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# JEE Main Math Previous Year Papers Sets Relations Functions Questions Answer Keys Solutions

Welcome to AMBiPi (Read as: एम्बीपाई) (Amans Maths Blogs). JEE Mains and JEE Advanced exams are the engineering entrance exams for taking admission in IITs, NITs and other engineering colleges. In this article, you will get JEE Main Math Previous Year Papers Sets Relations Functions Questions Answer Keys Solutions.

### JEE Mains Mathematics Sets Relations and Functions Questions Bank

Enter Questions No: 1

The domain of sin-1[log3 (x/3)] is

[2002]

Option A: [1, 9]

Option B: [-1, 9]

Option C: [-9, 1]

Option D: [-9, -1]

Option A: [1, 9]

Enter Questions No: 1

If f(x + y) = f(x) ∙ f(y) for all x and y and f(5) = 2, f'(0) = 3, then find f'(5).

[2002]

Option A: 0

Option B: 1

Option C: 6

Option D: 2

Option C: 6

Enter Questions No: 1

Which one is NOT periodic?

[2002]

Option A: |sin 3x| + sin2x

Option B: cos √x + cos2

Option C: cos 4x + tan2x

Option D: cos 2x + sin x

Option B: cos √x + cos2x

Enter Questions No: 1

The period of sin2θ is

[2002]

Option A: π2

Option B: π

Option C: π3

Option D: π/2

Option B: π

Enter Questions No: 1

The function f(x) = log(x + √(x2 + 1))

[2003]

Option A: An Even Function

Option B: An Odd Function

Option C: A Periodic Function

Option D: Neither an Even nor an Odd Function

Option B: An Odd Function

Enter Questions No: 1

Domain of definition of the function f(x) = 3 / (4 – x2) + log10(x3 – x) is

[2003]

Option A: (1, 2)

Option B: (-1, 0) ∪ (1, 2)

Option C: (1, 2) ∪ (2, ∞)

Option D: (-1, 0) ∪ (1, 2) ∪ (2, ∞)

Option D: (-1, 0) ∪ (1, 2) ∪ (2, ∞)

Enter Questions No: 1

If f : R → R satisfies f(x + y) = f(x) + f(y), for all x, y ∊ R and f(1) = 7, then

is

[2003]

Option A: 7n / 2

Option B: 7(n + 1) / 2

Option C: 7n(n + 1)

Option D: 7n(n + 1) / 2

Option D: 7n(n + 1) / 2

Enter Questions No: 1

A function f from the set of natural numbers to integers defined by

is

[2003]

Option A: One-One but Not Onto

Option B: Onto but Not One-One

Option C: One-One and Onto Both

Option D: Neither One-One Nor Onto

Option C: One-One and Onto Both

Enter Questions No: 1

Let R = {(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)} be a relation on the set A = {1, 2, 3, 4}. The relation R is

[2004]

Option A: a function

Option B: reflexive

Option C: not symmetric

Option D: transitive

Option C: not symmetric

Enter Questions No: 1

The domain of the function f(x) = sin-1(x – 3) / √(9 – x2) is

[2004]

Option A: [2, 3]

Option B: [2, 3)

Option C: [1, 2]

Option D: [1, 2)

Option C: One-One and Onto Both

Enter Questions No: 1

The graph of the function y = f(x) is symmetrical about the line x = 2, then

[2004]

Option A: f(x + 2) = f(x – 2)

Option B: f(2 + x) = f(2 – x)

Option C: f(x) = f(-x)

Option D: f(x) = -f(-x)

Option B: f(2 + x) = f(2 – x)

Enter Questions No: 1

If f : R → S, defined by f(x) = sin x – √3cos x + 1 is onto, then the interval of S is

[2004]

Option A: [0, 3]

Option B: [-1, 1]

Option C: [0, 1]

Option D: [-1, 3]

Option D: [-1, 3]

Enter Questions No: 1

The range of the function f(x) = 7-xPx-3 is

[2004]

Option A: {1, 2, 3}

Option B: {1, 2, 3, 4, 5}

Option C: {1, 2, 3, 4}

Option D: {1, 2, 3, 4, 5, 6}

Option A: {1, 2, 3}

Enter Questions No: 1

Let R = {(3, 3), (6, 6), (9,9), (12, 12), (6, 12), (3, 9), (3, 12), (3, 6)} be a relation on the set A = {3, 6, 9, 12} be a relation on the set A = {3, 6, 9, 12}. The relation is

[2005]

Option A: reflexive and transitive only

Option B: reflexive only

Option C: an equivalence relation

Option D: reflexive and symmetric only

Option A: reflexive and transitive only

Enter Questions No: 1

Let f : (-1, 1) → B, be a function defined by f(x) = tan-1(2x / (1 – x2)), then the function f is both one-one and onto when B is the interval

[2005]

Option A: (0, π/2)

Option B: [0, π/2)

Option C: [-π/2, π/2]

Option D: (-π/2, π/2)

Option D: (-π/2, π/2)

Enter Questions No: 1

A real valued function f(x) satisfies the functional equation f(x – y) = f(x)f(y) – f(a – x)f(a + y) where a is a given constant and f(0) = 0, f(2a – x) is equal to

