Let S , T , U be three non-void sets and f : S → T , g : T → U be so that g o f : S → U is surjective. Then,

g is surjective, f may not be so

f is surjective, g may not be so

f and g both may not be surjective

Let f : R → R be defined by f ( x ) = x 2 - x 2 1 + x 2 for all x ∈ R . Then,

f is one-one but not onto mapping

f is onto but not one-one mapping

Let R be the set of all real numbers and f : R → R be a continuous function. Suppose | f ( x ) - f ( y ) | ≥ | x - y | for all real numbers x and y . Then

f is one-one, but need not be onto

f is onto, but need not be one-one

f need not be either one-one or onto

MEDIUM

Earn 100

Which management function involves setting objectives and determining the course of action to achieve them?

50% studentsanswered this correctly

Important Questions on Linear Programming

MEDIUM

Mathematics>Algebra>Linear Programming>Different Types of Linear Programming Problems

Let

A

and

B

be finite sets and

P_{A}

and

P_{B}

, respectively denote their power sets. If

P_{B}

has

112

elements more than those in

P_{A}

, then the number of functions from

A

B

which are injective is

HARD

Mathematics>Algebra>Linear Programming>Different Types of Linear Programming Problems

If the function

f : R \to R

is defined by

f (x) = |x| (x - \sin x)

, then which of the following statements is TRUE?

MEDIUM

Mathematics>Algebra>Linear Programming>Different Types of Linear Programming Problems

Let

A = [- 1, 1]

and

f : A \to A

be defined as

f (x) = x |x|

for all

x \in A

, then

f (x)

MEDIUM

Mathematics>Algebra>Linear Programming>Different Types of Linear Programming Problems

Let

f : [0, 1] \to [- 1, 1]

and

g : [- 1, 1] \to [0, 2]

be two functions such that

g

is injective and

g o f : [0, 1] \to [0, 2]

is surjective. Then,

EASY

Mathematics>Algebra>Linear Programming>Different Types of Linear Programming Problems

Let

f : R \to R

be defined as

f (x) = 3 x .

Then

HARD

Mathematics>Algebra>Linear Programming>Different Types of Linear Programming Problems

Let

S, T, U

be three non-void sets and

f : S \to T, g : T \to U

be so that

g o f : S \to U

is surjective. Then,

EASY

Mathematics>Algebra>Linear Programming>Different Types of Linear Programming Problems

A = {1, 2, 3, 4},

then the number of functions on the set

A,

which are not one - one, is

MEDIUM

Mathematics>Algebra>Linear Programming>Different Types of Linear Programming Problems

Function $f : N \to Z; f (n) = \{\begin{array}{cl} \frac{n}{2}, & n - even \\ - (\frac{n - 1}{2}), & n - odd \end{array}$

MEDIUM

Mathematics>Algebra>Linear Programming>Different Types of Linear Programming Problems

If the function

f : R - \{1, - 1\} \to A

defined by

f (x) = \frac{x^{2}}{1 - x^{2}},

is surjective, then

A

is equal to

MEDIUM

Mathematics>Algebra>Linear Programming>Different Types of Linear Programming Problems

A = {x | x \in N, x \leq 5}, B = \{x | x \in Z, x^{2} - 5 x + 6 = 0\},

then the number of onto functions from

A

B

MEDIUM

Mathematics>Algebra>Linear Programming>Different Types of Linear Programming Problems

Let $f : R \to R$ be a continuous function such that $f (x^{2}) = f (x^{3})$ for all $x \in R$ . Consider the following statements.

I. $f$ is an odd function.

II. $f$ is an even function.

III. $f$ is differentiable everywhere.

Then,

EASY

Mathematics>Algebra>Linear Programming>Different Types of Linear Programming Problems

Consider the statement given below and decide out of which given presuppositions is it inherent in.
Statement
Doctors these days advise the consumption of rice in the dinner.
Presuppositions
I. Late night dinner produces toxin in the because the food remains undigested for a long time.
II. Rice digests quickly .

MEDIUM

Mathematics>Algebra>Linear Programming>Different Types of Linear Programming Problems

Let

f : [0, 1] \to R

be an injective continuous function that satisifes the condition

- 1 < f (0) < f (1) < 1

Then, the number of functions

g : [- 1, 1] \to [0, 1]

such that

(g o f) (x) = x

for all

x \in [0, 1]

MEDIUM

Mathematics>Algebra>Linear Programming>Different Types of Linear Programming Problems

Let

f : R \to R

be defined by

f (x) = x^{2} - \frac{x^{2}}{1 + x^{2}}

for all

x \in R .

Then,

HARD

Mathematics>Algebra>Linear Programming>Different Types of Linear Programming Problems

Let

R

be the set of all real numbers and

f : R \to R

be a continuous function. Suppose

| f (x) - f (y) | \geq | x - y |

for all real numbers

x

and

y .

Then

MEDIUM

Mathematics>Algebra>Linear Programming>Different Types of Linear Programming Problems

The function

f : R \to R,

is given by

f (x) = \frac{x}{1 + |x|}

, is

EASY

Mathematics>Algebra>Linear Programming>Different Types of Linear Programming Problems

E = \{1, 2, 3, 4\}

and

F = \{1, 2\}

. Then the number of onto functions from

E

F

EASY

Mathematics>Algebra>Linear Programming>Different Types of Linear Programming Problems

Which of the following function from

z

into

z

is bijection? (

z

is set of integers)

HARD

Mathematics>Algebra>Linear Programming>Different Types of Linear Programming Problems

Let

f : R \to R

be defined by

f (x) = \frac{|x| - 1}{|x| + 1},

then

f

EASY

Mathematics>Algebra>Linear Programming>Different Types of Linear Programming Problems

Which presupposition is inherent in the following statement?
Statement
Vimla said reminding her husband, "I hope you have taken your raincoat".
Presupposition
I. There is likelihood of rain.
II. Vimla is careful about the health of her husband.

Which management function involves setting objectives and determining the course of action to achieve them?

Important Questions on Linear Programming

Learn and Prepare for any exam you want !