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Relations and Functions

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

Cartesian Product of Sets

Subtopic

Cartesian Product of Sets under Relations and Functions for Grade 11 CBSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    If (2x−1,5)=(3,y+2)(2x - 1, 5) = (3, y + 2), find the value of x+yx + y.

    A.

    5

    B.

    3

    C.

    2

    D.

    7

  2. 2.

    If A⊂BA \subset B, then which of the following is true for any set CC?

    A.

    A×C⊂B×CA \times C \subset B \times C

    B.

    C×A=C×BC \times A = C \times B

    C.

    A×C=B×CA \times C = B \times C

    D.

    A×B⊂C×CA \times B \subset C \times C

  3. 3.

    If (x/2,y/3)=(1,2)(x/2, y/3) = (1, 2), then (x,y)(x, y) is:

    A.

    (2,6)(2, 6)

    B.

    (0.5,0.66)(0.5, 0.66)

    C.

    (1,2)(1, 2)

    D.

    (2,3)(2, 3)

Download the worksheet for Relations and Functions - Cartesian Product of Sets to practice offline. It includes additional chapter-level practice questions.

Relations

Subtopic

Relations under Relations and Functions for Grade 11 CBSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Find the values of xx and yy if the ordered pairs satisfy the equation (x+1,y−2)=(3,1)(x + 1, y - 2) = (3, 1).

    A.

    x=2,y=3x = 2, y = 3

    B.

    x=3,y=2x = 3, y = 2

    C.

    x=4,y=−1x = 4, y = -1

    D.

    x=2,y=1x = 2, y = 1

  2. 2.

    Let a relation RR be defined by R={(x,y):y=x+5,x∈{0,1,2}}R = \{(x, y) : y = x + 5, x \in \{0, 1, 2\}\}. What is the range of this relation?

    A.

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

    B.

    {0,5,1,6,2,7}\{0, 5, 1, 6, 2, 7\}

    C.

    {5,10,15}\{5, 10, 15\}

    D.

    {5,6,7}\{5, 6, 7\}

  3. 3.

    If set AA has 33 elements and set BB has 22 elements, how many different relations can be defined from set AA to set BB?

    A.

    66

    B.

    262^6

    C.

    323^2

    D.

    252^5

Download the worksheet for Relations and Functions - Relations to practice offline. It includes additional chapter-level practice questions.

Functions

Subtopic

Functions under Relations and Functions for Grade 11 CBSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    Which of the following represents (f−g)(x)(f - g)(x)?

    A.

    f(x)⋅g(x)f(x) \cdot g(x)

    B.

    f(x)/g(x)f(x) / g(x)

    C.

    f(x)+g(x)f(x) + g(x)

    D.

    f(x)−g(x)f(x) - g(x)

  2. 2.

    If f(x)=3x−2f(x) = 3x - 2, find xx if f(x)=−8f(x) = -8.

    A.

    -2

    B.

    2

    C.

    -3.33

    D.

    0

  3. 3.

    The domain of f(x)=x+5f(x) = \sqrt{x + 5} is:

    A.

    [−5,∞)[-5, \infty)

    B.

    (5,∞)(5, \infty)

    C.

    (−∞,−5](-\infty, -5]

    D.

    R\mathbb{R}

Download the worksheet for Relations and Functions - Functions to practice offline. It includes additional chapter-level practice questions.

Some functions and their graphs: Identity, Constant, Polynomial, Rational, Modulus, Signum, Greatest Integer Function

Subtopic

Some functions and their graphs: Identity, Constant, Polynomial, Rational, Modulus, Signum, Greatest Integer Function under Relations and Functions for Grade 11 CBSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    What is the value of the greatest integer function [x][x] for x=−4.9x = -4.9?

    A.

    -4

    B.

    -5

    C.

    4

    D.

    5

  2. 2.

    What is the domain of f(x)=1x2−4f(x) = \frac{1}{x^2 - 4}?

    A.

    R−{4}\mathbb{R} - \{4\}

    B.

    R−{2}\mathbb{R} - \{2\}

    C.

    R−{−2,2}\mathbb{R} - \{-2, 2\}

    D.

    R\mathbb{R}

  3. 3.

    Calculate the value of ∣−100∣|-100|.

    A.

    -100

    B.

    100

    C.

    0

    D.

    1

Download the worksheet for Relations and Functions - Some functions and their graphs: Identity, Constant, Polynomial, Rational, Modulus, Signum, Greatest Integer Function to practice offline. It includes additional chapter-level practice questions.

Algebra of real functions

Subtopic

Algebra of real functions under Relations and Functions for Grade 11 CBSE.

About Topic & Revision

Preview questions (no answers)

  1. 1.

    If f(x)=x2f(x) = x^2 and g(x)=xg(x) = \sqrt{x}, find the value of the product function (fg)(4)(fg)(4).

    A.

    1616

    B.

    6464

    C.

    88

    D.

    3232

  2. 2.

    Let f(x)=cf(x) = c be a constant function. Find the result of the addition (f+f)(x)(f + f)(x).

    A.

    c2c^2

    B.

    cc

    C.

    2c2c

    D.

    00

  3. 3.

    If f(x)=x+1f(x) = x + 1 and g(x)=x−1g(x) = x - 1, find the simplified expression for (f2−g2)(x)(f^2 - g^2)(x).

    A.

    22

    B.

    4x4x

    C.

    2x22x^2

    D.

    00

Download the worksheet for Relations and Functions - Algebra of real functions to practice offline. It includes additional chapter-level practice questions.