JEE Main202524 Jan 2025Evening ShiftMathematicsSets and RelationsActual

Let A = x (0, )- 2 : _ (2 / ) | x|+ _ (2 / ) | x|=2 and B = x 0: x ( x -4)-3| x -2|+6=0 . Then n ( A B ) is equal to :

Options

Correct answer

B. 8

Step-by-step solution

aligned & A : _ 2 | x |+ _ 2 | x |=2 & _ 2 (| x x |)=2 & | 2 x |= 8 ^2 aligned Number of solution 4 B : let x = t 2 then t ^2-4 t -3 t +6+6=0 aligned & t ^2-7 t +12=0 & t =3,4 & x =9,16 aligned Total number of solutions n ( ~A ~B )=4+4=8

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 JEE Main PYQs