Mathematics · Sequence and Series

JEE Main 2024 — 6 April, Shift 2 — Question 8

A software company sets up $m$ number of computer systems to finish an assignment in 17 days. If 4 computer systems crashed on the start of the second day, 4 more computer systems crashed on the start of the third day and so on, then it took 8 more days to finish the assignment. The value of $m$ is equal to :

Option A:
125
Option B:
150
Correct
Option C:
180
Option D:
160

Answer: B

Step-by-step solution

$\quad 17 \mathrm{~m}=\mathrm{m}+(\mathrm{m}-4)+(\mathrm{m}-4 \times 2) \ldots+\ldots(\mathrm{m}-4 \times 24)$

$17 \mathrm{~m}=25 \mathrm{~m}-4(1+2 \ldots 24)$

$8 \mathrm{~m}=\frac{4 \cdot 24 \cdot 25}{2}=150$

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Exam: JEE Main 2024
Paper: 6 April, Shift 2
Subject: Mathematics
Chapter: Sequence and Series
Topic: Introduction to Sequence and Series

If S(x)=(1+x)+2(1+x)^2+3(1+x)^3+ldots . . +60(1+x)^60, x neq 0 , and (60)^2 S(60)=a(b)^b+b , where a, b in N , then (a+b) equal to

Answer: B

Step-by-step solution

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