NIMCET PYQs 17 Set Thory Questions with All Concept - NIMCET Preparation

🚀 Supercharge Your NIMCET Exam Prep with Aspire Study Coaching! 📚 Let A and B be sets, A∩X=B∩X=ϕ and A∪X=B∪X for some set X, relation between A and B. (a) A=B (b) A∪B=X (c) B=X (d) A=X [NIMCET 2023] A survey is done among a population of 200 people who like either tea or coffee. It is found that 60% of the population like tea and 72% of the population like coffee. Let x be the number of people who like both tea & coffee. Let 𝑚≤𝑥≤𝑛, then choose the correct option. (a) n-m=56 (b) n-m=28 (c) n-m=32 (d) n+m=92 [NIMCET 2022] There are two sets A and B with |A|=𝑚 and |B|= 𝑛. If |𝑃(𝐴)|−|𝑃(𝐵)|=112 then choose the wrong option (where |A| denotes the cardinality of A, and P(A) denotes the power set of A) (a) m+n=11 (b) 2n-m=1 (c) 2m-n=1 (d) 3n-m=5 [NIMCET 2022] If A={1,2,3,4} and B={3,4,5}, then the number of elements in (A∪B)×(A∩B)×(AΔB) (a) 18 (b) 20 (c) 24 (d) 30 [NIMCET 2021] Suppose 𝐴_1,𝐴_2,…,𝐴_30 are 30 sets each with five elements and 𝐵_1,𝐵_2,𝐵_3,…,𝐵_𝑛 are n sets (each with three elements) such that ⋃24_(𝑖=1)^30▒𝐴_𝑖 =⋃24_(𝑗=1)^𝑛▒𝐵_𝑗 =𝑆 and each element of S belongs to exactly ten of the 𝐴_𝑖's and exactly 9 of the 𝐵_𝑗^′𝑠. Then n= (a) 15 (b) 45 (c) 75 (d) 90 [NIMCET 2021, 2019, 2008] If X and Y are two sets, then X∩Y^'∩(X∪Y)' is (a) X' (b) 𝑌^′ (c) ϕ (d) None of the above [NIMCET 2021] In a class of 50 students, it was found that 30 students read "Hitavad", 35 students read "Hindustan" and 10 read neither. How many students read both: "Hitavad" and "Hindustan" newspapers? (a) 25 (b) 20 (c) 15 (d) 30 [NIMCET 2020] If 𝐴= {4^𝑥 – 3𝑥 −1:𝑥 ∈ 𝑁} and 𝐵={9(𝑥 −1):𝑥 ∈ 𝑁}, where ℕ is the set of natural numbers, then (a) A ⊂ B (b) A⊆ B (c) A ⊃ B (d) A ⊇ B [NIMCET 2020] If A= {x,y,z}, then the number of subsets in power set of A is (a) 6 (b) 8 (c) 7 (d) 9 [NIMCET 2020] If A is a subset of B and B is a subset of C, then cardinality of A∪ B ∪ C is equal to (a) Cardinality of C (b) Cardinality of B (c) Cardinality of A (d) None of the above [NIMCET 2020] Number of onto (surjective) functions from A to B if 𝑛(𝐴)=6 and 𝑛(𝐵)=3, is (a) 2^6−2 (b) 3^6−3 (c) 340 (d) 540 [NIMCET 2019] Let 𝑃={𝜃:sin⁡〖𝜃−cos⁡〖𝜃=√2 cos⁡𝜃 〗 〗 } and 𝑄={𝜃:sin⁡〖𝜃+cos⁡〖𝜃=√2 sin⁡𝜃 〗 〗 } be two sets. Then (a) P⊂Q and Q-P≠0 (b) P⊄Q (c) Q⊄P (d) P=Q [NIMCET 2018] Which of the following functions is the inverse of itself? (a) 𝑓(𝑥)=(1−𝑥)/(1+𝑥) (b) 𝑓(𝑥)=3^log⁡𝑥 (c) 𝑓(𝑥)=3^𝑥(𝑥+1) (d) None of these [NIMCET 2018] In a survey where 100 students reported which subjects, they like, 32 students in total liked Mathematics, 38 students liked Business and 30 students liked Literature. Moreover 7 students liked both Mathematics and Literature, 10 students liked both Mathematics and Business, 8 students liked both Business and Literature, 5 students liked all three subjects. Then the number of people who liked exactly one subject is (a) 60 (b) 65 (c) 70 (d) 78 [NIMCET 2018] The function 𝑓(𝑥)=log⁡(𝑥+√(𝑥^2+1)) is (a) An even function (b) An odd function (c) A periodic function (d) Neither an even nor an odd function [NIMCET 2018] If the graph of 𝑦 = (𝑥 – 2)^2 – 3 is shifted by 5 units up along y-axis and 2 units to the right along the x-axis, then the equation of the resultant graph is (a) 𝑦 = 𝑥^2 + 2 (b) 𝑦 = (𝑥 – 2)^2 + 5 (c) 𝑦 = (𝑥 + 2)^2 + 2 (d) 𝑦 = (𝑥 – 4)^2 + 2 [NIMCET 2017] The number of elements in the power set P(S) of the set S = {2,(1,4)} is (a) 2 (b) 4 (c) 8 (d) 10 [NIMCET 2017] Let A and B two sets containing four and two elements respectively. The number of subsets of the A × B, each having at least three elements is (a) 270 (b) 239 (c) 219 (d) 256 [NIMCET 2017] Two finite sets A and B are having m and n elements. The total number of subsets of the first set is 56 more than the total number of subsets of the second set. The value of m and n are (a) 7, 6 (b) 6, 3 (c) 5, 3 (d) 8, 7 [NIMCET 2016] A professor has 24 text books on computer science and is concerned about their coverage of the topics (P) compilers, (Q) data structures and (R) operating systems. The following data gives the number of books that contain material on these topics: n(P) = 8, n(Q) = 13, n(R) = 13, n(P∩Q) = 3, n(P∩Q∩R) = 2, where n(x) is the cardinality of the set x. Then, the number of text books that have no material of compiler is (a) 4 (b) 8 (c) 12 (d) 16 [NIMCET 2015] The number of one-to-one functions from {1, 2, 3} to {1, 2, 3, 4, 5} is (a) 125 (b) 243 (c) 10 (d) 60 [NIMCET 2015] #NIMCET #nimcet2024 #AspireStudy #Coaching #nimcet_coaching #trending