Question 1 :
In order that a relation R defined on a non-empty set A is an equivalence relation, it is sufficient, if R
Question 2 :
If A = {1, 2, 3}, B{3, 4}, C{4, 5, 6}. Then, A ∪ (B ∩ C) is
Question 3 :
Let X be a family of sets and R be a relation on X defined by ′A is disjoint from B<sup>′</sup>. Then, R is
Question 4 :
<p>Universal set, U = {x : x<sup>5</sup> − 6x<sup>4</sup> + 11x<sup>3</sup> − 6x<sup>2</sup> = 0}</p> <p>And A = {x : x<sup>2</sup> − 5x + 6 = 0}</p> <p> B = {x : x<sup>2</sup> − 3x + 2 = 0}</p> <p>Then, (A ∩ B)′ is equal to</p>
Question 5 :
A, B and C are three non-empty sets. If A ⊂ B and B ⊂ C, then which of the following is true?
Question 6 :
In a class of 45 students, 22 can speak Hindi and 12 can speak English only. The number of students, who can speak both Hindi and English, is
Question 7 :
The relation R = {(1,3),(3,5)} is defined on the set with minimum number of elements of natural numbers. The minimum number of elements to be included in R so that R is an equivalence relation, is
Question 9 :
<p>Let A be the set of all students in a school. A relation R is defined on A as follows:</p> <p>$"\text{aRb}$ iff a and b have the same teacher”</p>
Question 10 :
Let $A=R-\left\{3\right\},B=R-\left\{1\right\} $ and $f:A \rightarrow B $ defined by $ f(x)\displaystyle =\frac{x-2}{x-3}$ Is $f$ bijective ? <br>If yes enter 1 else enter 0
Question 11 :
The number of solutions of {tex}\log_{sinx}2^{tanx}>0{/tex} in the interval of {tex} \left( 0 , \frac { \pi } { 2 } \right) {/tex}
Question 12 :
Let R be a relation on a set A such that R = R<sup> − 1</sup>, then R is
Question 13 :
If the function {tex} g ( x ) = \left\{ \begin{array} { l l } { k \sqrt { x + 1 } , } & { 0 \leq x \leq 3 } \\ { m x + 2 , } & { 3 < x \leq 5 } \end{array} \text { } \right. {/tex} is differentiable, then the value of {tex} k + m {/tex} is<br>
Question 14 :
A class has 175 students. The following data shows the number of students opting one or more subjects. Mathematics 100; Physics 70; Chemistry 40; Mathematics and Physics 30; Mathematics and Chemistry 28; Physics and Chemistry 23; Mathematics, Physics and Chemistry 18. Hoe many students have offered Mathematics alone?
Question 15 :
If A and B are two sets such that $n\left( A \cap \overline{B} \right) = 9,n\left( \overline{A} \cap B \right) = 10$ and n(A∪B) = 24, then n(A×B)=
Question 17 :
For any two sets A and B, A − (A − B) equals
Question 18 :
In an election, two contestants A and B contested x% of the total voters voted for A and (x+20)% for B. If 20% of the voters did not vote, then x=
Question 19 :
Let 𝒰 be the universal set for sets A and B such that n(A) = 200, n(B) = 300 and n(A∩B) = 100. Then, n(A′ ∩ B′) is equal to 300, provided that n( 𝒰) is equal to
Question 20 :
Consider the following relations:<br> {tex} R = \{ ( x , y ) | x , y {/tex}are real numbers and {tex}x = w y{/tex} for some rational number {tex}w\}{/tex}<br> {tex}S = \left\{ \begin{array} { l } { \left( \frac { m } { n } , \frac { p } { q } \right) | m , n , p \text { and } q } \ \end{array} \right\}{/tex} are integers such that {tex}n , q \neq 0{/tex} and {tex}q m = p n{/tex}. Then
Question 21 :
<p>If sets A and B are defined as</p> <p>$A = \left\{ \left( x,\ y \right):y = \frac{1}{x},0 \neq x \in R \right\}$,</p> <p>B = {(x, y):y=−x, x∈R}, then</p>
Question 22 :
Let A = {ONGC, BHEL, SAIL, GAIL, IOCL} and R be a relation defined as “two elements of A are related if they share exactly one letter”. The relation R is
Question 23 :
Let A and B be two sets, then (A∪B)<sup>′</sup> ∪ (A<sup>′</sup>∩B)is equal to
Question 24 :
Let R and S be two equivalence relations on a set A. Then,
Question 25 :
Two points P and Q in a plane are related if OP = OQ, where O is a fixed point. This relation is
Question 26 :
Let X = {1, 2, 3, 4, 5} and Y = {1, 3, 5, 7, 9}. Which of the following is/are not relations from X to Y?
