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Math Flashcards

1
Q

The perimeter of a parallelogram is given by ______ if A and B are the parallel sides

A

2(a+b)

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2
Q

Which of the following is the logarithm of a negative number?

A

The logarithm of a negative number is a complex number

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3
Q

Matrix multiplication is not commutative. True or false

A

True

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4
Q

The formula for the volume of a cone with a radius “r” & height “h” is π.r^2.h. True or false?

A

False
Volume of a cone = pie.r2h/3

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5
Q

What is the sum of 13 + 12j and 9 - 7j?

A

22 + 5j

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6
Q

In trigonometry, sec ° is equal to:
|5-2| - |6-9| =

A

Zero (0)

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7
Q

Which of the following Expressions is equivalent to cosine 2θ?

A

Cos2θ - Sin2θ

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8
Q

The question Ax + By + C = 0 represents which of the following?

A

Straight line

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9
Q

The eccentricity of the circle is 0. True or false

A

True

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10
Q

According to the law of cosine, which one of the following is correct?

A

C2 = a2+b2- 2ab cos C

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11
Q

A circular sector has a radius of 8 cm and an Arc Length of 14 cm. What is its area?

A

56 cm^2

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12
Q

Given f(X) has Maxima and Minima when X = Xn which of the following is the value of the derivative of, f’(x) when X = Xn?

A

All the above

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13
Q

What is the product of the complex number 4 + 3j and 7 - 3j?

A

37 + 9j

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14
Q

y’ + b.siny = 0 is an example of:

A

First-order non-linear homogeneous equation

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15
Q

What is the slope of the line AC?

A

Change in Y/ Change in X = Yc - a / Xc -Xa = 4-0/ 0-(3) = - 4/ 3

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16
Q

What is the slope - intercept form of the equation for the line 18x + 6y - 36 = 0?

A

y= -3x + 6

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17
Q

Considering the following equation of line y= 7x +2, which statement is accurate?

A

-2/7 is the x intercept of the line

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18
Q

What is the slope of a line that passes trough A(5,9) and b(1,2)?

A

7/4

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19
Q

Find the slope of the straight line the passes through (-2,3) and (-2,5)

A

undefined

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20
Q

The equation of a line with a slope of 12 and y intercept of 3 is:

A

12x - y +3 =0 ==> y= 2x +3

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21
Q

What is the slope of this line

A

5-0 / 0 -(-4) = 5/4

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22
Q

Considering the following equation of line y= 7x+2 , which statement is accurate?

A

-2/7 is the x intercept of the line

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23
Q

Line AB is perpendicular to line CD. If the equation f line AB is 4y + 8x, which one of these might be the equation of line CD?

A

y - 0.5x = 9

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24
Q

Line AB make a 50-degree angle, counter clockwise, with the y axis, and the y intercept is 3. What is the equation of this line?

A

y = - 0.84x + 3

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25
Q

Find the length of AB if (3,6) and B (4,8)

A

2.236

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26
Q

What is the y intercept of the line 9x -12x + 24 =0

A

9 (0) - 12y +24 = 0 ==> 2

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27
Q

If 2x -Ay = 2 and 4x + y + 6 = 0 are perpendicular, what is the value

A

8

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28
Q

A line going through A(6,9) and B (6,5)

A

Has an undefined slope and is parallel to the y axis

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29
Q

Line AB has a slope of 1/6, and line BC has a slope of -3/4. The lines intercept at the the point (5,3). What is most nearly the acute angle between the lines?

A

46.3

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30
Q

Find the equation of the line the passes through (2,5) with a slope of 6.

A

y = 6 = 6x -7

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31
Q

What is the area of this triangle? A(1,3) B(5,3) C(5,0)

A

AB = Xb - Xa = 5-1 = 4
BC = Yc - Ya = 0- 3 = -3

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32
Q

Consider line ax + by + c = 0. If the following relationship, 4x + 6y – 8 = 0, is satisfied, which of the following points will the line pass from?

