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Design and draw voltage regulator to provide 2 to 10V variable output voltage using IC 7812.
Online Library Management System
The Library Management System will provide a search functionality to facilitate the search of resources. This search will be based on various categories viz. book name or the ISBN. Also Advanced Search feature is provided in order to search various categories simultaneously. Further the library staff personnel can add/update/remove the resources and the resource users from the system.
1.1 Not in scope
It is not required to collect the student database as the functionality is provided to everyone who accesses this application.
1.2 Business context
The proposed system will help in easy management of the library resources by providing information such as the availability of books, request for books, total number of books which inturn will reduce the effort the library staff and also help in providing precise information to the users.
1.3 Proposed system
The Library Management System will provide a search functionality to facilitate the search of resources.
The Library Management System will provide a search functionality to facilitate the search of resources. This search will be based on various categories viz. book name or the ISBN. Also Advanced Search feature is provided in order to search various categories simultaneously. Further the library staff personnel can add/update/remove the resources and the resource users from the system.
1.1 Not in scope
It is not required to collect the student database as the functionality is provided to everyone who accesses this application.
1.2 Business context
The proposed system will help in easy management of the library resources by providing information such as the availability of books, request for books, total number of books which inturn will reduce the effort the library staff and also help in providing precise information to the users.
1.3 Proposed system
The Library Management System will provide a search functionality to facilitate the search of resources.
a) Which of the following functions are 1-1 and which are onto? Justify your answer.
i) f : R ! R
0
given by f (x) = x
2
where R
0
is the set fx 2 Rjx 0g.
ii) f : R ! R given by f (x) = x
2
+ x + 1. (3)
b) If we consider the expression
1
2 3x
as a function on R, what will be its domain and
range? Will it have an inverse? Justify your answer. (2)
c) Let a =
(
1
2
p
2
;
p
3
2
p
2
;
1
p
2
)
and b =
(
1
p
2
; 0;
1
p
2
)
.
i) Find the direct cosines of a and b.
ii) Find the angle between a and b. (2)
d) Check that the vectors u =
(
3
5
;
4
5
; 0
)
, v =
(
4
5
;
3
5
; 0
)
and w = (0; 0; 1) are orthonormal.
Further, write the vector a = (1; 1; 2) as a linear combination of the vectors.
i) f : R ! R
0
given by f (x) = x
2
where R
0
is the set fx 2 Rjx 0g.
ii) f : R ! R given by f (x) = x
2
+ x + 1. (3)
b) If we consider the expression
1
2 3x
as a function on R, what will be its domain and
range? Will it have an inverse? Justify your answer. (2)
c) Let a =
(
1
2
p
2
;
p
3
2
p
2
;
1
p
2
)
and b =
(
1
p
2
; 0;
1
p
2
)
.
i) Find the direct cosines of a and b.
ii) Find the angle between a and b. (2)
d) Check that the vectors u =
(
3
5
;
4
5
; 0
)
, v =
(
4
5
;
3
5
; 0
)
and w = (0; 0; 1) are orthonormal.
Further, write the vector a = (1; 1; 2) as a linear combination of the vectors.
Which of the following statements are true and which are false? Justify your answer with a
short proof or a counterexample. (20)
i) Subtraction is a binary operation on N.
ii) If fv
1
; v
2
;:::; v
n
g is a basis for vector space V , fv
1 + v
2 + + v
n
; v
2
;:::; v
n
g is also
a basis for V .
iii) If W1
and W2
are subspaces of vector space V and W1 + W2 = V , then W1 \ W2 = f0g.
iv) The rank of a matrix equals its number of nonzero rows.
v) The row-reduced echelon form of an invertible matrix is the identity matrix.
vi) If the characteristic polynomial of a linear transformation is (x 1)(x 2), its
minimal polynomial is x 1 or x 2.
vii) If zero is an eigenvalue of a linear transformation T , then T is not invertible.
viii) If a linear operator is diagonalisable, its minimal polynomial is the same as the
characteristic polynomial.
ix) No skew-symmetric matrix is diagonalisable.
x) There is no matrix which is Hermitian as well as Unitary.
short proof or a counterexample. (20)
i) Subtraction is a binary operation on N.
ii) If fv
1
; v
2
;:::; v
n
g is a basis for vector space V , fv
1 + v
2 + + v
n
; v
2
;:::; v
n
g is also
a basis for V .
iii) If W1
and W2
are subspaces of vector space V and W1 + W2 = V , then W1 \ W2 = f0g.
iv) The rank of a matrix equals its number of nonzero rows.
v) The row-reduced echelon form of an invertible matrix is the identity matrix.
vi) If the characteristic polynomial of a linear transformation is (x 1)(x 2), its
minimal polynomial is x 1 or x 2.
vii) If zero is an eigenvalue of a linear transformation T , then T is not invertible.
viii) If a linear operator is diagonalisable, its minimal polynomial is the same as the
characteristic polynomial.
ix) No skew-symmetric matrix is diagonalisable.
x) There is no matrix which is Hermitian as well as Unitary.
Obtain the geometric, polar and exponential representationsof (i5 – 1)
–1
.
–1
.
Obtain the solution set of the system x – 3y + 4z = 9, 4x +3y + 2z = 7, y – 2x = 5 – 10z by
elimination.
elimination.
A stamping machine produces ‘can tops’ whose diameters are normally distributed with a standard deviation of 0.02 inch. At what nominal mean diameter should the machine be set, so that no more than 9 % of the ‘can tops’ produced have diameters exceeding 3.5 inches?
Online Library Management System
The Library Management System will provide a search functionality to facilitate the search of resources. This search will be based on various categories viz. book name or the ISBN. Also Advanced Search feature is provided in order to search various categories simultaneously. Further the library staff personnel can add/update/remove the resources and the resource users from the system.
1.1 Not in scope
It is not required to collect the student database as the functionality is provided to everyone who accesses this application.
1.2 Business context
The proposed system will help in easy management of the library resources by providing information such as the availability of books, request for books, total number of books which inturn will reduce the effort the library staff and also help in providing precise information to the users.
1.3 Proposed system
The Library Management System will provide a search functionality to facilitate the search of resources.
The Library Management System will provide a search functionality to facilitate the search of resources. This search will be based on various categories viz. book name or the ISBN. Also Advanced Search feature is provided in order to search various categories simultaneously. Further the library staff personnel can add/update/remove the resources and the resource users from the system.
1.1 Not in scope
It is not required to collect the student database as the functionality is provided to everyone who accesses this application.
1.2 Business context
The proposed system will help in easy management of the library resources by providing information such as the availability of books, request for books, total number of books which inturn will reduce the effort the library staff and also help in providing precise information to the users.
1.3 Proposed system
The Library Management System will provide a search functionality to facilitate the search of resources.
why steel has carbon in its structure? is there any simple explanation? it's for homework
“There is a mismatch between man’s ability to produce and social incapacity to utilize”.
Explain the meaning of this statement
Explain the meaning of this statement
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#340153 on Dec 2023
#340153 on Dec 2023