[2005]

Option A: -f(x)

Option B: f(x)

Option C: f(a) + f(a – x)

Option D: f(-x)

Option A: -f(x)

Enter Questions No: 1

Let W denote the words in English dictionary. Define the relation R by R = {(x, y) ∈ W × W | the words x and y have at least one letter in common}. Then, R is

[2006]

Option A: not reflexive, symmetric and transitive

Option B: reflexive, symmetric and not transitive

Option C: reflexive, symmetric and transitive

Option D: reflexive, not symmetric and transitive

Option B: reflexive, symmetric and not transitive

Enter Questions No: 1

The largest interval lying in (-π/2, π/2) for which the function

is defined, is

[2007]

Option A: [0, π]

Option B: (-π/2, π/2)

Option C: [-π/4, π/2)

Option D: [0, π/2)

Option D: [0, π/2)

Enter Questions No: 1

Let R be the real line. Consider the following subsets of the plane R × R. S = {(x, y) : y = x + 1 and 0 < x < 2}, T = {(x, y) : x-y is an integer}. Which one of the following is true?

[2008]

Option A: neither S nor T is an equivalence relation on R

Option B: both S and T are equivalence relations on R

Option C: S is an equivalence relation on R but T is not

Option D: T is an equivalence relation on R but S is not

Option D: T is an equivalence relation on R but S is not

Enter Questions No: 1

Let f : N → Y be a function defined as f(x) = 4x + 3, where Y = {y ∈ N : y = 4x + 3 for some x ∈ N}. If f is invertible function, then its inverse function is

[2008]

Option A: g(y) = (3y + 4) / 3

Option B: g(y) = 4 + (y + 3) / 4

Option C: g(y) = (y + 3) / 4

Option D: g(y) = log | sin (x – π / 4) | + c

Option D: g(y) = log | sin (x – π / 4) | + c

Enter Questions No: 1

If A, B and C are three sets such that A ∩ B = A ∩ C and A ∪ B = A ∪ C, then

[2009]

Option A: A = B

Option B: A = C

Option C: B = C

Option D: A ∩ B = φ

Option C: B = C

Enter Questions No: 1

For real x, let f(x) = x3 + 5x + 1, then

[2009]

Option A: f is one-one but not onto R

Option B: f is onto R but not one-one

Option C: f is one-one and onto R

Option D: f is neither one-one nor onto R

Option C: f is one-one and onto R

Enter Questions No: 1

Consider the following relations:

= {(x, y) | x, y are real numbers and x = wy for some rational number w}

= {(m/n, p/q) | m,n, p and q are integers such that n, q ≠ 0 and qm = pn}. Then,

[2010]

Option A: neither R nor S is an equivalence relation

Option B: S is an equivalence relation but R is not an equivalence relation

Option C: R and S both are equivalence relations

Option D: R is an equivalence relation but S is not an equivalence relation

Option B: S is an equivalence relation but R is not an equivalence relation

Enter Questions No: 1

The domain of the function f(x) = 1 / √(|x| – x) is

[2011]

Option A: (0, ∞)

Option B: (-∞, 0)

Option C: (-∞, ∞) – {0}

Option D: (-∞, ∞)

Option B: (-∞, 0)

Enter Questions No: 1

The range of the function f(x) = x / (1 + |x|), x ∈ R, is

[2012]

Option A: R

Option B: (-1, 1)

Option C: R – {0}

Option D: [-1, 1]

Option B: (-1, 1)

Enter Questions No: 1

Let A and B be two sets containing two elements and four elements respectively. The number of subsets of A × B having three or more elements is

[2013]

Option A: 220

Option B: 219

Option C: 211

Option D: 256

Option B: 219

Enter Questions No: 1

If X = {4n – 3n – 1 : n ∈ N} and Y = {9(n – 1) : n ∈ N}, where N is the set of natural numbers, then X ∪ Y is equal to

[2014]

Option A: N

Option B: Y – X

Option C: X

Option D: Y

Option D: Y

Enter Questions No: 1

If g is the inverse of a function f and f ‘(x) = 1 / (1 + x5), then g ‘(x) is equal to

[2014]

Option A: 1 + x5

Option B: 5x4

Option C: 1 / [1 + {g(x)}5]

Option D: 1 + {g(x)}5

Option D: 1 + {g(x)}5

Enter Questions No: 1

If a ∈ R and the equation -3(x – [x])2 + 2(x – [x]) + a2 = 0 (where [x] denotes the greatest integer ≤ x) has no integral solution, then all possible values of a lie in the interval

[2014]

Option A: (-1, 0) ∪ (0, 1)

Option B: (1, 2)

Option C: (-2, -1)

Option D: (-∞, -2) ∪ (2, ∞)

Option A: (-1, 0) ∪ (0, 1)

Enter Questions No: 1

Let f(n) = [1/3 + 3n/100]n, where [n] denotes the greatest integer less than or equal to n. Then

is equal to

[2014]

