practice trial run training to master 321.pptx

Practice Questions
Mechanical Engineering
Mathematics
Quiz Bowl

1. What do you call the angle with rays touching a
circle with vertex located in the center of the circle?

2. Solve for x when x:16=y-7 and y=6x-1.

3. Find the length of the hypotenuse of a right triangle
when its area is 128 sq. cm when a side spans 8.9 cm.

4. What is the numerical coefficient of
the 3rd
term in the expansion of (x+3)3
?

5. Find the sum of all even integers from
2 to 66.

6. Ferdy has to work 3 hours to make his homework done
while his classmate Bea needs 4 hours to do such homework.
Find the time required for them to finish a homework.

7. A two-digit number has a unit number twice the
tens place and is 3 greater than it. Find the number.

8. An airplane flies at a height of 1500ft. When an anti-
aircraft gun is fired at it at an angle of 250
with a speed of
1000 ft/sec. Will the bullet be able to reach the airplane?

9. A spherical balloon is being inflated at a rate of 16
cu. cm/sec. Find the rate at which the surface area
increases 5.5 secs after.

10. Find the slope of the function
y=x3
-x2
+6x at x=3/2.

11. A box is made from a 20 by 20 in cardboard. Find the
maximum volume of the box that can be made by cutting
equal square parts in each corner of the cardboard.

12. Assuming that the earth is sphere whose radius is
6400 km. Find the distance along a 30
arc at the
equator of the earth’s surface.

13. The angle subtended by an arc is 24 deg. If the
radius of the circle is 45cm, find the length of arc.

14. What is the surface area of a sphere
whose volume is 36 cu. m?

15. A 2m rope is used to demonstrate the shape of an
ellipse. Find the length of the major axis in cm when
the a=2b.

16. How many real roots does the
equation y=-x6
-5x5
-16x4
-12x3
-x2
-x-24 have?

17. Find the sum of the interior angles
of a square and triangle.

18. Find the equation of the directrix of
the parabola y=2x2
-6x.

19. Find the acute angle between the
lines 2x-3y=1 and x=y.

20. What time after 1 o’clock pm will the hour
and minute hand will subtend an angle 1000
.

21. A can do a piece of work in p days, B in q days, and
C in r days. In how many days can they do the work
together?

22. A motorboat has an average speed of 20kph in still water. It can
travel upstream 5km against a river current in the same time it can
travel 7km with the river current. What is the speed of the current?

23. Find the area of the largest circular garden which
can be made from a triangular lot with sides 5, 8, and
10m.

24. Express cos 2x in terms of sin x.

25. Find the derivative of y=x1/2
with
respect to variable t.

26. Find the amplitude of the function
defined by y= πsin πx.

27. Three fighter plane pilots were tasked to
rendezvous with a bomber squad bound for
Wake Island from the same airbase. Captain
Williams flies north at 200kph while Lt.
Winters flies at the same speed at N 50
E. Lt.
Peppers flies at the same speed at N 110
E.
What is the distance of two pilots from the
Captain after 3.5 hours of flying?

Answer: Captain Williams to Lt. Peppers = 134.18 km
Captain Williams to Lt. Winters = 61.07 km

28. An annulus has an area of 6.2 cm2
the outer radius
measures 3cm. Find the circumference of the inner
radius.

29. Express the distance D travelled in t
hr by a car whose speed is 60 kph.

30. Find the error in computing the volume
of a 15 cm high conical vessel if there is a
0.2% error in measuring the radius when
the height is always thrice the radius.

31. Find the coefficient of friction between a 3.5kg
mass and a horizontal surface when a force of 9.5N is
needed to push it to a constant velocity.

32. A particle’s position is defined by the equation
s=t3
-t2
where is the position in m and t is the time in
secs, find the velocity when the acceleration is 0.

33. If sinx – cosx = -1/3 what is the value
of sin 2x.

34. What is the eccentricity of the
parabola y2
=9-3x?

35. What is the length of the latus
rectum of the hyperbola 16x2
+ 9y2
= 144?

36. A line segment joining two points on
a circle is called:

37. Bobby wanted to know the chances of him passing a 20 item
dichotomous examination. If the passing score is 80% of the total perfect
score. What is the chance for him to pass the exam using pure
guesswork?

38. A cyclist travelled a certain distance at her usual speed. If her speed
had been 2 mph faster, she could have travelled the distance in hr less
time. If her speed had been 2 mph slower, she would have taken 2hr
longer. Find her usual speed.

39. Find the dimensions of the right circular cylinder
of maximum lateral surface area which can be
inscribed in a sphere of radius 4cm.

Answer: r=2.8284 cm, h=5.657cm

40. The hypotenuse of a right triangle is 25 ft. If one of the
acute angles increases at the rate 4 degrees per second,
how fast is the area increasing when the angle is 30 degrees?

41. A ball is dropped from a height of 1.7m and is
always bouncing ¼ of its preceding height. Find the
total distance it will travel.

42. Find the mean, median, and mode
2.4, 2.4, 2.25, 2.9, 2.67, 2.36.

Answer: Mean = 2.50, Median = 2.4,
Mode = 2.4

43. Find the square root of 6-5i.

Answer: 611/4
<19.90
and 611/4
< 199.90

44. A thermometer reading 15 deg C is brought in a room whose
temperature is 26 deg C. 1 min and 30 secs later, the thermometer
reading is 16.5 deg C. How long does it take for the thermometer to
read 18 deg C?

45. An unstretched spring is 10 ft. Long. A pull of 40 lb
stretches the spring by ½ ft. Find the work done in
stretching the spring from 10 ft to 14 ft.

46. A conical tank is 12 ft across the top amd 8 ft deep. It contains
water to a depth of 6ft. Find the work done in pumping the water to a
point 2 ft above the top of the tank. Use sp. weight = 62.5 lb/ft3

47. In a card game using a deck of cards without face cards, you will win
60 dollars if you picked up an even red card and lose 10 dollars if you
picked any other card. What is the expected winning for one picking of
a card?

48. Peter, Paul, and Mary went to a ball sponsored by their friend Harry. Each table
serves 8 persons. The four of them decided to seat to observe the magnificent
ballet dance on the stage and decided to seat beside each other on a table with 4
other persons seated randomly. Find the number of ways they can seat together.

49. In a triangle find the side c if angle
C=100 deg, side b=20, and side a=15.

50. Find the coordinates of the centroid of the area
bounded by y=9-x2
and the coordinate axes in the first
quadrant.

practice trial run training to master 321.pptx

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