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Sets and Functions

Each subtopic includes About section, revision page link, 10 preview questions, and practice CTAs.

Sets, their representations, and types

Subtopic

Sets, their representations, and types under Sets and Functions for Grade 11 ICSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    What is the cardinality of the power set of a set with 0 elements?

    A.

    0

    B.

    1

    C.

    2

    D.

    Infinite

  2. 2.

    The set A={1,2,3}A = \{1, 2, 3\} and B={a,b,c}B = \{a, b, c\} are:

    A.

    Equal sets

    B.

    Equivalent sets

    C.

    Empty sets

    D.

    Subsets of each other

  3. 3.

    If U={1,2,3,4,5,6,7,8,9,10}U = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\} is the universal set, which of the following is not a subset of UU?

    A.

    {2,4,6}\{2, 4, 6\}

    B.

    {1,10}\{1, 10\}

    C.

    {0,1,2}\{0, 1, 2\}

    D.

    {9}\{9\}

Download the worksheet for Sets and Functions - Sets, their representations, and types to practice offline. It includes additional chapter-level practice questions.

Venn Diagrams and Operations on Sets

Subtopic

Venn Diagrams and Operations on Sets under Sets and Functions for Grade 11 ICSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Which of the following is true for any two sets AA and BB?

    A.

    A∩B=B∩AA \cap B = B \cap A

    B.

    A−B=B−AA - B = B - A

    C.

    A∪B=A∩BA \cup B = A \cap B

    D.

    A⊂BA \subset B always

  2. 2.

    In set builder notation, the set {1,1/2,1/3,1/4,...}\{1, 1/2, 1/3, 1/4, ...\} can be written as:

    A.

    {x:x=n,n∈N}\{x : x = n, n \in \mathbb{N}\}

    B.

    {x:x=1/n,n∈N}\{x : x = 1/n, n \in \mathbb{N}\}

    C.

    {x:x=n2,n∈N}\{x : x = n^2, n \in \mathbb{N}\}

    D.

    {x:x=2n,n∈N}\{x : x = 2n, n \in \mathbb{N}\}

  3. 3.

    If n(A)=15,n(A∪B)=25n(A) = 15, n(A \cup B) = 25 and n(A∩B)=5n(A \cap B) = 5, what is n(B)n(B)?

    A.

    10

    B.

    15

    C.

    20

    D.

    5

Download the worksheet for Sets and Functions - Venn Diagrams and Operations on Sets to practice offline. It includes additional chapter-level practice questions.

Relations, Domain, Co-domain, and Range

Subtopic

Relations, Domain, Co-domain, and Range under Sets and Functions for Grade 11 ICSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    If the range of a relation RR is {a,b}\{a, b\}, then the domain of R−1R^{-1} is:

    A.

    {a,b}\{a, b\}

    B.

    Set AA

    C.

    Set BB

    D.

    The same as the domain of RR

  2. 2.

    If R={(a,b):a+b=0}R = \{(a, b) : a+b = 0\} on the set {1,2,3}\{1, 2, 3\}, then RR is:

    A.

    {(1,−1),(2,−2)}\{(1, -1), (2, -2)\}

    B.

    {}\{\}

    C.

    {(0,0)}\{(0, 0)\}

    D.

    {(1,1),(2,2),(3,3)}\{(1, 1), (2, 2), (3, 3)\}

  3. 3.

    Let A={1,2,3}A = \{1, 2, 3\}. The number of elements in A×∅A \times \emptyset is:

    A.

    3

    B.

    1

    C.

    0

    D.

    Undefined

Download the worksheet for Sets and Functions - Relations, Domain, Co-domain, and Range to practice offline. It includes additional chapter-level practice questions.

Functions, their Domain, Range, and Graphs

Subtopic

Functions, their Domain, Range, and Graphs under Sets and Functions for Grade 11 ICSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    What is the shape of the graph of the function f(x)=x2f(x) = x^2?

    A.

    Straight line

    B.

    Circle

    C.

    Parabola

    D.

    Hyperbola

  2. 2.

    A function ff is called an even function if:

    A.

    f(−x)=−f(x)f(-x) = -f(x)

    B.

    f(−x)=f(x)f(-x) = f(x)

    C.

    f(x)=0f(x) = 0

    D.

    f(x)=xf(x) = x

  3. 3.

    If f(x)=1xf(x) = \frac{1}{x}, find f(0.5)f(0.5).

    A.

    0.5

    B.

    1

    C.

    2

    D.

    5

Download the worksheet for Sets and Functions - Functions, their Domain, Range, and Graphs to practice offline. It includes additional chapter-level practice questions.

Sum, Difference, Product and Quotients of Functions

Subtopic

Sum, Difference, Product and Quotients of Functions under Sets and Functions for Grade 11 ICSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    If f(x)=xf(x) = x and g(x)=xg(x) = x, find (fg)(x)(fg)(x).

    A.

    2x2x

    B.

    x2x^2

    C.

    11

    D.

    00

  2. 2.

    Find (f+g)(−2)(f + g)(-2) if f(x)=3xf(x) = 3x and g(x)=2xg(x) = 2x.

    A.

    -10

    B.

    -1

    C.

    10

    D.

    0

  3. 3.

    If f(x)=x2−9f(x) = x^2 - 9 and g(x)=x+3g(x) = x + 3, find (f/g)(x)(f/g)(x) for xeq−3x eq -3.

    A.

    x+3x + 3

    B.

    x−3x - 3

    C.

    11

    D.

    x2x^2

Download the worksheet for Sets and Functions - Sum, Difference, Product and Quotients of Functions to practice offline. It includes additional chapter-level practice questions.

Sets and Functions - ICSE Class 11 Maths Notes & Revision | Krit.club