Question bank/JEE Main/Mathematics

Identify the following statements for in order
Let X and Y be two sets.
S-$1:X \cap (Y \cup X)^{'} = \phi$
S-$2\:\ If\ X \cup Y$ has m elements and $X \cap Y$ has n elements
then symmetric difference $X\Delta Y$ has m - n elements.
S-$3:\ If\ |x - 5| + |x - 11| = |2x - 16|$, then
$x \leq 5\ or\ x \geq 11$
S-$4:|x - a| + |x - b| = b - a$ has infinitely many solutions, for
a<b.

ATTTTBFFTTCTFFFDTFTF

Show answer and solution▾

[IMAGE] S-2: $n(x \cup y) = m$
$n(x \cap y) = n$
$n(x\Delta y) = n(x \cup y) - n(x \land y)$
= m - n
S-3: $|x - 5| + |x - 1| \mid = (2x - 16)$
Case 1: x < 5
- x + 5 - x +11 = - 2x + 16
(LHS = RHS)
Case 2: $5 \leq x < 8$
$\Rightarrow x - 5 - x + 11 \neq - 2x + 16$
Case 3: $8 \leq x < 11$
$x - 5 - x + 11 + 2x - 16$
Case 4: $x \geq 11$
$n - 5 + x - 11 = 2n - 16$
$\Rightarrow \ \$ (LHS = RHS)
S- 4: $|n - a| + |x - b| = b - a$
for a < b
Case 1: x < a
$–\ x\ + \ a\ –\ x\ + \ b$
$= \ \ –\ 2\ x\ + \ a\ + \ b\ \neq b - a$
Case 2: $a < x < b$
$x - a - x + b = b - a$
Case 3: $x > b$
$x - a + x - b$
$2x - a - b \neq b - a$

Source: Grass-G / M-05 Mathematics Paper 10 October.docx