A

B.
(1/2, 1)

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33
Q

Consider points A (0, 2), B (2.5, 0), and C (1, 1.2). If line segments are drawn between each pair of points, then the points could best be described as:

A. vertices of a right triangle.

B. vertices of an isosceles triangle.

C. vertices of an equilateral triangle.

D. are on a straight line.

A

Solution:
The slope of line AB is: D

M subscript A B end subscript equals fraction numerator Y b minus Y a over denominator X b minus X a end fraction equals fraction numerator 0 minus 2 over denominator 2.5 minus 0 end fraction equals negative 0.8

The slope of line BC is:

M subscript B C end subscript equals fraction numerator Y c minus Y b over denominator X c minus X b end fraction equals fraction numerator 1.2 minus 0 over denominator 1 minus 2.5 end fraction equals negative 0.8

The slope of line CA is:

M subscript C A end subscript equals fraction numerator Y c minus Y a over denominator X c minus X a end fraction equals fraction numerator 1.2 minus 2 over denominator 1 minus 0 end fraction equals negative 0.8

Additionally, if we consider y=mx+b we can also see point A is our y-intercept, or b value. Thus the line with the equation y=(-0.8)x+2 should describe the line connecting the two points. Verifying with the given points, we see:

Point A –> 2=(-0.8*0)+2, thus 2=2.

Point B –> 0=(-0.8*2.5)+2, thus 0=0.

Point C –> 1.2=(-0.8*1)+2, thus 1.2=1.2.

Therefore, A, B, and C must be on a straight line since the lines have the same slope and connecting the segments together would produce a straight line.

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34
Q

In the following figure, which line has a slope of zero?

A

Correct Option: B Solution:

Definition:

The general form of the equation of a line is y = mx + b.

When m = 0, y = b.

Line 2 matches this general form of the equation of a line.

The general form of the equation of line 1 is x = c; in this equation, m is unknown.

Slope space of space zero space means space m space equals space fraction numerator increment y over denominator increment x end fraction space equals space 0 space left parenthesis only space numerator space can space be space 0 right parenthesis
That space means space any space line space where space increment y space equals space 0 space will space be space the space answer.
Therefore comma space option space straight B space is space correct.

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35
Q

What are the two roots of:
x^2 + 4x +2 =0

A. 0.4, 2.5

B. 0.6, 4.5

C. 4.0, .145

D. -0.5858, -3.4142

A

Correct Option: D

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36
Q

Find the root of this equation:
x^3 + 3x^2 - 5x +3 =0

A. –4.3

B. 2.7

C. 3.3

D. 4.12

A

Your Option: –
Correct Option: A
Solution:
Analytically finding the roots of a polynomial of order beyond two is difficult. In a question like this, the fastest approach is to use a calculator. For instance, on a Casio FX-115ES calculator, do the following:

1) MODE
2) 5 – FOR EQN
3) 4 – FORa x cubed b x squared plus c x plus d equals 0
4) INPUT a = 1, b = 3, c = 5 and d = 3 (followed by =)
5) PRESS = FOR x1, x2, and x3

Alternatively, one can plug all values into the polynomial and determine which one brings it to 0. In this case, for example:

(4.12)3+3(4.12)2−5(4.12)+3=69.93+50.92−20.6+3=103.25 (−4.3)3+3(−4.3)2−5(−4.3)+3=−79.51+55.47+21.5+3=0.46 (3.3)3+3(3.3)2−5(3.3)+3=35.94+32.67−16.5+3=55.11 (2.7)3+3(2.7)2−5(2.7)+3=19.68+21.87−13.5+3=25.05
0.46 is the closest to zero, and not zero just because of rounding.
Therefore, -4.3 is the root of the equation.

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37
Q

What does this equation represent?

B(y-5)^2 = A(x-h)

A. Ellipse

B. Circle

C. Hyperbola

D. Parabola

A

Correct Option: D

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38
Q

What does this equation represent? Assuming A, B, C are constant, positive non-zero numbers.

