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JEE Advanced Unit 1A1: Relations, Functions and Graphs — practice questions

Explore 16 free Unit 1A1: Relations, Functions and Graphs questions in JEE Advanced Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Unit 1A1: Relations, Functions and Graphs questions and exercises with answers

Showing questions 1–16 of 16.

arctan(x) is an _____ function (odd/even):Read the answer and worked solution →Maximum value of x² + (arcsin(x))² for x in [-1, 1]:Read the answer and worked solution →Which of the following sets of ordered pairs represents a function?Read the answer and worked solution →For finite sets, $n(A\times B)$ equals:Read the answer and worked solution →A relation $R$ on a set $A$ is reflexive if:Read the answer and worked solution →An equivalence relation is one that is:Read the answer and worked solution →A function $f:A\to B$ is one-one (injective) if:Read the answer and worked solution →A function $f:A\to B$ is onto (surjective) if:Read the answer and worked solution →A bijective function is one that is:Read the answer and worked solution →The function $f:\mathbb{R}\to\mathbb{R}$ given by $f(x) = 2x + 3$ is:Read the answer and worked solution →The function $f:\mathbb{R}\to\mathbb{R}$ given by $f(x) = x^2$ is:Read the answer and worked solution →The number of one-one functions from $\{1,2\}$ to $\{a,b,c\}$ is:Read the answer and worked solution →For functions $f$ and $g$, the composition $(g\circ f)(x)$ means:Read the answer and worked solution →If $f(x) = 2x$ and $g(x) = x + 1$, then $(g\circ f)(x)$ equals:Read the answer and worked solution →A function is invertible if and only if it is:Read the answer and worked solution →The number of bijective functions from a set with $n$ elements onto itself is:Read the answer and worked solution →

Worked practice questions

arctan(x) is an _____ function (odd/even):

  1. Even
  2. ODD (arctan(-x) = -arctan(x))
  3. Neither
  4. Both
Show answer and solution

Correct answer: B. ODD (arctan(-x) = -arctan(x))

arctan(-x) = -arctan(x). Odd function. (Graph symmetric about origin.) Same for arcsin. arccos is neither (arccos(-x) = π - arccos(x)).

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Maximum value of x² + (arcsin(x))² for x in [-1, 1]:

  1. At x = 1: 1 + (π/2)² ≈ 3.47
  2. 0
  3. Cannot determine without calculus
  4. Always 1
Show answer and solution

Correct answer: A. At x = 1: 1 + (π/2)² ≈ 3.47

f(x) = x² + (arcsin(x))² on [-1, 1]. f'(x) = 2x + 2 arcsin(x) × 1/sqrt(1-x²). At x = 1: f = 1 + (π/2)² ≈ 1 + 2.47 = 3.47. By symmetry same value at x = -1. So max ≈ 3.47.

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Which of the following sets of ordered pairs represents a function?

  1. $\{(1,2),(1,4),(2,5)\}$
  2. $\{(1,2),(2,3),(3,4)\}$
  3. $\{(1,2),(1,3)\}$
  4. $\{(2,1),(2,2)\}$
Show answer and solution

Correct answer: B. $\{(1,2),(2,3),(3,4)\}$

Only {(1,2),(2,3),(3,4)} has each first-coordinate appearing once the others repeat an input with different outputs.

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