Quiz: Random Problems Set 2

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Quiz: Random Problems 04

Question 1

Solve for x:   x - 1/x = 0.

1,   -1

-1

-1/2,   -1

1,   1/2

Question 2

A circle is described by the equation x2 + y2 - 16x = 0. What is the length of the chord that is 4 units from the center of the circle?

12.563 units

8.523 units

13.856 units

9.632 units

Question 3

The inner surface area in sq. m. of an open (both ends) cylinder 2 m in height and 3 m in diameter is:

6π

2.5π

30π

3.75π

Question 4

A hot air balloon rising straight up from a level field is track by a range finder 500 ft from the point of lift off. At the moment the lift finder’s elevation is 45 degrees, the angle is increasing at the rate of 0.14 rad per minute. How fast is the balloon rising?

120 fpm

150 fpm

140 fpm

130 fpm

Question 5

Given a right triangle where the hypotenuse is r, the acute angle θ, the opposite vertical side y and adjacent side x. Which of the following relations does not apply?

$x^2 + y^2 = r^2$

$\sin 2\theta = 2 (\sin \theta) (\cos \theta)$

$\cos 2\theta = 1 + 2\sin^2 \theta$

$1 + \tan^2 \theta = \sec^2 \theta$

Question 6

A vending machine dispenses gumballs in a regular repeating cycle of ten different colors. If a quarter buys 3 gumballs, what is the minimum amount of money that must be spent before three gumballs of the same color are dispense?

$2.25

$2.0

$1.75

$1.0

Question 7

If two points in the number line have coordinates 1 and 7, find the coordinate of a point on the line which is twice as far from 1 as from 7.

5

2

3

4

Question 8

Instead of multiplying the number by 17, Fred divided it by 17. If the answer he obtained was 1, what should have been the correct answer?

291

289

285

287

Question 9

An automobile tire is 30 inches in diameter. How fast in rpm does the wheel turn on the axle when the automobile maintains a speed of 50 mph?

551

450

504

560

Question 10

You deposit \$1,000 into a 9% account today. At the end of two years, you will deposit another \$3,000. In five years, you plan a \$4,000 purchase. How much is left in the account one year after the purchase?

$1,424

$1,552

$1,691

$925

Question 11

If sec 2A = 1 / sin 13A, determine the value of A in degrees.

6

5

7

3

Question 12

CPM factory employs 60 workers. If 4 out of every 5 workers are married, how many married workers are employed by the factory?

40

20

24

48

Question 13

If the interest rate on an account is 8.5% compounded yearly, approximately how many years will it take to triple the amount?

12.5 yrs

13.4 yrs

15 yrs

14.4 yrs

Question 14

A pump discharges 50 ton of water per hour at the height of 8 m. The overall efficiency of the pumping system being 69%. Calculate the energy consumed by the pump in 2 hours, expressed in MJ.

11.68

11.38

12.68

13.38

Question 15

A wire with length of 52 cm is cut into two unequal lengths. Each par is bent to form a square. If the sum of the area of the two squares is 97 sq. cm., what is the area of the smaller square?

16

81

49

64

Question 16

An equilateral triangle has an altitude of $5\sqrt{3}$ cm long. Find its area.

$100\sqrt{3} ~ \text{cm}^2$

$\frac{5}{4}\sqrt{3} ~ \text{cm}^2$

$25\sqrt{3} ~ \text{cm}^2$

$50\sqrt{3} ~ \text{cm}^2$

Question 17

In a lifting machine, a load of 50 kN is moved by a distance of 10 cm using an effort of 10 kN which moves through a distance of 1 m, the efficiency of the machine is…

20%

40%

10%

50%

Question 18

A factory is running at 80% efficiency with a fixed cost of P78,000.00, variable cost per unit of P130.00, selling price per unit of P416.00, and production capacity of 5000 units. What is the current profit of the factory if all products manufactured are sold?

P1,352,000.00

P1,066,000.00

P1,144,000.00

P1,430,000.00

Question 19

How long will each side of the hexagon with perimeter 108 in.?

36

24

18

12

Question 20

What is the present worth of $100 annuity starting at the end of the third year and continuing to the end of the fourth year, if the annual interest rate is 8%?

$162

$122

$153

$160

Question 21

A rectangle with sides parallel to the axes has vertices at (-3, 2), (2, 5), and (-3, 5). Find the coordinate of the fourth vertex.

(3, 5)

(2, 2)

(-5, 2)

(2, -5)

Question 22

Find the slope of the line passing through the points (2, 6) and (2, -4).

-2

7

∞

0

Question 23

A businessman wishes to earn 7% on his capital after payment of taxes. If the income from an available investment will be taxed at an average rate of 42%, what minimum rate of return, before payment of taxes, must the investment offer to be justified?

12.7%

10.7%

11.1%

12.1%

Question 24

Two forces of 20 units and 30 units act at right angles. What is the magnitude of the resultant force?

36

42

44

24

Question 25

The total number of diagonals of an N-gon is 77, then what is N?

8

5

14

11