A(x-h)^2 - B(y-p)^2 =C

A. Ellipse

B. Circle

C. Hyperbola

D. Parabola

A

Correct Option: C

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39
Q

Find the vertex of this parabola:

x^2 + 8x - 4 y +12 = 0

A. V(1,4)

B. V(4,1)

C. V(-1,-4)

D. V(-4,-1)

A

Correct Option: D

Solution:
Step one:

Rewrite the equation in vertex form by moving all terms not containing y to the right side of the equation:

y = x^2/4 + 2x + 3

Vertex is at V left parenthesis h comma k right parenthesis

The vertex is at point V (-4, -1)

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40
Q

Find the eccentricity of this parabola:
y^2 + 8y +

y squared plus 8 y plus 4 x plus 12 equals 0

A. e=1

B. e=0

C. e=0.76

D. e=1.87

A

Correct Option: A
Solution:
The eccentricity of a parabola is always 1.

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41
Q

Which is the equation of an ellipse that is centered in (5,6) and passes through A (3,2)?

A. x^2 + 5y^2 =3
B. (x-5)^2 + 4(y-6)^2 = 25
C. 4(x-5)^2 + (y-6)^2 =27
D. (x -5)^2 + 2(y-6)^2 =36

A

Correct Option: D
Solution:
Standard Ellipse Equation:

m1(x-h)^2 + m2(y-k)^3 = m3

where m1, m2,and m3 are constants.

the center is (h,k), using center coordinates (5,6):

m 1 (x-5)^2 + m2(y-6)^2 =m3

Substitute x = 3 and y = 2 into the three answer options above that satisfy the above format. If the equation satisfies, it is correct. Arriving at Option D:

(3-5)^2 + 2(2-6)^2 = 36

36 space equals space 36

Options B, C, and D agree with the ellipse center coordinates.

Only option D works if the coordinates of A (3, 2) are substituted into the ellipse equation

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42
Q

AB is known to be the diameter of a circle with the following coordinates; A(3,0) and B(-1,-4). What is the equation of this circle?
A. (x-1)^2 + (y+2)^2
B. (x+1)^2 + (y+2)^2 =16
C. (x - 1/2)^2 + (y+1)^2 = 4
D. (x-1)^2 + (y+2)^2 =16

A

Correct Option: A

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43
Q

What do these equations represent?

Equation 1: 9x = 8sin(t) + 18

Equation 2: 6y = 10cos(t) - 12

A. Ellipse

B. Circle

C. Hyperbola

D. No curve

A

Correct Option: A

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44
Q

What are the coordinates for the vertex of a parabola with a directrix at y = 2 and a focus at F(4, 8)?

A. V(3, 5)

B. V(4, 3)

C. V(4, 5)

D. V(-4, 6)

A

Correct Option: C
Solution:
Since the directrix is at y = 2, the parabola opens up or down.

This means that the x coordinate of the vertex and the focus is the same, eliminating answers a and d.

The y coordinate of the vertex can be found using y = (2 + 8)/2 = 5. The vertex is at V(4,5).

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45
Q

Find the eccentricity of the following ellipse:

(x-7)^2 / 29 + (y+6)^2/4 =1

A. 0.93

B. 0.7

C. 0.8

D. 0.4

A

Correct Option: A

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46
Q

Find an ellipse with foci at (2, 0) and (-2, 0).

A. x^2/9 + y^2/5 =1

B. x^2/4 + y^2/9 =1

C. x^2/43 + y^2/8 =1

D. x^2/25 + y^2/16 =1

A

Correct Option: A

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47
Q

Which statement is correct about the following parabola?

