1
JEE Main 2019 (Online) 12th January Morning Slot
+4
-1
Let S = {1, 2, 3, … , 100}. The number of non-empty subsets A of S such that the product of elements in A is even is :
A
250 – 1
B
250 (250 $$-$$ 1)
C
2100 $$-$$ 1
D
250 + 1
2
JEE Main 2019 (Online) 10th January Morning Slot
+4
-1
In a class of 140 students numbered 1 to 140, all even numbered students opted Mathematics course, those whose number is divisible by 3 opted Physics course and those whose number is divisible by 5 opted Chemistry course. Then the number of students who did not opt for any of the three courses is
A
42
B
102
C
1
D
38
3
JEE Main 2018 (Online) 16th April Morning Slot
+4
-1
Let N denote the set of all natural numbers. Define two binary relations on N as R = {(x, y) $$\in$$ N $$\times$$ N : 2x + y = 10} and R2 = {(x, y) $$\in$$ N $$\times$$ N : x + 2y = 10}. Then :
A
Range of R1 is {2, 4, 8).
B
Range of R2 is {1, 2, 3, 4}.
C
Both R1 and R2 are symmetric relations.
D
Both R1 and R2 are transitive relations.
4
JEE Main 2018 (Offline)
+4
-1
Two sets A and B are as under :

A = {($$a$$, b) $$\in$$ R $$\times$$ R : |$$a$$ - 5| < 1 and |b - 5| < 1};

B = {($$a$$, b) $$\in$$ R $$\times$$ R : 4($$a$$ - 6)2 + 9(b - 5)2 $$\le$$ 36 };

Then
A
neither A $$\subset$$ B nor B $$\subset$$ A
B
B $$\subset$$ A
C
A $$\subset$$ B
D
A $$\cap$$ B = $$\phi$$ ( an empty set )
EXAM MAP
Medical
NEET