=3 \times \left (\frac{1}{12} \right )^2\left (\frac{11}{12} \right )=0.02

Question 5 |

Match the following attributes of a city with the appropriate scale of
measurements.

\begin{array}{|l|l|}\hline \text{Attribute}&\text{Scale of measurement} \\ \hline \text{(P) Average temperature } (^{\circ}C)\text{ of a city} & \text{((I) Interval} \\ \hline \text{(Q) Name of a city} & \text{(II) Ordinal}\\ \hline \text{(R) Population density of a city}& \text{(III) Nominal}\\ \hline \text{(S) Ranking of a city based on ease of business}& \text{(IV) Ratio}\\ \hline \end{array}

Which one of the following combinations is correct?

\begin{array}{|l|l|}\hline \text{Attribute}&\text{Scale of measurement} \\ \hline \text{(P) Average temperature } (^{\circ}C)\text{ of a city} & \text{((I) Interval} \\ \hline \text{(Q) Name of a city} & \text{(II) Ordinal}\\ \hline \text{(R) Population density of a city}& \text{(III) Nominal}\\ \hline \text{(S) Ranking of a city based on ease of business}& \text{(IV) Ratio}\\ \hline \end{array}

Which one of the following combinations is correct?

(P)-(I), (Q)-(III), (R)-(IV), (S)-(II) | |

(P)-(II), (Q)-(I), (R)-(IV), (S)-(III) | |

(P)-(II), (Q)-(III), (R)-(IV), (S)-(I) | |

(P)-(I), (Q)-(II), (R)-(III), (S)-(IV) |

Question 5 Explanation:

Meaning of

Nominal -> a name or term

Ordinal -> in an ordered sequence

Ratio -> quantitative relation between two things

Interval -> indicates average of a range

Nominal -> a name or term

Ordinal -> in an ordered sequence

Ratio -> quantitative relation between two things

Interval -> indicates average of a range

There are 5 questions to complete.