neither divergence free nor irrotational

divergence free, but not irrotational

irrotational, but not divergence free

divergence free and irrotational

neither divergence free nor irrotational

Let X be a normal random variable with mean 1 and variance 4. The probability P{X < 0} is

greater than 0.5 and less than 1.0

greater then a zero and less than 0.5

greater than 0.5 and less than 1.0

If a square matrix A is real and symmetric, then the eigenvalues

are always real and non-negative

occur in complex conjugate pairs

The eigen values of a symmetric matrix are all

complex with non-zero positive imaginary part

complex with non-zero negative imaginary part

cannot be determined without specifying the path

Stokes theorem connects

a surface integral and a volume integral

a line integral and a surface integral

a surface integral and a volume integral

a line integral and a volume integral

gradient of a function and its surface integral

Which one of the following describes the relationship among the three vectors, + &jcirc; + k , 2 + 3&jcirc; + k and 5 + 6&jcirc; + 4k ?

The vectors are linearly independent

The vectors are mutually perpendicular

The vectors are linearly dependent

The vectors are linearly independent

A unique solution of x = 1, y = 1 and z = 1

only the two solutions of (x = 1, y = 1, z = 1) and (x = 2, y = 1, z = 0)

218 + Mcqs in Engineering Mathematics Miscellaneous in Engineering Mathematics Page 4 McqOptions

151.	The angle between two unit-magnitude coplanar vectors P(0.866, 0.500, 0) and Q(0.259, 0.966, 0) will be
A.	0
B.	30
C.	45
D.	60
Answer» D. 60

Discussion

152.	The vector field
A.	divergence free, but not irrotational
B.	irrotational, but not divergence free
C.	divergence free and irrotational
D.	neither divergence free nor irrotational
Answer» D. neither divergence free nor irrotational

Discussion

153.

If y = f(x) is the solution of d y = 0
dx

A.

25

B.

35

C.

28

D.

32

Answer» C. 28

Discussion

154.	The set of equations
A.	4
B.	3
C.	4
D.	3
Answer» D. 3

Discussion

155.	A group consists of equal number of men and women. Of this group 20% of the men and 50% of the women are unemployed. If a person is selected at random from this group, the probability of the selected person being employed is _______ .
A.	95%
B.	65%
C.	75%
D.	61%
Answer» C. 75%

Discussion

156.	The value of [(3x - 8y )dx (4y - 6xy) dy] (where C is the boundary of the region boundary by x = 0, y = 0 and x + y = 1) is ________.
A.	1.524
B.	3.66
C.	1.666
D.	2.65
Answer» C. 1.666

Discussion

157.

Finding the solution of d y + 16y = 0 for y(x) with the two boundary
dx

A.

no solution

B.

exactly two solutions

C.

exactly one solution

D.

infinitely many solutions

Answer» B. exactly two solutions

Discussion

158.	The number of accidents occurring in a plant in a month follows Poisson distribution with mean as 5.2. The probability of occurrence of less than 2 accidents in the plant during a randomly selected month is
A.	0.029
B.	0.034
C.	0.039
D.	0.044
Answer» C. 0.039

Discussion

159.	Let X be a normal random variable with mean 1 and variance 4. The probability P{X < 0} is
A.	0.5
B.	greater then a zero and less than 0.5
C.	greater than 0.5 and less than 1.0
D.	1.0
Answer» C. greater than 0.5 and less than 1.0

Discussion

160.	A six-face fair dice is rolled a large number of times. The mean value of the outcomes is ___.
A.	3.9
B.	3.6
C.	3.5
D.	3.4
Answer» D. 3.4

Discussion

161.	A six-faced fair dice is rolled five times. The probability (in%) of obtaining "ONE" at least four times is
A.	33.3
B.	3.33
C.	0.33
D.	0.0033
Answer» D. 0.0033

Discussion

162.	Two coins are tossed simultaneously. The probability (upto two decimal points accuracy) of getting at least one head is ___.
A.	1.25
B.	1.75
C.	0.75
D.	1
Answer» D. 1

Discussion

163.	The value of the following definite integral is _____ (round off to there decimal places).
A.	2.15
B.	3.12
C.	2.097
D.	2.01
Answer» D. 2.01

Discussion

164.