X+ 4 - y^2 + 6y - 9 = 0

A. This parabola opens up.

B. This parabola opens down.

C. This parabola opens to the right.

D. This parabola opens to the left.

A

Correct Option: C

48
Q

Which curve do the following parametric equations represent?

x = cos t(t)y = sin t(t) < t < π/2

A. A circle

B. A semi-circle

C. ¼ of a circle in the first quadrant

D. ¼ of a circle in the third quadrant

A

Correct Option: C

49
Q

Cos^4(A) -Sin^4(A) =?

A. 1-3cos^2 (A)

B. cos(2A)

C. Sin(2A)

D. 1-2cos^2(A)

A

Correct Option: B

50
Q

If A = (sec(a)cot(a))^2 - (cos(a)csc(a))^2

A. 0

B. 1

C. 2

D. Cos(2a)

A

Correct Option: B

51
Q

If we use the triangle below and the values sin A = a/10 and b = 5, what is the value of B?

A. B = 45

B. B = 60

C. B = 30

D. B = 32.7

A

Correct Option: C

52
Q

Represent Cos left(x) as a series using the Taylor series around x = 0 is:
A. Cos(x) = 1 - x^2/2! +x^4/4! + …
B. Cos(x) = 1 + x^2/2! + x^4/4! + …
C. Cos(x) = 1 - x^3/3! + x^5/5! + …
D. Cos(x) = 1 - x^2/2! + x^6/ 4! + …

A

Correct Option: A

53
Q

For the following function:

y = - 2 x^2 + 4x + 6

A. the minimum of this curve is 1.

B. the minimum of this curve is 8.

C. the curve has no minimum

D. none of the above.

A

Correct Option: C

54
Q

Find the equation of a curve that passes through A(0,3), with the slope of the tangent to the curve at any arbitrary point following this function:

F(x) = 3x^2 +5x +e^x

A

Y= x^3+ (5/2)x^2 + e^x +2

55
Q

Find dy/dx if :
x= 2t^3 - 6 t and
y= 3t^2 + 6t

A

C. 1/t-2

56
Q

Find the area bounded by y = x^2 and x = y^2 and located in the first quadrant.

A. 0.78

B. 0.33

C. 1.54

D. 0.35

A

B. 0.33

57
Q

The equation of a line perpendicular to
y = 2x^2 -6 at point (1, -1/4) is:

A

4 y + x = 0

58
Q

Find lim x -> ∞ 3x^3 + 2x^2 +5 / s5x^3 + 7x^2 + 6

A

Correct Option: B = 3/5

59
Q

Find the volume of a sphere in cubic inches having an area of 6 ft^2.

A.14.5 ft3

B. 2,395.1 in^3

C. 2,146.5 in^3

D. 12.5 ft^3

A

B. V= 2,395.1 in^3

60
Q

In the regular polygon shown, r = 5in.

Find the area of the regular polygon.

A. 95in^2

B. 86.6 in^2

C. 63.4in^2

D. 72.6in^2

A

Correct Option: B

61
Q

A perfect hexagon of side a is inscribed in a circle of radius (R) 6. Find a.

A. 6

B. 7

C. 8

D. 9

A

Correct Option: A

62
Q

What is the solution to this equation?

Y^2 + 5Y + 6 = 0

A. 3,2

B. 3,-2

C. -3,2

D. -3,-2

A

Correct Option: D

63
Q

Any mathematical expression that contains a first up to nth order of derivatives or differentials (y’, y”, …) of a continuous function with only one independent variable is called:

A. a difference equation.

B. a differential equation.

C. a partial differential equation.

D. a polynomial equation.

A

Correct Option: B

64
Q

What is the solution of the following differential equation, as t –>∞

Y ‘’+ 4 Y’ +4Y = 20

A. Y = 0
B. Y = e^-(2t)
C. Y = te^-(2t)
D. Y = 5

A

Correct Option: D

65
Q

The motion of a particle is given as:
d^2x/dt^2 + 9 x = 0

If the particle starts from x = 1 at t = 0 with a velocity of 3, what is the equation of motion of this particle?

