The Hour Hand And Minute Hand Of The Clock Exchanged Places

Problem
Between 3:00 and 4:00, Kathryn looked at her watch and noticed that the minute hand was between 5 and 6. Later, Kathryn looked again and noticed that the hour hand and the minute hand had exchanged places. What time was it in the second case?
 

Time After 3:00 O'clock When The Hands Of The Clock Are Perpendicular

Problem
How many minutes after 3:00 o’clock will the hands of the clock be perpendicular to each other for the 1st time?

A.   35 C.   32.73
B.   33.15 D.   34.12

 

Smallest Part From The Circle That Was Divided Into Four Parts By Perpendicular Chords

Problem
Divide the circle of radius 13 cm into four parts by two perpendicular chords, both 5 cm from the center. What is the area of the smallest part.
 

Continuous Beam With Equal Support Reactions

Situation
A beam 100 mm × 150 mm carrying a uniformly distributed load of 300 N/m rests on three supports spaced 3 m apart as shown below. The length x is so calculated in order that the reactions at all supports shall be the same.
 

design-practice-2-given.png

 

1.   Find x in meters.

A.   1.319 C.   1.217
B.   1.139 D.   1.127

2.   Find the moment at B in N·m.

A.   -240 C.   -242
B.   -207 D.   -226

3.   Calculate the reactions in Newton.

A.   843.4 C.   863.8
B.   425.4 D.   827.8

 

Continuous Beam With a Gap and a Zero Moment in Interior Support

Situation
A beam of uniform cross section whose flexural rigidity EI = 2.8 × 1011 N·mm2, is placed on three supports as shown. Support B is at small gap Δ so that the moment at B is zero.
 

design-practice-1-given.gif

 

1.   Calculate the reaction at A.

A.   4.375 kN C.   5.437 kN
B.   8.750 kN D.   6.626 kN

2.   What is the reaction at B?

A.   4.375 kN C.   5.437 kN
B.   8.750 kN D.   6.626 kN

3.   Find the value of Δ.

A.   46 mm C.   34 mm
B.   64 mm D.   56 mm

 

Probability that a Large Shipment is Accepted or Not Accepted due to Defective Items

Problem
A stationery store has decided to accept a large shipment of ball-point pens if an inspection of 20 randomly selected pens yields no more than two defective pens. Find the probability that this shipment is...

  1. accepted if 5% of the total shipment is defective.
  2. not accepted if 15% of the total shipment is defective.

 

1 - Probability for cars to pass through a point on road in a 5-minute period

Problem
The number of cars passing a point on a road may be modelled by Poisson distribution. At an average, 4 cars enters the Caibaan Diversion Road in Tacloban City every 5 minutes. Find the probability that in a 5-minute period (a) two cars go past and (b) fewer than 3 cars go past.
 

Three Men Shoot and Only One of Them Hits the Target. Find the Probability that it was the First Man

Problem
The probabilities that three men hit a target are 1/6, 1/4, and 1/3, respectively. Each shoot once at the target. If only one of them hits the target, find the probability that it was the first man.
 

Answer Key

 

Poisson Probability Distribution

The number of occurrences in a given time interval or in a given space can be modeled using Poisson Distribution if the following conditions are being satisfied:

  • The events occur at random.
  • The events are independent from one another.
  • The average rate of occurrences is constant.
  • There are no simultaneous occurrences.

 

The Poisson distribution is defined as

$P(x) = \dfrac{e^{-\mu} \mu^x}{x!}$

where x is a discrete random variable

P(x) = probability for x occurrences
μ = the mean number of occurrences

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