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Correl 1 > MATH OTD > Flashcards

MATH OTD Flashcards

1
Q

Time scaling is an operation performed on ___

A

Independent variable

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2
Q

The autocorrelation of x(n) = (2, 1) is

A

(2, 5, 2)

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3
Q

A system has a transfer function, G(s)=22/(s+22).
Find the rise time Tr.

A

182 ms

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4
Q

The poles of a transfer function are the values of the Laplace transform variable, s, that cause the transfer

A

Infinite

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5
Q

If the damping ratio is equal to 2, what kind of response is expected?

A

Overdamped

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6
Q

Given the transfer function G(s) = 121/(s^2 + 12s +121), find the percent overshoot.

A

12.94%

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7
Q

Given the transfer function G(s) = 121/(s^2 + 12s +121), what kind of response is expected?

A

Underdamped

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8
Q

Evaluate the Laplacian of R=(x^2) (y^2) (z^2)

A

2(y^2z^2)+2 (x^2z^2)+( x^2y^2)

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9
Q

Find the enclosed volume for the given closed surfaces: r=2 to 4, =30 deg to 50 deg, =20 deg to 60 deg.

A

2.91 units^3

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10
Q

Given A=(3x + y^2) a_x + (x-y^2) a_y, Find A

A

3-2y

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11
Q

Divergence and Curl of a vector field are ___ respectively.

A

Scalar & Vector

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12
Q

If x1(n)={1,2,3} and x2(n)={1,1,1}, then what is the convolution sequence of the given two signals?

A

{1,2,6,5,3}

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13
Q

What is the inverse z-transform of X(z)=1/(1 – 1.5z^1 + 0.5z^-2) if ROC is |z|>1?

A

(2 – 0.5^n)u(n)

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14
Q

Find m(k) at k=4 for the equation m(k)=e(k)-e(k-1) m(k-1) for k≥0 where e(k)=2 if k is even and e(k)=1 if k is odd. Find m(-1) are zero.

A

6

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15
Q

Find the convolution of f and g if f(t)=tu and g(t)=sin(t)u(t)

A

t-sin(t)

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16
Q

Suppose that you are watching people arriving at a doctor’s office and they are arriving at an average rate of 3 per hour. Were probability that from 12 pm – 5 pm there will be 2 full hours that are not necessarily continuous in which no one will arrive?

A

0.0498

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17
Q

In the ECE board examinations, the probability that an examinee will pass each subject is 0.8. what is the
probability examinee will pass at least two subjects out of
the three board subjects?

A

89.6%

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18
Q

Find the probability of getting between 3 and 6 heads inclusive in 10 tosses of a fair coin

A

0.7734

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19
Q

On the average, a certain computer part lasts ten years. The length of time the computer part lasts is exponentially distant is the probability that a computer part last more than 7 years?

A

0.4966

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20
Q

Vector and scalar quantities differ in that scalar only have

A

Magnitude

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21
Q

… the curl of the gradient of a scalar function U

A

0

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22
Q

The vector Rab extends from A(1,2,3) to B. If the length of Rab is 10 units and its direction is given by a = 0.60. Find the coordinates of B.

A

(7, 8.4, 7.8)

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23
Q

The dot product of two vectors is -3 while their cross product is <19, -6, -2>. What is the value of the tangent
… the vector?

A

-6.67

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24
Q

The three vertices of a triangle are located A(6, -1, 2), B(-2,3-4) and C(3,1,5). Find the area of the triangle.

A

42

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25
Q

The following measurements were recorded for the
drying time, in hours, of a certain brand of latex paint. 3.4,
2.5, 4.8, 2.9, 2.8, 3.3, 5.6, 3.7, 4.4, 4.0, 5.2, 3.0, 3.6, 2.8,
4.8

A

0.971

26
Q

Students at a private liberal arts college classified as being freshmen, sophomores, juniors, or seniors, and also according to whether they are male or female. Find the total number of possible classifications for the students of that college.

A

8

27
Q

Four married couples have bought 8 seats in the same row for a concert. In how many different ways can they be seated if all the men sit together to the right of all the women?

A

384

28
Q

How many three-digit numbers greater than 330 can be formed from the digits 0, 1, 2, 3, 4, 5, and 6, if each digit can be used only once?

A

105

29
Q

Suppose that in a senior college class of 500 students it is found that 210 smoke, 258 drink alcoholic beverages, 216 eat between meals, 122 smoke and drink alcoholic beverages, 83 eat between meals and drink alcoholic beverages, 97 smoke and eat between meals and 52 engage in all three of these bad health practices. If a member of this senior class is class is selected at random, find the probability that the student smokes but does not drink alcoholic beverages

A

0.176

30
Q

A pair of fair dice is tossed. Find the probability of getting a total of 8

A

5/36

31
Q

Interest centers around the life of an electronic
component. Suppose it is known that the probability that
the component survives for more than 6000 hours is 0.42.
Suppose also that the probability that the component
survives no longer than 4000 hours is 0.04. What is the
probability that the life of the component is less than or
equal to 6000 hours?

