1
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 __________.

2
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 ___________.

3
JEE Main 2022 (Online) 25th July Evening Shift
Numerical
+4
-1

Let $$A=\{1,2,3,4,5,6,7\}$$. Define $$B=\{T \subseteq A$$ : either $$1 \notin T$$ or $$2 \in T\}$$ and $$C=\{T \subseteq A: T$$ the sum of all the elements of $$T$$ is a prime number $$\}$$. Then the number of elements in the set $$B \cup C$$ is ________________.

4
JEE Main 2022 (Online) 28th June Morning Shift
Numerical
+4
-1

Let R1 and R2 be relations on the set {1, 2, ......., 50} such that

R1 = {(p, pn) : p is a prime and n $$\ge$$ 0 is an integer} and

R2 = {(p, pn) : p is a prime and n = 0 or 1}.

Then, the number of elements in R1 $$-$$ R2 is _______________.