A

cos(3t) + sin (3t)

66
Q

Find the following integral using Simpson’s rule.

a=2 , b =8 , f(x) = x^2 + 2x + 4 , n=2.
f(x) a –>b dx

A. 288

B. 192

C. 234

D. 252

A

Correct Option: D

67
Q

Find the following integral using Simpson’s rule (n = 2).

A

Lim 0 –> 0.6 (cos(x) + x)

A. 0.78

B. 0.92

C. 0.834

D. 0.624

68
Q

What is the area of the region bounded by the curve y = sin x and the x axis on the interval between x = π/2 and x = 2π?

A

A.1

B. 2

C. 3

D. 4

69
Q

What is the solution of this equation?
Y’’ + 6Y = cos(x)

A

Correct Option: B = 1/5 cos(x)

70
Q

How many inflection points does y = cos(x) have between 0 and 2π?
A. 1

B. 2

C. 3

D. 4

A

Correct Option: B

71
Q

A particle is moving in a path that is defined by the following equation:
Y= 5X^4 -X^2 -6
It is known that the speed of a particle in a horizontal direction is 3 m/s when x = 1 m. What is the speed at the Y direction at this moment?

A. 24 m/s

B. 0

C. 12 m/s

D. 18 m/s

A

Correct Option: A

72
Q

Find the slope of y= x^2 -4x -5 when it intersects the x-axis at the border of the third and second quadrants.

A. 6

B. -6

C. 7

D. -7

A

Correct Option: B

73
Q

In the parallelogram shown, a = 6 space in, b = 8 space in and θ = 30.

Find the area of the parallelogram.

A. 24 space in^2

B. 26 space in^2

C. 16 space in^2

D. 18.8 space in^2

A

Correct Option: A

74
Q

Find the area of the orange portion. Assume r = 6 cm , space beta = 60 deg , and d =1 space cm (r is the radius of the circle)

A. 15.6

B. 18.7

C. 12.6

D. 16.9

A

Correct Option: A

75
Q

If y= f(x) then the following differential equation
AY’’ + Bf(x)Y’ + C = G(x) is:

A

A. linear, first order, and homogeneous.

B. a second-order, non-linear differential equation.

C. homogeneous, linear, and second order.

D. nonhomogeneous, linear, and second order.

76
Q

A particular radioactive material decays 4% every year. How long will it take the material to decay to 50% of its original weight?

A

A. 15 years

B. 17 years

C. 12 years

D. 19 years

77
Q

What is the solution to the following differential equation?
y” + 3y’ + 2y = 1

A

Correct Option: D

78
Q

What is the acute angle between line AB, y = 2x + 3, and line BC, y = 7x – 5?

A. 11.87 degrees

B. 18.43 degrees

C. 36.17 degrees

D. 26.87 degrees

A

Correct Option: B

79
Q

What does this equation represent?

A(x-h)^2 -B(y-p)^2 = C

A. Ellipse

B. Circle

C. Hyperbola

D. Parabola

A

Correct Option: C

80
Q

Find the focus of this parabola:

y^2 + 8y - 4x + 12 = 0

A. F (0, -4)
B. F(-2,1)
C. F(4,0)
D. F(-4,0)

A

Correct Option: A

81
Q

Find the eccentricity of this circle:
y^2 + 8y + x^2 +4x +12 = 0

A. e =1

B. e = 0

C. e = 0.76

D. e = 1.87

A

Correct Option: B

82
Q

A plane makes a 45-degree angle with the y-axis when intersecting a 30-degree conic section. Assuming the resulting conic section is an ellipse, what is the eccentricity of this conic section?

A. 0.816

B. 0.65

C. 0.45

D. 0.33

A

Correct Option: A

83
Q

Find one of the points of intersection.

