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Functions Maths - Functions

Gujarat Board (GSEB) - STD 12 Science - Maths (GSEB - English Medium). 205 questions in this chapter.

Question types

Functions question types

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

205
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
If $\text{g(f(x))}=|\sin\text{x}|$ and $\text{f(g(x))}=(\sin\sqrt{\text{x}})^2,$ then

  1. $\text{f(x)}=\sin^2\text{x},\ \text{g(x)}=\sqrt{\text{x}}$

  2. $\text{f(x)}=\sin\text{x},\ \text{g(x)}=|\text{x}|$

  3. $\text{f(x)}=\text{x}^2,\ \text{g(x)}=\sin\sqrt{\text{x}}$

  4. $\text{f and g cannot be determined.}$

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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:
  1. Injective but not surjective.
  2. Surjective but not injective.
  3. Bijective.
  4. None of these.
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Q 3M.C.Q (1 Marks)1 Mark
The range of the function $\text{f(x)}=^{7-\text{x}}\text{P}_{\text{x}-3}$ is:
  1. {1, 2, 3, 4, 5}
  2. {1, 2, 3, 4, 5, 6}
  3. {1, 2, 3, 4}
  4. {1, 2, 3}
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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):
  1. x for all $\text{x}\in\text{R}$
  2. x for all $\text{x}\in\text{R}-\{1\}$
  3. x for all $\text{x}\in\text{R}-\{0,1\}$
  4. None of these.
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Q 5M.C.Q (1 Marks)1 Mark
The function $\text{f}:[0,\infty)\rightarrow\ \text{R}$ given by $\text{f(x)}=\frac{\text{x}}{\text{x}+1}$ is:
  1. One-one and onto.
  2. One-one but not onto.
  3. Onto but not one-one.
  4. Onto but not one-one.
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Q 62 Marks2 Marks
If A = {1, 2, 3, 4} and B = {a, b, c, d} define any four bijections from A to B. Also give their inverse functions.
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Q 92 Marks2 Marks
Let $\text{f}:\text{R}-\Big\{-\frac{3}{5}\Big\}\rightarrow\ \text{R}$ be a function defined as $\text{f(x)}=\frac{2\text{x}}{5\text{x}+3}.$ Write f-1: Range of $\text{f}\rightarrow\ \text{R}-\Big\{-\frac{3}{5}\Big\}.$
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Q 102 Marks2 Marks
Let A = {1, 2, 3}, B = {4, 5, 6, 7} and let f = {(1, 4), (2, 5), (3, 6)} be a function from A to B. State whether f is one-one or not.
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Q 143 Marks3 Marks
If f : R → (0, 2) defined by $\text{f(x)}=\frac{\text{e}^{\text{x}}-\text{e}^{-\text{x}}}{\text{e}^{\text{x}}+\text{e}^{-\text{x}}}+1$ is invertible, find f-1.
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Q 164 Marks4 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 174 Marks4 Marks
The relation R = {(1, 1), (2, 2), (3, 3)} on the set {1, 2, 3} is:
  1. Symmetric only.
  2. Reflexive only.
  3. An equivalence relation.
  4. Transitive only.
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Q 184 Marks4 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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Q 194 Marks4 Marks
R is a relation from {11, 12, 13} to {8, 10, 12} defined by y = x - 3. Then, R-1 is:
  1. {(8, 11), (10, 13)}
  2. {(11, 8), (13, 10)}
  3. {(10, 13), (8, 11)}
  4. None of these.
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Q 204 Marks4 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:
  1. Symmetric and transitive only.
  2. Reflexive and symmetric only.
  3. Antisymmetric relation.
  4. An equivalence relation.
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