Given a vector U = 1 (-y + x &jcirc; + z k)
3

A.

- /2

B.

C.

/2

D.

/3

Answer» D. /3

Discussion

165.	If a square matrix A is real and symmetric, then the eigenvalues
A.	are always real
B.	are always real and positive
C.	are always real and non-negative
D.	occur in complex conjugate pairs
Answer» B. are always real and positive

Discussion

166.	The area enclosed between the straight line y = x and the parabola y = x in the x y plane is
A.	1/6
B.	1/4
C.	1/3
D.	1/2
Answer» B. 1/4

Discussion

167.	The area enclosed between the curves y = 4x and x = 4y is
A.	16/3
B.	8
C.	32/3
D.	16
Answer» B. 8

Discussion

168.	Eigenvalues of a real symmetric matrix are always
A.	positive
B.	negative
C.	real
D.	complex
Answer» D. complex

Discussion

169.	A nationalized bank has found that the daily balance available in its savings accounts follows a normal distribution with a mean of Rs. 500 and a standard deviation of Rs. 50. The percentage of savings account holders, who maintain an average daily balance more than Rs. 500 is ___.
A.	0.90
B.	0.60
C.	0.40
D.	0.50
Answer» E.

Discussion

170.	A box contains 2 washers, 3 nuts and 4 bolts. Items are drawn from the box at random one at a time without replacement. The probability of drawing 2 washers first followed by 3 nuts and subsequently the 4 bolts is
A.	<table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>2</center></td></tr><td align="center">315</td></table>
B.
C.	<table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td></tr><td align="center">630</td></table>
D.	<table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td></tr><td align="center">1260</td></table>
E.	<table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td></tr><td align="center">2520</td></table>
Answer» D. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td></tr><td align="center">1260</td></table>

Discussion

171.	The function f(t) satisfies the differential equation (d f / dt ) + f = 0 and the auxilliary conditions, f(0) = 0, (df / dt) (o) = 4. The Laplace transform of f(t) is given by
A.	<table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>2</center></td><td rowspan="2"></td></tr><td align="center">s + 1</td></table>
B.	<table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>4</center></td><td rowspan="2"></td></tr><td align="center">s + 1</td></table>
C.	<table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>4</center></td><td rowspan="2"></td></tr><td align="center">s + 1</td></table>
D.	<table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>2</center></td><td rowspan="2"></td></tr><td align="center">s + 1</td></table>
Answer» D. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>2</center></td><td rowspan="2"></td></tr><td align="center">s + 1</td></table>

Discussion

172.

Given two complex numbers Z₁ = 5 + (5 3)i and Z₂ = 2 + 2i the arguement of Z₁ in degree is
3 Z₂

A.

0

B.

30

C.

60

D.

90

Answer» B. 30

Discussion

173.	A box contains 5 black and 5 red balls. Two balls are randomly picked one after another from the box, without replacement. The probability for both balls being red is
A.	<table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td></tr><td align="center">90</td></table>
B.	<table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td></tr><td align="center">2</td></table>
C.	<table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>19</center></td></tr><td align="center">90</td></table>
D.	<table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>2</center></td></tr><td align="center">9</td></table>
Answer» E.