4x^2 +y^2 -48x - 2y + 129 = 0

x^2+y^2-2x-2y-7 = 0

A. (4,3)
B. (5,2)
C. (5, 8)
D. (4,1)

A

Correct Option: D

84
Q

Find a hyperbola with foci at (0,5) and (0,-5) and vertices at (0,4) and (0,-4)

A

y^2/16 - x^2/9 =1

85
Q

Find d.
log (38x10^d) =log(3.8)

A. d = 6

B. d = 5

C. d = 9

D. d = -1

A

Correct Option: D

86
Q

[A], [B] and [C] represent three different matrices. Which statement is accurate?

A. [ A ][ B ]=[ B ][ A ]
B. [B ]+[C]=[ B ][ A ]+[ A ][C]
C. ([A]+[B])[C]+[B][C] = ([A+2 [B])[C]
D. [A ][ C ]+[ B ][ C ]= C

A

Correct Option: C

Solution:
In matrix multiplication, commutative law does not apply; A, B, and D are not accurate.

87
Q

The center of a circle is located at (3,4) and is tangent to the x axis. What is the equation of this circle?

A. x^2+ y^2 -6x -8y +9 = 0
B. x^2 + y^2 -10y +9 = 0
C. x^2 + y^2 +4x -10y + 50 = 0
D. x^2+ y^2+ 12x -16y + 45 =0

A

Correct Option: A

88
Q

Find the coordinates of the foci of the following hyperbola:

36y^2 - 64x^2 = 2,304

A. (+/- 5,0)
B. (0,+/- 10)
C. (0, +/- 2)
D.(+/- 3, 0)

A

Correct Option: B

89
Q

Given the following directed graph, how many edges does initial vertex 4 have?

A. 6

B. 2

C. 3

D. 4

A

Correct Option: C

90
Q

A university receives books from three different companies. This year, it received a total of 130 new books out of which 60 are from company A, 45 are from company B, and 25 are from company C. Three books are selected from the 130 new ones. Find the probability that all three books came from company C

A. 2,300/357,760

B. 230/3,577

C. 25/123

D. 230/35,678

A

Correct Option: A

91
Q

Two cards are picked from a standard 52-card deck. What is the probability that both cards are kings without replacement?

A. 0.00045

B. 0.0045

C. 0.0023

D. 0.007

A

Correct Option: B

92
Q

From five different companies named A, B, C, D, and E , three are selected. If the order of selection is not important, how many different ways can the companies be selected?

A. 10

B. 12

C. 15

D. 18

A

Correct Option: A

93
Q

If we have 16 different cereal boxes, how many ways can five boxes be lined up on a store shelf when the order is not important?

A. 4,368

B. 5,896

C. 8,547

D. 9,512

A

Correct Option: A

94
Q

In a fleet of 15 cars at a local dealership, ten were to be allocated as loaner cars, three for service department as customers’ pickup vehicles, and two as backup. How many ways this be done?

A

A. 30,003

B. 30,030

C. 30,300

D. 33,000

95
Q

In a class of 25 students, how many ways can a grade of one A, one B and four Cs be given to six students who turn in an assignment for extra credit?

A. 5,131,000

B. 5,113,000

C. 5,133,000

D. 5,313,000

A

Correct Option: D

96
Q

How many ways are there to choose a committee of ten members from a group of 20 people? Mike or John must be selected as a committee member, but they cannot both be chosen into the committee.

A. 97,240

B. 97,420

C. 97,042

D. 97,024

A

Correct Option: A

97
Q

You have passes allowing you to attend four games at an arena. In how many possible ways can you go to three arena football games and one other game when there are five football gamess, three soccer games, and seven volleyball games scheduled?

A

A. 10

B. 100

C. 1,000

D. 10,000

98
Q

During club elections, ten people ran for three positions. Club presidency will be awarded to the person with the most votes, treasury to the second most, and outside relations position will be awarded for the third most votes. How many outcomes can this voting session have?

A

A. 420

B. 520

C. 620

D. 720

99
Q

How many different ways can the letters of the word OPTIONS be arranged?

