JEE 2023 — Mathematics PYQ

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Question

JEE 2023 — Mathematics PYQ

JEE | Mathematics | 2023

Number of 4-digit numbers (the repetition of digits is allowed) which are made using the digits 1, 2, 3 and 5 and are divisible by 15 , is equal to

Choose the correct answer:

Explanation

Step 1: Divisibility Conditions

$15$ se divide hone ke liye number ko $3$ aur $5$ dono se divide hona chahiye.

$\text{Digits given: } \{1, 2, 3, 5\}$

Step 2: Condition for 5

Unit digit ( $D$ ) hamesha 5 hona chahiye.

D = 5 \implies \text{(1 option)}

Step 3: Condition for 3

Sum of digits $A+B+C+D$ must be divisible by $3$ .

A+B+C+5 \equiv 0 \pmod 3 \implies A+B+C \equiv 1 \pmod 3

Step 4: Possible Combinations for (A, B, C)

Niche diye gaye combinations ka sum $(A+B+C)$ check karein:

Digits Set	Arrangements (p!n!)	Count
$\{3, 3, 1\}$	$\frac{3!}{2!}$	$3$
$\{1, 1, 2\}$	$\frac{3!}{2!}$	$3$
$\{1, 1, 5\}$	$\frac{3!}{2!}$	$3$
$\{3, 2, 2\}$	$\frac{3!}{2!}$	$3$
$\{3, 5, 5\}$	$\frac{3!}{2!}$	$3$
$\{3, 2, 5\}$	$3!$	$6$

Step 5: Final Answer

\text{Total Numbers} = 3 + 3 + 3 + 3 + 3 + 6

\text{Total Numbers} = 21

Choose the correct answer:

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