Discussion

174.	The product of two complex numbers (1+ i) and 2 5i is
A.	7 3i
B.	3 4i
C.	3 4i
D.	7 + 3i
Answer» B. 3 4i

Discussion

175.	Curl of vector V(x, y, z) = 2x2i + 3z2j + y3k at x = y = z = 1 is
A.	3i
B.	3i
C.	3i 4j
D.	3i 6k
Answer» C. 3i 4j

Discussion

176.	If (x, y) and (x, y) are functions with continuous second derivatives, then (x, y) + i (x, y)
A.	<table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> </center></td><td rowspan="2">= -<br></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> </center></td><td rowspan="2">,<br></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> <center><td rowspan="2">= <br></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> <center><td rowspan="2"><br></td></center></center></td></center></center></td></tr><td align="center"> x</td><td align="center"> x</td><td align="center"> y</td><td align="center"> y</td></table>
B.	<table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> </center></td><td rowspan="2">= -<br></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> </center></td><td rowspan="2">,<br></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> <center><td rowspan="2">= <br></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> <center><td rowspan="2"><br></td></center></center></td></center></center></td></tr><td align="center"> y</td><td align="center"> x</td><td align="center"> x</td><td align="center"> y</td></table>
C.	<table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> </center></td><td rowspan="2">= -<br></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> </center></td><td rowspan="2">,<br></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> <center><td rowspan="2">= <br></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> <center><td rowspan="2">= 1<br></td></center></center></td></center></center></td></tr><td align="center"> x </td><td align="center"> y </td><td align="center"> x </td><td align="center"> y </td></table>
D.	<table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> </center></td><td rowspan="2">= -<br></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> </center></td><td rowspan="2">,<br></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> <center><td rowspan="2">= <br></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> <center><td rowspan="2">= 0<br></td></center></center></td></center></center></td></tr><td align="center"> x </td><td align="center"> y </td><td align="center"> x </td><td align="center"> y </td></table>
Answer» C. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> </center></td><td rowspan="2">= -<br></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> </center></td><td rowspan="2">,<br></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> <center><td rowspan="2">= <br></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> <center><td rowspan="2">= 1<br></td></center></center></td></center></center></td></tr><td align="center"> x </td><td align="center"> y </td><td align="center"> x </td><td align="center"> y </td></table>

Discussion

177.	If three coins are tossed simultaneously, the probability of getting at least one head is
A.	<table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td></tr><td align="center">8</td></table>
B.	<table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>3</center></td></tr><td align="center">8</td></table>
C.	<table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td></tr><td align="center">2</td></table>
D.	<table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>7</center></td></tr><td align="center">8</td></table>
Answer» E.

Discussion

178.	Divergence of the vector field
A.	0
B.	3
C.	5
D.	6
Answer» D. 6

Discussion

179.	The argument of the complex number {(1 + i) / (1 - i)} , where i =
A.	-
B.	- / 2
C.	/ 2
D.
Answer» D.

Discussion

180.	The eigen values of a symmetric matrix are all
A.	complex with non-zero positive imaginary part
B.	complex with non-zero negative imaginary part
C.	real
D.	pure imaginary
Answer» D. pure imaginary

Discussion

181.	The product of eigenvalues of the matrix P is
A.	6
B.	2
C.	6
D.	2
Answer» C. 6

Discussion

182.	The number of linearly independent eigenvectors of matrix
A.	= 2, 2, 3
B.	= 2, 3, 3
C.	= 2, 3, 2
D.	= 3, 2, 3
Answer» B. = 2, 3, 3

Discussion

183.	The condition for which the eigenvalues of the
A.	<table><tr><td rowspan="2">k ></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td><td rowspan="2"></td></tr><td align="center">2</td></table>
B.	k > - 2
C.	k > 0
D.	<table><tr><td rowspan="2">k < -</td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td><td rowspan="2"></td></tr><td align="center">2</td></table>
Answer» B. k > - 2

Discussion

184.	The divergence of the vector field (x - y) + (y - x)ĵ + (x + y + z)k is
A.	0
B.	1
C.	2
D.	3
Answer» E.

Discussion

185.	The area of a triangle formed by the tips of vectors
A.	<table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td><td rowspan="2">(<span style="text-decoration:overline;">a</span> - <span style="text-decoration:overline;">b</span>).(<span style="text-decoration:overline;">a</span> - <span style="text-decoration:overline;">c</span>)</td></tr><td align="center">2</td></table>
B.	<table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td><td rowspan="2">\|(<span style="text-decoration:overline;">a</span> - <span style="text-decoration:overline;">b</span>) (<span style="text-decoration:overline;">a</span> - <span style="text-decoration:overline;">c</span>)\|</td></tr><td align="center">2</td></table>
C.	<table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td><td rowspan="2">\|<span style="text-decoration:overline;">a</span> <span style="text-decoration:overline;">b</span> <span style="text-decoration:overline;">c</span> \|</td></tr><td align="center">2</td></table>
D.	<table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td><td rowspan="2">(<span style="text-decoration:overline;">a</span> <span style="text-decoration:overline;">b</span>).<span style="text-decoration:overline;">c</span></td></tr><td align="center">2</td></table>
Answer» C. <table><tr><td rowspan="2"></td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td><td rowspan="2">\|<span style="text-decoration:overline;">a</span> <span style="text-decoration:overline;">b</span> <span style="text-decoration:overline;">c</span> \|</td></tr><td align="center">2</td></table>

