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JEE Main 202528 JanuaryEvening Shift
Exam
JEE Main
Year
2025
Date
28 January
Shift
Evening Shift
Subject
Mathematics
Chapter
Permutation and Combination

JEE Main 2025 · 28 January · Evening Shift · Mathematics · Permutation and Combination

The number of natural numbers, between 212 and 999 , such that the...

The number of natural numbers, between 212 and 999 , such that the sum of their digits is 15 , is

Correct answer

64

Step-by-step solution

Let the number be 2ab,a+b=13⇒a,b∈{0,9}⇒6 numbers {(9,4),(8,5)…(4,9)}\begin{aligned} & 2 a b, a+b=13 \\ & \Rightarrow a, b \in\{0,9\} \\ & \Rightarrow 6 \text{ numbers }\{(9,4),(8,5) \ldots(4,9)\} \end{aligned} Similarly, for 3ab,a+b=12⇒73 a b, a+b=12 \Rightarrow 7 numbers For 4ab,a+b=11⇒4 a b, a+b=11 \Rightarrow Numbers For 5ab,a+b=10⇒95 a b, a+b=10 \Rightarrow 9 numbers For 6ab,a+b=9⇒106 a b, a+b=9 \Rightarrow 10 numbers For 7ab,a+b=8⇒97 a b, a+b=8 \Rightarrow 9 numbers For 8ab,a+b=7⇒88 a b, a+b=7 \Rightarrow 8 numbers For 9ab,a+b=6⇒79 a b, a+b=6 \Rightarrow 7 numbers ∴\therefore Total ways =64=64.
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