A

0.58

32
Q

The total number of hours, measured in units of 100
hours, that a family runs a vacuum cleaner over a period
of one year is a continuous random variable X that has
density function f(x)=x, for 0 < x < 1; for 1 ≤ x < 2; f(x)=x,
elsewhere. Find the probability that over a period of one
year, a family runs their vacuum cleaner less than 120
hours.

A

0.680

33
Q

Suppose that an antique jewelry dealer is interested
in purchasing a gold necklace for which the probabilities
are 0.22, 0.36, 0.28, and 0.14, respectively, that she will
be able to sell it, for a profit of $250, sell it for a profit of
$150, break even, or sell it for a loss of $150. What is her
expected profit?

A

$88

34
Q

Find the adjoint of matrix A, if A=[6 2; -1 3]

A

[3 -2; 1 6]

35
Q

Evaluate the sum of the infinite series: (3/7) – 2(3/7)^2 + 4(3/7)^3

A

3/13

36
Q

Find the 3rd term of Taylor series expansion of e^(2x) about x0=1.

A

(positive) (2e^2)(x-1)^2

37
Q

Find a_n of the Fourier series of the piecewise function f(x)=-4 where -5<x<0 and f(x)=4 where 0<x<5.

A

0

38
Q

Determine the radius of convegrence for the power series ∑((2^n)/n)(4x-8)^n from n=1 to infinity

A

1/8

39
Q

For a skew symmetric odd ordered matrix A of integers, which of the following will hold true?

A

det(A) = 0

40
Q

If the Laplace transform of the function f(t) is given by (s+3)/[(s+1)(s+2)], then f(0) is

A

1

41
Q

Find the conjugate of (i-i^2)^3

A

-2-2i

42
Q

Which of the followng equations is a variable of separable DE?

A

2ydx

43
Q

Find the general solutions of y’ysecx

A

c.y=c(secx+tanx)

44
Q

What is the differential equation of the family of parabolas having their vertices at the origin and their foci on the x-axis?

A

2xdy-ydx=0

45
Q

On a community of 200 residents, one started to
spread a rumor. If the rate at which the rumor spreads is
proportional to the number
of people who know the rumor x as well as the number of
people who do not know. Fifty people know about the
rumor after one day
How many people will have heard of the rumor after 2
days?

A

D.192

46
Q

Evaluate i^(0!) + i^(1!) + i^(2!)+… i^(20!).

A

a. 2i+15

47
Q

Evaluate (4+j3)^(2+j)

A

a.-12.74+j3.19

48
Q

For matrix A if AA^T=I, I is identity matrix then A is?

A

Idempotent matrix

49
Q

The radioactive isotope Indium-111 is often used for diagnosis and imaging in nuclear medicine. Its half-life is
2.8 days. What was the initial mass of the isotope before decay, if the mass in 2 weeks was 5g?

A

a. 160 g

50
Q

A 300-gal capacity tank contains a solution of 200 gal of water and 50 lb of salt. A solution containing 3 lb. of
salt per gal is allowed to flow into the tank at the rate of 4 gal/min. When does the tank start to overflow?

A

50 mins

51
Q

The population of a community is known to increase at a rate proportional to the number of people present at time t. If an initial
population has doubled in 5 years, how long will it take to quadruple?

A

b. 10

52
Q

In a murder investigation, a corpse was found by a detective at exactly 8 P.M. Being alert, the detective also measured the body temperature, and found it to be 70F. Two hours later, the detective measured the body temperature again and found it to be 60F. If the room temperature is 50F, and assuming that the body temperature of the person before death was 98.6 F, at what time did the murder

A

a. 5:30 pm

53
Q

Solve the given DE: y(2xy+1)dx-xdy=0

A

x(xy+1)=cy

54
Q

Determine the differential equation of the family of circles with center on the y-axis.

A

xy”-(y’)^3-y’=0

55
Q

Find the moment of inertia, with respect to x-axis of the area bounded by the parabola y^2=4x and the line

A

c. 2.13

56
Q

Locate the centroid of the plane area bounded by the equation y^2=4x, x=1 and x-axis on the first quadrant.

A

(3/5, 3/4)

57
Q

Find the area bounded by the lemniscate of Bernoulli
r^2=a^2cos20

A

a^2

58
Q

If f(x)=arctan(x), find the 99th derivative of f(x) evaluated x=0.

A

b. -(99!)

59
Q

Differentiate: yxln(1/x).

A

a. ln(1/x) - 1

60
Q

Find dy/dx of x = acos3t, y=asin3t

A

d. -x/y

61
Q

Find the integral of e^(2x)/(e^x + 1)

A

e^x-ln(e^x+1)+C

Correl 1 (5 decks)

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