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Functions Maths - Functions

Uttarakhand Board (UBSE) - STD 12 Science - Maths (Uttarakhand - English Medium). 204 questions in this chapter.

Question types

Functions question types

204 questions across 4 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.

204
Questions
4
Question groups
5
Question types
Sample Questions

Functions questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1M.C.Q (1 Marks)1 Mark
The range of the function $\text{f(x)}=^{7-\text{x}}\text{P}_{\text{x}-3}$ is:
  • A
    $\{1, 2, 3, 4, 5\}$
  • B
    $\{1, 2, 3, 4, 5, 6\}$
  • C
    $\{1, 2, 3, 4\}$
  • ✓
    $\{1, 2, 3\}$

Answer: D.

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Q 2M.C.Q (1 Marks)1 Mark
Let $\text{A}=\{\text{x}\in\text{R}:-1\leq\text{x}\leq1\}=\text{B}.$ Then, the mapping $f : A → B$ given by $f(x) = x|x|$ is:
  • A
    Injective but not surjective.
  • B
    Surjective but not injective.
  • ✓
    Bijective.
  • D
    None of these.

Answer: C.

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Q 3M.C.Q (1 Marks)1 Mark
If $f : R \rightarrow R$ is given by $f(x) = x^3 + 3$, then $f^{-1}(x)$ is equal to:
  • A
    $\text{x}^\frac{1}{3}-3$
  • B
    $\text{x}^\frac{1}{3}+3$
  • ✓
    $(\text{x}-3)^\frac{1}{3}$
  • D
    $\text{x}+3^\frac{1}{3}$

Answer: C.

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Q 4M.C.Q (1 Marks)1 Mark
Let $\text{f(x)}=\frac{1}{1-\text{x}}.$ Then, {fo(fof)}(x):
  • A
    x for all $\text{x}\in\text{R}$
  • B
    x for all $\text{x}\in\text{R}-\{1\}$
  • ✓
    x for all $\text{x}\in\text{R}-\{0,1\}$
  • D
    None of these.

Answer: C.

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Q 5M.C.Q (1 Marks)1 Mark
If $g(x) = x^2 + x - 2$ and $\frac{1}{2}\text{gof(x)}=2\text{x}^2-5\text{x}+2,$ then $f(x)$ is equal to:
  • ✓
    $2x - 3$
  • B
    $2x + 3$
  • C
    $2x^2 + 3x + 1$
  • D
    $2x^2 - 3x - 1$

Answer: A.

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Q 165 Marks Questions5 Marks
The relation S defined on the set R of all real number by the rule aSb iff a ≥ b is:
  1. An equivalence relation.
  2. Reflexive, transitive but not symmetric.
  3. Symmetric, transitive but not reflexive.
  4. Neither transitive nor reflexive but symmetric.
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Q 175 Marks Questions5 Marks
$S$ is a relation over the set $R$ of all real numbers and it is given by $(\text{a, b})\in\text{S}\Leftrightarrow\text{ab}\geq0.$ Then, $S$ is:
  • A
    Symmetric and transitive only.
  • B
    Reflexive and symmetric only.
  • C
    Antisymmetric relation.
  • ✓
    An equivalence relation.

Answer: D.

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Q 195 Marks Questions5 Marks
Let L denote the set of all straight lines in a plane. Let a relation R be defined by lRm if l is perpendicular to m for all l, m ∈ L. Then, R is:
  1. Reflexive.
  2. Symmetric.
  3. Transitive.
  4. None of these.
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Q 205 Marks Questions5 Marks
In the set Z of all integers, which of the following relation R is not an equivalence relation?
  1. xRy : if $\text{x}\leq\text{y}$
  2. xRy : if x = y
  3. xRy : if x - y is an even integer
  4. xRy : if $\text{x}\equiv\text{y}\ (\text{mod 3})$
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