Find y’ if x = 2 arccos 2t and y = 4 arcsin 2t

Problem
Find y’ if x = 2 arccos 2t and y = 4 arcsin 2t.

A.   2 C.   4
B.   -2 D.   -4

 

Probability That A Randomly Selected Chord Exceeds The Length Of The Radius Of Circle

Situation
If a chord is selected at random on a fixed circle what is the probability that its length exceeds the radius of the circle?

  1. Assume that the distance of the chord from the center of the circle is uniformly distributed.
    A.   0.5 C.   0.866
    B.   0.667 D.   0.75
  2. Assume that the midpoint of the chord is evenly distributed over the circle.
    A.   0.5 C.   0.866
    B.   0.667 D.   0.75
  3. Assume that the end points of the chord are uniformly distributed over the circumference of the circle.
    A.   0.5 C.   0.866
    B.   0.667 D.   0.75

 

Regular Octagon Made By Cutting Equal Triangles Out From The Corners Of A Square

Problem
A regular octagon is made by cutting equal isosceles right triangles out from the corners of a square of sides 16 cm. What is the length of the sides of the octagon?

A.   6.627 cm C.   6.762 cm
B.   6.267 cm D.   6.276 cm

 

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

 

Probability that a Point Inside a Square Will Subtend an Obtuse Angle to Adjacent Corners of the Square

Problem
Point P is randomly chosen inside the square ABCD. Lines AP and PB are then drawn. What is the probability that angle APB is obtuse?
 

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.

 

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