A. 2,215

B. 2,565

C. 5,250

D. 2,520

A

Correct Option: D

100
Q

A group of 50 students took two exams: math and physics. Each student took both exams. It is known that there are 40 and 31 students who passed the math and physics exams, respectively, and four students who failed both exams. How many students passed both exams?

A. 35

B. 25

C. 15

D. 28

A

Correct Option: B

101
Q

A group of 50 students took two exams: math and physics. Each student took both exams. It is known that four students failed both exams. How many students passed at least one exam?

A. 46

B. 4

C. 32

D. 28

A

Correct Option: A

102
Q

Alex found ten counters in a bag: three are red, two are blue, and five are green. What is the probability that he does not pick a red counter?

A. 6/10

B. 5/10

C. 7/10

D. 8/10

A

Correct Option: C

103
Q

H is the event of getting at least two tails in tossing a fair coin ten times. If Z is the event that the first tossing would land a head, what is P(H|Z)?

A. 0.980469

B. 0.689001

C. 0.290001

D. 0.798801

A

Correct Option: A

104
Q

Only 1 in 5,000 people has a disease for which a particular diagnostic test is available. When someone has the disease, the test can detect it with an accuracy of 98%, but when someone does not have the disease, the test will still give a positive result 1% of the time. If a randomly chosen person tests positive, what is the probability that he/she actually has the disease?

A. 0.02

B. 0.01

C. 0.42

D. 0.98

A

Correct Option: A

105
Q

A group of students is taking two exams: math and physics. It is known that each student participates in at least one exam, and there are 18 students in the math exam, 22 students in the physics exam, and three students who are in both exams. How many students total are in the group?

A. 43

B. 37

C. 40

D. 22

A

Correct Option: B

106
Q

If we have 16 different cereal boxes, how many ways can five boxes be lined up on a store shelf when the order is important?

A. 524,180

B. 521,548

C. 524,160

D. 521,465

A

Correct Option: C

107
Q

In how many ways can five different necklaces be arranged on a display?

A. 120

B. 68

C. 55

D. 5

A

Correct Option: A

108
Q

Eight-card hands are randomly picked from a standard 52-card deck. How many of these will have three clubs and five spades?

A. 368,802

B. 368,082

C. 368,028

D. 386,082

A

Correct Option: B

109
Q

There are nine marbles of different colors on a table. In how many combinations can you grab two at a time?

A. 36

B. 46

C. 56

D. 66

A

Correct Option: A

110
Q

One card is randomly pulled from a standard 52-card deck. What is the probability that the selected card is a king?

A. 0.08

B. 0.25

C. 0.16

D. 0.02

A

Correct Option: A

111
Q

There are five marbles in a bag: four red and one blue. If one marble is randomly chosen from the bag, what is the probability that the picked marble is red?

A. 0.4

B. 0.1

C. 0.8

D. 0.67

A

Correct Option: C

112
Q

A box contains eight white balls and four red balls. An experiment consists of drawing two balls from the box without replacement. Find the probability that both balls drawn are white.

A. 0.424

B. 0.45

C. 0.37

D. 0.66

A

Correct Option: A

113
Q

What is square root of -25

A. 5

B. -5

C. 5i

D. cannot be found

A

Correct Option: C

114
Q

Z = 2 + 3i is rotated 90-degree CCW about the origin of its coordinate. The complex number obtained after this transformation is:

A. 2 - 3i

B. -3 + 2i

C.- 2 - 3i

D. 2 + 3i

A

Correct Option: B
2 + 3i is in the first quadrant, when it is rotated 90, it will be in the second quadrant. That means z = -3 + 2i.

115
Q

Find B:

B = (-3+2I)^6/1000

A. 3i + 4

B. 2.4 + 1.3i

C. 2.035 + 0.83i

D. 1.54 + 4.24i

A

Correct Option: C

116
Q

5/(2+i) = ?

A

A. 2-i

B. 2+ I

C. 2/5 - i/5

D. 2/5+ i/5

FEexam (10 decks)

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