Mathematics Question Paper for 2nd PUC

I need Karnataka Second PUC Mathematics Question Paper, can you please provide here?

Here are some questions for Karnataka Second PUC Mathematics:

Give an example of a relation which is symmetric and transitive but not reflexive.

Define optimal solution in linear programming problem.

An urn contains 5 red and 2 black balls. Two balls are randomly selected. Let X represents the number of black balls, what are the possible values of X?

If the radius of a sphere is measured as with an error, , then find the approximate error in calculating its volume.

A die is thrown. If E is the event ‘the number appearing is a multiple of 3’ and F is the event ‘ the number appearing is even’, then find whether E and F are independent?

For detailed paper here is attachment:






Karnataka Second PUC Mathematics question paper has question from following topics:

UNIT I: RELATIONS AND FUNCTIONS
1. Rela
tions and Functions
Types of relations
: Reflexive, symmetric, transitive
, empty,
universal
and equivalence
relations.
Examples and problems.
Types of functions
:
One to one and onto functions,
inverse of a
function
composite functions,
mentioning
their
properties only ,
examples and
problems
.
Binary operations
: associative, commutative, identity, inverse with examples
2. Inverse Trig
onometric Functions
Definition, range, domain, principal value branches.
Mentioning domain and range of
trigonometric and
inverse trigonometric functions.
Graphs of inverse trigonometric
functions.
P
roperties
and proof
s
of
inverse trigonometric functions given in NCERT prescribed text
book, mentioning formulae for sin
-
1
x

sin
-
1
y, cos
-
1
x

cos
-
1
y,
2 tan
-
1
x = tan
-
1
(
) =
sin
-
1
(
) =
cos
-
1
(
)
without proof.
Conversion of one inverse trigonometric function to another w.r.t to right angled triangle.
Problems.
UNIT II: ALGEBRA
1. Matrices
Concept, notation, order,
Types of matrices
: column matrix, row matrix, rectangular matrix, square matrix, zero
matrix, diagonal matrix, scalar matrix and unit matrix.
Algebra of matrices
:
E
quality
of matrices, Addition, multiplication, sc
alar multiplication
of matrices
, T
ranspose of a matrix
.
Mentioning properties
with
respect to
a
ddition, multiplication
,
scalar multiplica
tion
and
transpose
of matrices
.
S
ymmet
ric and skew symmetric matrices
: Definition
s
,
properties of symmetric and skew symmetric matrices
: proof
s
of
i) If A is any square matrix A+A′ is symmetric and A
-
A′
is skew symmetric
ii) Any square matrix can be expressed as the sum of a symmetric and
a
skew
symmetric
matrix
.
Concept of elementary row and column operations
and finding inv
erse of a matrix
restricted to 2x2 matrices only
.
Invertible matrices and proof of the uniqueness of inverse, if it exists; (Here all matrices will have real entries)

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Please provide Karnataka Second PUC Mathematics Question Paper???

can you please upload the basic mathematics question papers of 2016