Sets And Relations - Algebra - Mathematics Previous Year Questions

1

2016 · Mathematics · Algebra · Sets And Relations

WB JEE 2016

Let R be a relation defined on the set Z of all integers and xRy, when x + 2y is divisible by 3, then

A

R is not transitive

B

R is symmetric only

C

R is an equivalence relation

D

R is not an equivalence relation

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2

2016 · Mathematics · Algebra · Sets And Relations

WB JEE 2016

If A = {5ⁿ \(-\) 4n \(-\) 1 : n\(\in\)N} and B = {16(n \(-\) 1) : n\(\in\)N}, then

A

A = B

B

A \(\cap\) B = \(\phi\)

C

A \(\subseteq\) B

D

B \(\subseteq\) A

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3

2017 · Mathematics · Algebra · Sets And Relations

WB JEE 2017

On R, the relation \(\rho\) be defined by 'x\(\rho\)y holds if and only if x \(-\) y is zero or irrational'. Then,

A

\(\rho\) is reflexive and transitive but not symmetric

B

\(\rho\) is reflexive and symmetric but not transitive

C

\(\rho\) is symmetric and transitive but not reflexive

D

\(\rho\) is equivalence relation

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4

2017 · Mathematics · Algebra · Sets And Relations

WB JEE 2017

On set A = {1, 2, 3}, relations R and S are given by

R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 1)},

S = {(1, 1), (2, 2), (3, 3), (1, 3), (3, 1)}. Then,

A

R \(\cup\) S is an equivalence relation

B

R \(\cup\) S is reflexive and transitive but not symmetric

C

R \(\cup\) S is reflexive and symmetric but not transitive

D

R \(\cup\) S is symmetric and transitive but not reflexive

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5

2017 · Mathematics · Algebra · Sets And Relations

WB JEE 2017

On R, the set of real numbers, a relation \(\rho\) is defined as 'a\(\rho\)b if and only if 1 + ab > 0'. Then,

A

\(\rho\) is an equivalence relation

B

\(\rho\) is reflexive and transitive but not symmetric

C

\(\rho\) is reflexive and symmetric but not transitive

D

\(\rho\) is only symmetric

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6

2017 · Mathematics · Algebra · Sets And Relations

WB JEE 2017

On the set R of real numbers we define xPy if and only if xy \(\ge\) 0. Then, the relation P is

A

reflexive but not symmetric

B

symmetric but not reflexive

C

transitive but not reflexive

D

reflexive and symmetric but not transitive

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7

2018 · Mathematics · Algebra · Sets And Relations

WB JEE 2018

On the set R of real numbers, the relation \(\rho\) is defined by x\(\rho\)y, (x, y) \(\in\) R.

A

If | x \(-\) y | < 2, then \(\rho\) is reflexive but neither symmetric nor transitive.

B

If x \(-\) y < 2, then \(\rho\) is reflexive and symmetric but not transitive.

C

If | x | \(\ge\) y, then \(\rho\) is reflexive and transitive but not symmetric

D

If x > | y |, then \(\rho\) is transitive but neither reflexive nor symmetric.

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8

2018 · Mathematics · Algebra · Sets And Relations

WB JEE 2018

Let \(\rho\) be a relation defined on N, the set of natural numbers, as

\(\rho\) = {(x, y) \(\in\) N \(\times\) N : 2x + y = 41}. Then

A

\(\rho\) is an equivalence relzation.

B

\(\rho\) is only reflexive relation

C

\(\rho\) is only symmetric relation

D

\(\rho\) is not transitive

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9

2018 · Mathematics · Algebra · Sets And Relations

WB JEE 2018

On R, a relation \(\rho\) is defined by x\(\rho\)y if and only if x \(-\) y is zero or irrational. Then,

A

\(\rho\) is equivalence relation

B

\(\rho\) is reflexive but neither symmetric nor transitive

C

\(\rho\) is reflexive and symmetric but not transitive

D

\(\rho\) is symmetric and transitive but not reflexive

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10

2019 · Mathematics · Algebra · Sets And Relations

WB JEE 2019

Let the relation \(\rho\) be defined on R as a\(\rho\)b if 1 + ab > 0. Then,

A

\(\rho\) is reflexive only.

B

\(\rho\) is equivalence relation.

C

\(\rho\) is reflective and transitive but not symmetric.

D

\(\rho\) is reflexive and symmetric but not transitive.

