Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app

NTA Abhyas JEE Main2020MathematicsSets and RelationsPractice

Let Z be the set of integers, if A = x ∈ Z : x - 3 x 2 - 5 x + 6 = 1 and B = x ∈ Z : 10 < 3 x + 1 < 22 , then the number of subsets of the set A × B is

Options

A2 6
B2 8
C2 15
D2 9

Correct answer

A. 2 6

Step-by-step solution

For A , x - 3 = 1 ⇒ x = 2,4 or x 2 - 5 x + 6 = 0 ⇒ x = 2,3 but x ≠ 3 ∴ A = 2,4   For B , B = 4 ,5 , 6 n A × B = 6 ∴ number of subsets = 2 6

Practice Sets and Relations on Quantrex Academy →

More from Sets and Relations

Let S = 1, 2, 3, , 10 . Consider the set X = R : R is an equivalence relation on the set S such that R has exactly 42 elements . Then the number of elements in X is _____________. 2026 Consider the relation R on the set -2,-1,0,1,2 defined by (a, b) R if and only if 1+ab > 0 . Then, among the statements: I. The number of elements in R is 17 II. R is an equivalenc 2026 Let R = (x, y) N N : _e(x + y) 2 . Then the minimum number of elements, required to be added in R to make it a transitive relation, is __________. 2026 Let A = 1, 4, 7 and B = 2, 3, 8 . Then the number of elements, in the relation R = ((a₁, b₁), (a₂, b₂)) ((A B) (A B)) : a₁ + b₂ divides a₂ + b₁ is _______. 2026 Let A = 2, 3, 4, 5, 6 . Let R be a relation on the set A A given by (x, y) R (z, w) if and only if x divides z and y w . Then the number of elements in R is _______. 2026 Let R be a relation defined on the set 1,2,3,4 1,2,3,4 by R = ((a, b),(c, d)): 2 a+3 b=3 c+4 d . Then the number of elements in R is 2026 Let A = 0,1,2, , 9 . Let R be a relation on A defined by (x, y) R if and only if |x-y| is a multiple of 3. Given below are two statements: Statement I : n( R )=36 . Statement II : 2026 Let A = -2,-1,0,1,2,3,4 . Let R be a relation on A defined by x Ry if and only if 2 x+y 2 . Let l be the number of elements in R. Let m and n be the minimum number of elements requ 2026 Full Sets and Relations list All NTA Abhyas JEE Main PYQs