Option A: 56

Option B: 689

Option C: 1287

Option D: 1399

Option D: 1399

Enter Questions No: 1

Let f be an odd function defined on the set of real numbers such that for x ≥ 0, f(x) = 3 sin x + 4 cos x. Then, f(x) at x = -11π/6 is equal to

[2014]

Option A: 3/2 + 2√3

Option B: –3/2 + 2√3

Option C: 3/2 – 2√3

Option D: –3/2 – 2√3

Option C: 3/2 – 2√3

Enter Questions No: 1

Let A and B be two sets containing four and two elements respectively. Then, the number of subsets of the set A × B, each having at least three elements os

[2015]

Option A: 256

Option B: 275

Option C: 510

Option D: 219

Option D: 219

Enter Questions No: 1

If f(x) + 2f(1 / x) = 3x, x ≠ 0, and S = {x ∈ R : f(x) = f(-x)} ; then S

[2016]

Option A: contains exactly one element

Option B: contains exactly two elements

Option C: contains more than two elements

Option D: is an empty set

Option B: contains exactly two elements

Enter Questions No: 1

Let a, b, c ∈ R. If f(x) = ax2 + bx + c is such that a + b + c = 3 and f(x + y) = f(x) + f(y) + xy, for all x, y ∈ R, then

is equal to

[2017]

Option A: 330

Option B: 165

Option C: 190

Option D: 255

Option A: 330

Enter Questions No: 1

The function f : R → [-1/2, 1/2] defined as f(x) = x / (1 + x2) is

[2017]

Option A: invertible

Option B: injective but not surjective

Option C: surjective but not injective

Option D: neither injective nor surjective

Option C: surjective but not injective

Enter Questions No: 1

Let f(x) = ax (a > 0) be written as f(x) = f1(x) + f2(x), where f1(x) is an even function and f2(x) is an odd function. Then, f1(x + y) + f2(x – y) equals

[2019]

Option A: 2f1(x)f1(y)

Option B: 2f1(x + y)f1(x – y)

Option C: 2f1(x)f2(y)

Option D: 2f1(x + y)f2(x – y)

Option A: 2f1(x)f1(y)

Enter Questions No: 1

If f(x) = loge((1 – x) / (1 + x)), |x| < 1, then f(2x / (1 + x2)) is equal to

[2019]

Option A: 2f(x)

Option B: 2f(x2)

Option C: f(f(x))2

Option D: –2f(x)

Option A: 2f(x)

Enter Questions No: 1

Let f : R → R be defined by f(x) = x / (1 + x2), Then the range of f is

[2019]

Option A: [-1/2, 1/2]

Option B: R – [-1, 1]

Option C: R – [-1/2, 1/2]

Option D: (-1, 1) – {0}

Option A: [-1/2, 1/2]

Enter Questions No: 1

The domain of the definition of the function f(x) = 1 / (4 – x2) + log10(x3 – x) is

[2019]

Option A: (-1, 0) ∪ (1, 2) ∪ (3, ∞)

Option B: (-2, -1) ∪ (-1, 0) ∪ (2, ∞)

Option C: (-1, 0) ∪ (1, 2) ∪ (2, ∞)

Option D: (1, 2) ∪ (2, ∞)

Option C: (-1, 0) ∪ (1, 2) ∪ (2, ∞)

Enter Questions No: 1

Let f(1, 3) → R be a function defined by f(x) = x[x] / (1 + x2), where [x] denotes the greatest integer ≤ x. Then, the range of f is

[2020]

Option A: (2/5, 3/5) ∪ (3/4, 4/5)

Option B: (2/5, 1/2) ∪ (3/5, 4/5)

Option C: (2/5, 4/5)

Option D: (3/5, 4/5)

Option B: (2/5, 1/2) ∪ (3/5, 4/5)

Enter Questions No: 1

Let f(x) be a quadratic polynomial such that f(-1) + f(2) = 0. If one of the roots of f(x) = 0 is 3, then its other root is lies in

[2020]

Option A: (-1, 0)

Option B: (1, 3

Option C: (-3, -1)

Option D: (0, 1)

Option A: (-1, 0)

Enter Questions No: 1

Let [t] denote the greatest integer ≤ t. Then, the equation in x, [x]2 + [x + 2] – 7 = 0 has

[2020]

Option A: exactly two solutions

Option B: exactly four integral solutions

Option C: no integral solutions

Option D: infinitely many solutions

Option D: infinitely many solutions

Enter Questions No: 1

If R = {(x, y) : x, y ∈ Z, x2 + 3y2 ≤ 8} is a relation on the set of integers Z, then the domain of R-1 is

[2020]

Option A: {-2, -1, 1, 2}

Option B: {0, 1}

Option C: {-2, -1, 0, 1, 2}

Option D: {-1, 0, 1}

Option D: {-1, 0, 1}

Enter Questions No: 1

The domain of the function f(x) = sin-1(|x| + 5)/(x2 + 1) is (-∞, -a] ∪ [a, ∞), Then a is equal to

[2020]

Option A: √17 / 2

Option B: (√17 – 1) / 2

Option C: (√17 + 1) / 2

Option D: √17 / 2 + 1