Question 27 :
In a class of 35 students, 17 have taken Mathematics, 10 have taken Mathematics but not Economics. If each student has taken either Mathematics or Economics or both, then the number of students who have taken Economics but not Mathematics is
Question 28 :
Let L denote the set of all straight lines in a plane. Let a relation R be defined by α R β ⇔ α⊥β, α, β ∈ L. Then R is
Question 29 :
Let A be a set represented by the squares of natural number and x, y are any two elements of A. Then,
Question 30 :
The number of solution(s) of the equation {tex} x ^ { 2 } - 2 - 2 [ x ] = 0 {/tex} ([.] denotes the greatest integer function) is (are)
Question 31 :
If a set A contains n elements, then which of the following cannot be the number of reflexive relations on the set A?
Question 33 :
Which one of the following relations on R is an equivalence relation?
Question 34 :
<p>If A is a non-empty set, then which of the following is false?</p> <p>p : There is at least one reflexive relation on A</p> <p>q : There is at least one symmetric relation on A</p>
Question 35 :
If A = {1, 2, 3, 4, 5, 6}, then how many subsets of A contain the elements 2, 3 and 5?
Question 36 :
The range of the function {tex} f ( x ) = \sin ^ { - 1 } \left[ x ^ { 2 } + \frac { 1 } { 2 } \right] + \cos ^ { - 1 } \left[ x ^ { 2 } - \frac { 1 } { 2 } \right] {/tex} where [-] is the greatest integer function, is<br>
Question 37 :
Let R be a reflexive relation on a set A and I be the identity relation on A. Then,
Question 38 :
The number of elements in the set {(a,b) : 2a<sup>2</sup> + 3b<sup>2</sup> = 35, a, b ∈ Z}, where Z is the set of all integers, is
Question 39 :
In a city 20% of the population travels by car, 50% travels by bus and 10% travels by both car and bus. Then, persons travelling by car or bus is
Question 40 :
Let A = {1,2,3,4}, and let R = {(2,2), (3,3), (4,4), (1, 2)} be a relation on A. Then, R is
Question 41 :
Let $U=R$. If $A=(x\epsilon R : 0 < x < 2), B=(x\epsilon R: 1 < x \leq 3)$, which of the following is false?
Question 42 :
Let A = {1, 2, 3, 4}, B = {2, 4, 6}. Then, the number of sets C such that A ∩ B ⊆ C ⊆ A ∪ B is
Question 43 :
Let {tex} P {/tex} be the relation defined on the set of all real numbers such that {tex} P = \left\{ ( a , b ) : \sec ^ { 2 } a - \tan ^ { 2 } b = 1 \right\} . {/tex} Then {tex} P {/tex} is<br>
Question 44 :
Consider the set A of all determinants of order 3 with entries 0 or 1 only. Let B be the subset of A consisting of all determinants with value 1. Let C be the subset of the set of all determinants with value − 1. Then
Question 45 :
Out of 800 boys in a school 224 played cricket, 240 played hockey and 336 played basketball. Of the total, 64 played both basketball and hockey; 80 played cricket and basketball and 40 played cricket and hockey; 24 played all the three games. The number of boys who did not play any game is
Question 46 :
If A = {a,b, c}, B = {b, c, d} and C = {a, d, c}, then (A−B) × (B ∩ C) is equal to
Question 48 :
Let X be the set of all engineering colleges in a state of Indian Republic and R be a relation on X defined as two colleges are related iff they are affiliated to the same university, then R is
Question 49 :
If A = {1, 2, 3, 4}, then the number of subsets of set A containing element 3, is
Question 50 :
If a N = {a x : x ∈ N} and b N ∩ c N = d N, where b, c ∈ N then