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11

2019 · Mathematics · Algebra · Sets And Relations

WB JEE 2019

Let f : X \(\to\) Y and A, B are non-void subsets of Y, then (where the symbols have their usual interpretation)

A

\({f^{ - 1}}(A) - {f^{ - 1}}(B) \supset {f^{ - 1}}(A - B)\) but the opposite does not hold.

B

\({f^{ - 1}}(A) - {f^{ - 1}}(B) \subset {f^{ - 1}}(A - B)\) but the opposite does not hold.

C

\({f^{ - 1}}(A - B) = {f^{ - 1}}(A) - {f^{ - 1}}(B)\)

D

\({f^{ - 1}}(A - B) = {f^{ - 1}}(A) \cup {f^{ - 1}}(B)\)

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12

2019 · Mathematics · Algebra · Sets And Relations

WB JEE 2019

Let S, T, U be three non-void sets and f : S \(\to\) T, g : T \(\to\) U be so that gof : s \(\to\) U is surjective. Then,

A

g and f are both surjective

B

g is surjective, f may not be so

C

f is surjective, g may not be so

D

f and g both may not be surjective

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13

2020 · Mathematics · Algebra · Sets And Relations

WB JEE 2020

Let p₁ and p₂ be two equivalence relations defined on a non-void set S. Then

A

both p₁ \(\cap\) p₂ and p₁ \(\cup\) p₂ are equivalence relations

B

\({p_1} \cap {p_2}\) is equivalence relation but \({p_1} \cup {p_2}\) is not so

C

\({p_1} \cup {p_2}\) is equivalence relation but \({p_1} \cap {p_2}\) is not so

D

neither \({p_1} \cap {p_2}\) nor \({p_1} \cup {p_2}\) is equivalence relation.

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14

2020 · Mathematics · Algebra · Sets And Relations

WB JEE 2020

Let the relation p be defined on R by a p b holds if and only if a \(-\) b is zero or irrational, then

A

p is equivalence relation

B

p is reflexive and symmetric but is not transitive

C

p is reflexive and transitive but is not symmetric

D

p is reflexive only

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15

2021 · Mathematics · Algebra · Sets And Relations

WB JEE 2021

Let A, B, C be three non-void subsets of set S. Let (A \(\cap\) C) \(\cup\) (B \(\cap\) C') = \(\phi\) where C' denote the complement of set C in S. Then

A

A \(\cap\) B = \(\phi\)

B

A \(\cap\) B \(\ne\) \(\phi\)

C

A \(\cap\) C = A

D

A \(\cup\) C = A

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16

2021 · Mathematics · Algebra · Sets And Relations

WB JEE 2021

Let R be the real line. Let the relations S and T or R be defined by

\(S = \{ (x,y):y = x + 1,0 < x < 2\} ,T = \{ (x,y):x - y\) is an integer}. Then

A

both S and T are equivalence relations on R

B

T is an equivalence on R but S is not

C

neither S nor T is an equivalence relation on R

D

S is an equivalence relation on R but T is not

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17

2022 · Mathematics · Algebra · Sets And Relations

WB JEE 2022

For the mapping \(f:R - \{ 1\} \to R - \{ 2\}\), given by \(f(x) = {{2x} \over {x - 1}}\), which of the following is correct?

A

f is one-one but not onto

B

f is onto but not one-one

C

f is neither one-one nor onto

D

f is both one-one and onto

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18

2022 · Mathematics · Algebra · Sets And Relations

WB JEE 2022

Let S, T, U be three non-void sets and f : S \(\to\) T, g : T \(\to\) U and composed mapping g . f : S \(\to\) U be defined. Let g . f be injective mapping. Then

A

f, g both are injective.

B

neither f nor g is injective.

C

f is obviously injective.

D

g is obviously injective.

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19

2022 · Mathematics · Algebra · Sets And Relations

WB JEE 2022

A is a set containing n elements. P and Q are two subsets of A. Then the number of ways of choosing P and Q so that P \(\cap\) Q = \(\varphi\) is

A

\({2^{2n\_2n}}{C_n}\)

B

\({2^n}\)

C

\({3^n} - 1\)

D

\({3^n}\)

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20

2022 · Mathematics · Algebra · Sets And Relations

WB JEE 2022

Let R and S be two equivalence relations on a non-void set A. Then

A

R \(\cup\) S is equivalence relation

B

R \(\cap\) S is equivalence relation

C

R \(\cap\) S is not equivalence relation

D

R \(\cup\) S is not equivalence relation

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