Discussion

186.	The line integral
A.	is 1
B.	is zero
C.	is 1
D.	cannot be determined without specifying the path
Answer» B. is zero

Discussion

187.	Stokes theorem connects
A.	a line integral and a surface integral
B.	a surface integral and a volume integral
C.	a line integral and a volume integral
D.	gradient of a function and its surface integral
Answer» B. a surface integral and a volume integral

Discussion

188.	The solution to the system of equations is
A.	6, 2
B.	6, 2
C.	6, 2
D.	6, 2
Answer» E.

Discussion

189.	From a pack of regular playing cards, two cards are drawn at random. What is the probability that both cards will be Kings, if first card in NOT replaced?
A.	<table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td></tr><td align="center">26</td></table>
B.	<table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td></tr><td align="center">52</td></table>
C.	<table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td></tr><td align="center">169</td></table>
D.	<table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center>1</center></td></tr><td align="center">221</td></table>
Answer» E.

Discussion

190.	The lowest eigenvalue of the 2 2 matrix
A.	2
B.	3
C.	4
D.	5
Answer» B. 3

Discussion

191.	Which one of the following describes the relationship among the three vectors, + ĵ + k , 2 + 3ĵ + k and 5 + 6ĵ + 4k ?
A.	The vectors are mutually perpendicular
B.	The vectors are linearly dependent
C.	The vectors are linearly independent
D.	The vectors are unit vectors
Answer» C. The vectors are linearly independent

Discussion

192.	The following surface integral is to be evaluated over a sphere for the given steady velocity vector field
A.
B.	2
C.	3 /4
D.	4
Answer» B. 2

Discussion

193.	A is a 3 4 real matrix and Ax = b is an inconsistent system of equations. The highest possible rank of A is
A.	1
B.	2
C.	3
D.	4
Answer» D. 4

Discussion

194.	Consider the system of simultaneous equations
A.	unique solution
B.	infinite number of solutions
C.	no solution
D.	exactly two solutions
Answer» D. exactly two solutions

Discussion

195.	The determinant of a 2 2 matrix is 50. If one eigenvalue of the matrix is 10, the other eigen value is ________.
A.	7
B.	5
C.	10
D.	15
Answer» C. 10

Discussion

196.	x + 2y + z = 4
A.	A unique solution of x = 1, y = 1 and z = 1
B.	only the two solutions of (x = 1, y = 1, z = 1) and (x = 2, y = 1, z = 0)
C.	infinite number of solutions
D.	No feasible solution
Answer» D. No feasible solution

Discussion

197.	Consider the following system of equations
A.	a unique solution
B.	no solution
C.	infinite number of solutions
D.	five solutions
Answer» D. five solutions

Discussion

198.	For what value of a, if any, will the following system of equation in x, y and z have a solution?
A.	any real number
B.	0
C.	1
D.	There is no such value
Answer» C. 1

Discussion

199.	With a 1 unit change in b, what is the change in x in the solution of the system of equations x + y = 2, 1.01x + 0.99 y = b?
A.	zero
B.	2 units
C.	50 units
D.	100 units
Answer» D. 100 units

Discussion

200.

The length of the curve y = 2 x^{3 / 2} between x = 0 and x = 1 is
3

A.

0.27

B.

0.67

C.

1

D.

1.22

Answer» E.

Discussion

Explore topic-wise MCQs in Engineering Mathematics.

The angle between two unit-magnitude coplanar vectors P(0.866, 0.500, 0) and Q(0.259, 0.966, 0) will be

The vector field

If y = f(x) is the solution of d y = 0dx

The set of equations

A group consists of equal number of men and women. Of this group 20% of the men and 50% of the women are unemployed. If a person is selected at random from this group, the probability of the selected person being employed is _______ .

The value of [(3x - 8y )dx (4y - 6xy) dy] (where C is the boundary of the region boundary by x = 0, y = 0 and x + y = 1) is ________.

