JEE 2023 — Mathematics PYQ

Q: How do I solve JEE 2023 Mathematics questions?

Practice JEE 2023 Mathematics previous year questions with step-by-step solutions on Mathem Solvex. Each question includes a detailed explanation and video solution to help you master the concept quickly.

Q: What is the difficulty level of JEE Mathematics questions?

JEE Mathematics questions range from moderate to advanced difficulty. Consistent practice with official previous year papers and topic-wise drills on Mathem Solvex is the most effective preparation strategy.

Q: Are JEE previous year papers available for free?

Yes. Mathem Solvex provides free access to JEE previous year question papers and topic-wise PDFs. You can download them or attempt them as timed live mock tests directly on the platform.

Question

JEE 2023 — Mathematics PYQ

JEE | Mathematics | 2023

Let $A_1, A_2, A_3$ be three A.P.s with common difference $d$ and first terms $A, A+1, A+2$ . Let $a, b, c$ be $7^{th}, 9^{th}, 17^{th}$ terms of $A_1, A_2, A_3$ respectively. If $\begin{vmatrix} a & 7 & 1 \\ 2b & 17 & 1 \\ c & 17 & 1 \end{vmatrix} + 70 = 0$ and $a = 29$ , find the sum of first $20$ terms of an A.P. with first term $c - a - b$ and common difference $\frac{d}{12}$ .

Choose the correct answer:

Explanation

Solving Steps

1. Terms define karein:

$a = A + 6d$
$b = (A+1) + 8d = A + 8d + 1$
$c = (A+2) + 16d = A + 16d + 2$

2. Determinant expand karein ( $R_2 \to R_2 - R_3$ ):

\begin{vmatrix} a & 7 & 1 \\ 2b-c & 0 & 0 \\ c & 17 & 1 \end{vmatrix} + 70 = 0

-(2b - c)(7 - 17) + 70 = 0

(2b - c)(10) + 70 = 0

2b - c + 7 = 0

3. $A$ aur $d$ ki value nikalein:

2(A + 8d + 1) - (A + 16d + 2) + 7 = 0

2A + 16d + 2 - A - 16d - 2 + 7 = 0

A + 7 = 0 \implies \mathbf{A = -7}

Given $a = 29$ :

-7 + 6d = 29 \implies 6d = 36 \implies \mathbf{d = 6}

4. $b$ aur $c$ calculate karein:

$b = -7 + 8(6) + 1 = 42$
$c = -7 + 16(6) + 2 = 91$

5. Nayi A.P. ka Sum ( $S_{20}$ ):

First term ( $a'$ ) $= c - a - b = 91 - 29 - 42 = \mathbf{20}$
Common difference ( $d'$ ) $= \frac{d}{12} = \frac{6}{12} = \mathbf{0.5}$

S_{20} = \frac{20}{2} [2(20) + (19)(0.5)]

S_{20} = 10 [40 + 9.5]

S_{20} = 10 \times 49.5 = \mathbf{495}

Final Answer: 495

Choose the correct answer:

Explore More