Mathematics questions
18011 published questions with worked solutions.
- Set A has m elements and set B has n elements. If the total number of subsets of A is 112 more than the total number of subsets...
- Let X= n N:1 n 50 . If A= n X:n is a multiple of 2 and B= n X:n is a multiple of 7 , then the number of elements in the smallest...
- The sum of all the elements in the set n 1,2, ,100 H.C.F. of n and 2040 is 1 is equal to (JEE Main 2021)
- Let A= n N n^2 n+10 , 000 , B= 3k+1 k N and C= 2k k N , then the sum of all the elements of the set A (B-C) is equal to (JEE Main...
- If A= x R :|x-2|>1 , B= x R : x^2-3 >1 , C= x R :|x-4| 2 and Z is the set of all integers, then the number of subsets of the set...
- Let S= 1,2,3,4,5,6,9 . Then the number of elements in the set T= A S:A and the sum of all the elements of A is not a multiple of...
- Let A= n N : H.C.F. (n,45)=1 and B= 2k:k 1,2, ,100 . Then the sum of all the elements of A B is (JEE Main 2022)
- Let A= 1,a_1,a_2, ,a_ 18 ,77 be a set of integers with 1<a_1<a_2< <a_ 18 <77. Let the set A+A= x+y:x,y A contain exactly 39...
- Let A= 1,2,3,4,5,6,7 . Define B= T A: either 1 T or 2 T and C= T A: the sum of all the elements of T is a prime number . Then the...
- Let r be a relation from R (set of real numbers) to R defined by r= (a,b) a,b R and a-b+ 3 is an irrational number . The relation...
- The number of reflexive relations of a set with four elements is equal to
- Let R be the relation on the set R of all real numbers defined by aRb if |a-b| 1, then R is
- Let A= 1,2,3 and B= 2,3,4 , then which of the following relations is a function from A to B?
- R is a relation on N given by R= (x,y):4x+3y=20 . Which of the following belongs to R?
- Which of the following statements is not correct for the relation R defined by aRb if and only if b lives within one kilometre...
- Let W denote the words in the English dictionary. Define the relation R by R= (x,y) W W: the words x and y have at least one...
- On the set N of all natural numbers define the relation R by aRb if and only if the GCD of a and b is 2, then R is
- If R is an equivalence relation on a set A, then R^ -1 is
- If R is a relation defined as aRb iff |a-b|>0, then the relation is
- 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 and T= (x,y):x-y is an integer...