Sets & Relations14 questions

Sets & Relations — JEE Maths Practice Questions & Solutions

14 questions on Sets & Relations with full step-by-step solutions, including past-year (PYQ) problems. Free to practice.

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The relation RR defined on the set A={1,2,3,4,5}A = \{1, 2, 3, 4, 5\} by R={(x,y):∣x2−y2∣<16}R = \{(x, y) : |x^2 - y^2| < 16\} is given by:
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A survey shows that 63%63\% of the Americans like cheese whereas 76%76\% like apples. If x%x\% of the Americans like both cheese and apples, then:
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medium
Suppose A1,A2,…,A30A_1, A_2, \ldots, A_{30} are thirty sets each having 55 elements and B1,B2,…,BnB_1, B_2, \ldots, B_n are nn sets each with 33 elements. Let ⋃i=130Ai=⋃j=1nBj=S\bigcup_{i=1}^{30} A_i = \bigcup_{j=1}^{n} B_j = S, and each element of SS belongs to exactly 1010 of the AiA_i and exactly 99 of the BjB_j. Then nn is equal to:
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easy
The relation R={(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)}R = \{(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)\} on the set A={1,2,3}A = \{1, 2, 3\} is:
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easy
The relation RR is defined in A={1,2,3}A = \{1, 2, 3\} by aRbaRb if ∣a2−b2∣≤5|a^2 - b^2| \le 5. Which of the following is false?
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easy
If AA is the set of even natural numbers less than 88 and BB is the set of prime numbers less than 77, then the number of relations from AA to BB is:
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easy
The relation RR is defined on the set of natural numbers as {(a,b):a=2b}\{(a, b) : a = 2b\}. Then R−1R^{-1} is given by:
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easy
If A={1,2,3}A = \{1, 2, 3\}, B={4,5,6}B = \{4, 5, 6\}, which of the following is not a relation from AA to BB?
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easy
Let RR be a relation on the set NN defined by {(x,y):x,y∈N, 2x+y=41}\{(x, y) : x, y \in N,\ 2x + y = 41\}. Then RR is:
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easy
Let SS be the set of points inside a square, TT the set of points inside a triangle and CC the set of points inside a circle. If the triangle and circle intersect each other and are contained in the square, then:
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easy
The smallest set AA such that A∪{1,2}={1,2,3,5,9}A \cup \{1, 2\} = \{1, 2, 3, 5, 9\} is:
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easy
If AA and BB are any two sets, then A∪(A∩B)A \cup (A \cap B) is equal to:
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easy
If A={a,b,c}A = \{a, b, c\}, B={b,c,d}B = \{b, c, d\} and C={a,d,c}C = \{a, d, c\}, then (A−B)×(B∩C)(A - B) \times (B \cap C) is equal to
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easy
Let A={1,2,3,4}A = \{1, 2, 3, 4\}, and let R={(2,2),(3,3),(4,4),(1,2)}R = \{(2, 2), (3, 3), (4, 4), (1, 2)\} be a relation on AA. Then RR is:
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