Let S={4,6,9} and T={9,10,11, ldots, 1000} . If A=left{a_{1}+a_{2}+ldots+a_{k}: k ∈ N, a_{1}, a

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1.Set Theory

hard

Let $S=\{4,6,9\}$ and $T=\{9,10,11, \ldots, 1000\}$. If

$A=\left\{a_{1}+a_{2}+\ldots+a_{k}: k \in N, a_{1}, a_{2}, a_{3}, \ldots, a_{k} \in S\right\}$ then the sum of all the elements in the set $T - A$ is equal to $......$

$10$

$9$

$11$

$12$

(JEE MAIN-2022)

$S =\{4,6,9\} \quad T =\{9,10,11 \ldots 1000\}$

$A \left\{ a _{1}+ a _{2}+\ldots . .+ a _{ k }: K \in N \right\} \,and\, a _{ i } \in S$

Here by the definition of set '$A$'

$A=\{a: a=4 x+6 y+9 z\}$

Except the element $11$,every element of set $T$ is of of the form $4 x+6 y+9 z$ for some $x, y, z \in W$

$\therefore T – A =\{11\}$

Standard 11

Mathematics

normal

(KVPY-2017)

hard

(JEE MAIN-2021)

normal

hard

(JEE MAIN-2024)

hard