Physics, Math, and Probability Quiz

Mathematics Problems

Parabolic Arch

• The width of a parabolic arch is 18m across the bottom and 12m at a vertical distance of 3m above the bottom.
• The height of the arch can be calculated.

Combinatorics

• The number of different bracelets that can be made with 9 differently colored beads is 362,880 or 40,320 or 20,160 or 181,440.

Distance Between Points

• The distance between the points (8, 7) and (3, y) is 13, and the value of y that is positive can be calculated.

Polynomial Roots

• The number of positive real roots in the polynomial 3x4 - x3 + 2x>> + x +1 =0 is 2 or 0 or 3 or 1 or 1 or 0.

Probability

• The probability that out of 15 reservations, more than 8 but less than 12 will be cancelled is 0.0084 or 0.000784 or 0.0784 or 0.784.
• The probability that a student chosen likes only Algebra is 1/10 or 1/12 or 2/11 or 1/5.

Area Bounded by Curve

• The area bounded by the curve y>> = 16x and x>> = 16y is 96.35 or 85.33 or 102.34 or 89.63.

Moment of Inertia

• The moment of inertia, with respect to the x-axis of the area bounded by the parabola y>>=4x and the line x=1, is 4.12 or 3.16 or 2.13 or 5.18.

Focus of Parabola

• The location of the focus of the parabola x>>+4y−4x−8=0 is (-2,-2) or (2,-2) or (-2,2) or (2,2).

Plane

• The plane x/2 + y/3 + z/6 =1 is part of the surface.

Cooling

• A steel ball cools from 110 deg C to 90 deg C in 8 minutes in a room temperature of 30 deg C.
• The temperature of the ball after 20 minutes can be calculated.

Graph

• The graph r = 2 sec θ is a circle or line or parabola or ellipse.

Clock

• The hands of a clock will be at right angles at 21.82 minutes or 40 minutes or 27.27 minutes or 43.63 minutes past 8 o'clock.

Volume of Solid

• The volume of the solid obtained by revolving the region bounded by y=x-x2 and about the x-axis is D/15 or D/45 or D/60 or D/30.

Difference of Squares

• The difference of the squares of two numbers is 157, and the square of their difference is equal to 25.
• The greater number can be calculated.

Water Funnel

• Water is running out of a conical funnel at the rate of 1 cu in/sec.
• The rate at which the water level is dropping when it is 2 in from the top can be calculated.

Circle

• The circumference of the circle x>> + y>> -12x + 10y + 15 = 0 is 24.6 or 42.6 or 62.4 or 64.2.

LCM

• The LCM of 9 and 15 is 15.385 or 9.375 or 12.635 or 10.325.

Conic

• The conic having an eccentricity equal to 1 is a circle or parabola or ellipse or hyperbola.

Fourth Proportional

• The fourth proportional to 7, 9, and 28 is 36 or 22 or 35 or 32.

Voice Recognition

• The probability that at least 3 out of 20 one-year-old children didn't recognize their mother's voice is 0.677 or 0.729 or 0.323 or 0.271.

Temperature

• The z-score for a temperature of 68 degrees with an average temperature of 67 degrees Fahrenheit and a standard deviation of 5 degrees can be calculated.

Probability of Boys

• The probability that a couple with 4 children will have at least one boy is 1/2 or 15/16 or 1/16 or 2/3.

Parallel Vectors

• The value of k such that A = 5i + 3j and B = 2i + kj are parallel is 6 or 6/5 or 3 or 3/5.

Suspension Bridge

• The cable of a suspension bridge hangs in the form of a parabola when the load is uniformly distributed horizontally.
• The distance between towers is 150m, the points of the cable on the towers are 22m above the roadway, and the lowest point on the cable is 7m above the roadway.