Finding the solution of d y + 16y = 0 for y(x) with the two boundarydx

The number of accidents occurring in a plant in a month follows Poisson distribution with mean as 5.2. The probability of occurrence of less than 2 accidents in the plant during a randomly selected month is

Let X be a normal random variable with mean 1 and variance 4. The probability P{X < 0} is

A six-face fair dice is rolled a large number of times. The mean value of the outcomes is ___.

A six-faced fair dice is rolled five times. The probability (in%) of obtaining "ONE" at least four times is

Two coins are tossed simultaneously. The probability (upto two decimal points accuracy) of getting at least one head is ___.

The value of the following definite integral is _____ (round off to there decimal places).

Given a vector U = 1 (-y + x &jcirc; + z k)3

If a square matrix A is real and symmetric, then the eigenvalues

The area enclosed between the straight line y = x and the parabola y = x in the x y plane is

The area enclosed between the curves y = 4x and x = 4y is

Eigenvalues of a real symmetric matrix are always

A nationalized bank has found that the daily balance available in its savings accounts follows a normal distribution with a mean of Rs. 500 and a standard deviation of Rs. 50. The percentage of savings account holders, who maintain an average daily balance more than Rs. 500 is ___.

A box contains 2 washers, 3 nuts and 4 bolts. Items are drawn from the box at random one at a time without replacement. The probability of drawing 2 washers first followed by 3 nuts and subsequently the 4 bolts is

The function f(t) satisfies the differential equation (d f / dt ) + f = 0 and the auxilliary conditions, f(0) = 0, (df / dt) (o) = 4. The Laplace transform of f(t) is given by

Given two complex numbers Z1 = 5 + (5 3)i and Z2 = 2 + 2i the arguement ofZ1in degree is 3Z2

A box contains 5 black and 5 red balls. Two balls are randomly picked one after another from the box, without replacement. The probability for both balls being red is

The product of two complex numbers (1+ i) and 2 5i is

Curl of vector V(x, y, z) = 2x2i + 3z2j + y3k at x = y = z = 1 is

If (x, y) and (x, y) are functions with continuous second derivatives, then (x, y) + i (x, y)

If three coins are tossed simultaneously, the probability of getting at least one head is

Divergence of the vector field

The argument of the complex number {(1 + i) / (1 - i)} , where i =

The eigen values of a symmetric matrix are all

The product of eigenvalues of the matrix P is

The number of linearly independent eigenvectors of matrix

The condition for which the eigenvalues of the

The divergence of the vector field (x - y) + (y - x)ĵ + (x + y + z)k is

The area of a triangle formed by the tips of vectors

The line integral

Stokes theorem connects

The solution to the system of equations is

From a pack of regular playing cards, two cards are drawn at random. What is the probability that both cards will be Kings, if first card in NOT replaced?

The lowest eigenvalue of the 2 2 matrix

Which one of the following describes the relationship among the three vectors, + ĵ + k , 2 + 3ĵ + k and 5 + 6ĵ + 4k ?

The following surface integral is to be evaluated over a sphere for the given steady velocity vector field

A is a 3 4 real matrix and Ax = b is an inconsistent system of equations. The highest possible rank of A is

Consider the system of simultaneous equations

The determinant of a 2 2 matrix is 50. If one eigenvalue of the matrix is 10, the other eigen value is ________.

x + 2y + z = 4

Consider the following system of equations

For what value of a, if any, will the following system of equation in x, y and z have a solution?

With a 1 unit change in b, what is the change in x in the solution of the system of equations x + y = 2, 1.01x + 0.99 y = b?

The length of the curve y = 2x3 / 2 between x = 0 and x = 1 is 3

If y = f(x) is the solution of d y = 0
dx

Finding the solution of d y + 16y = 0 for y(x) with the two boundary
dx

Given a vector U = 1 (-y + x &jcirc; + z k)
3

Given two complex numbers Z₁ = 5 + (5 3)i and Z₂ = 2 + 2i the arguement of Z₁ in degree is
3 Z₂

The length of the curve y = 2 x^{3 / 2} between x = 0 and x = 1 is
3