JEE MAIN - Mathematics (2019 - 12th January Evening Slot - No. 17)
Let Z be the set of integers.
If A = {x $$ \in $$ Z : 2(x + 2) (x2 $$-$$ 5x + 6) = 1} and
B = {x $$ \in $$ Z : $$-$$ 3 < 2x $$-$$ 1 < 9},
then the number of subsets of the set A $$ \times $$ B, is
If A = {x $$ \in $$ Z : 2(x + 2) (x2 $$-$$ 5x + 6) = 1} and
B = {x $$ \in $$ Z : $$-$$ 3 < 2x $$-$$ 1 < 9},
then the number of subsets of the set A $$ \times $$ B, is
212
218
210
215
Explanation
A ={x $$ \in $$ z : 2(x+2)(x2 $$-$$ 5x + 6) = 1}
2(x+2)(x2 $$-$$ 5x + 6) = 20 $$ \Rightarrow $$ x = $$-$$ 2, 2, 3
A = {$$-$$2, 2, 3}
B = {x $$\varepsilon $$ Z : $$-$$ < 2x $$-$$ 1 < 9}
B = {0, 1, 2, 3, 4}
A $$ \times $$ B has is 15 elements so number of subsets of A $$ \times $$ B is 215.
2(x+2)(x2 $$-$$ 5x + 6) = 20 $$ \Rightarrow $$ x = $$-$$ 2, 2, 3
A = {$$-$$2, 2, 3}
B = {x $$\varepsilon $$ Z : $$-$$ < 2x $$-$$ 1 < 9}
B = {0, 1, 2, 3, 4}
A $$ \times $$ B has is 15 elements so number of subsets of A $$ \times $$ B is 215.
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