1
JEE Main 2023 (Online) 25th January Morning Shift
Numerical
+4
-1 Let S = {1, 2, 3, 5, 7, 10, 11}. The smaller of non-empty subsets of S that have the sum of all elements a multiple of 3, is _____________.

2
JEE Main 2023 (Online) 24th January Evening Shift
Numerical
+4
-1 The minimum number of elements that must be added to the relation R = {(a, b), (b, c), (b, d)} on the set {a, b, c, d} so that it is an equivalence relation, is __________.

3
JEE Main 2022 (Online) 29th July Morning Shift
Numerical
+4
-1 Let $$S=\{4,6,9\}$$ and $$T=\{9,10,11, \ldots, 1000\}$$. If $$A=\left\{a_{1}+a_{2}+\ldots+a_{k}: k \in \mathbf{N}, a_{1}, a_{2}, a_{3}, \ldots, a_{k}\right.$$ $$\epsilon S\}$$, then the sum of all the elements in the set $$T-A$$ is equal to __________.

4
JEE Main 2022 (Online) 26th July Evening Shift
Numerical
+4
-1 Let $$A=\{1,2,3,4,5,6,7\}$$ and $$B=\{3,6,7,9\}$$. Then the number of elements in the set $$\{C \subseteq A: C \cap B \neq \phi\}$$ is ___________.

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