JEE 2023 — Mathematics PYQ

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Question

JEE 2023 — Mathematics PYQ

JEE | Mathematics | 2023

Let $s_1, s_2, s_3, \dots, s_{10}$ , respectively be the sum to $12$ terms of $10$ A.P.s whose first terms are $1, 2, 3, \dots, 10$ and the common differences are $1, 3, 5, \dots, 19$ , respectively. Then, $\sum_{i=1}^{10} s_i$ .

Choose the correct answer:

Explanation

1. General sum $s_i$ ka formula

Kisi bhi $i^{th}$ A.P. ke liye sum ka formula hota hai:

s_i = \frac{n}{2} [2a_i + (n-1)d_i]

Yahan $n = 12$ hai, toh:

s_i = \frac{12}{2} [2a_i + (12-1)d_i]

s_i = 6 [2a_i + 11d_i]

2. Summation nikalna

Hume $\sum_{i=1}^{10} s_i$ nikalna hai:

\sum_{i=1}^{10} s_i = \sum_{i=1}^{10} 6 [2a_i + 11d_i]

\sum s_i = 12 \sum_{i=1}^{10} a_i + 66 \sum_{i=1}^{10} d_i

3. Values put karna

$\sum a_i$ : Ye $1$ se $10$ tak ka sum hai: $1+2+3+\dots+10 = 55$ .
$\sum d_i$ : Ye pehle $10$ odd numbers ka sum hai: $1+3+5+\dots+19 = 10^2 = 100$ .

Ab in values ko equation mein rakhte hain:

\sum s_i = 12(55) + 66(100)

\sum s_i = 660 + 6600

\sum s_i = 7260

Choose the correct answer:

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