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

$\text{Let } f^1(x) = \frac{3x + 2}{2x + 3}, x \in \mathbb{R} - \left\{ \frac{-3}{2} \right\}$ $\text{For } n \geq 2, \text{ define } f^n(x) = f^1(f^{n-1}(x))$ $\text{If } f^5(x) = \frac{ax + b}{bx + a}, \gcd(a, b) = 1, \text{ then } a + b \text{ is equal to}$

Choose the correct answer:

Explanation

Step 1: Matrix Form

$f^1(x) = \frac{3x+2}{2x+3} \implies M = \begin{pmatrix} 3 & 2 \\ 2 & 3 \end{pmatrix}$

Step 2: Finding $M^2$

$M^2 = \begin{pmatrix} 3 & 2 \\ 2 & 3 \end{pmatrix} \begin{pmatrix} 3 & 2 \\ 2 & 3 \end{pmatrix} = \begin{pmatrix} 13 & 12 \\ 12 & 13 \end{pmatrix}$

Step 3: Finding $M^4$

$M^4 = M^2 \cdot M^2 = \begin{pmatrix} 13 & 12 \\ 12 & 13 \end{pmatrix} \begin{pmatrix} 13 & 12 \\ 12 & 13 \end{pmatrix} = \begin{pmatrix} 313 & 312 \\ 312 & 313 \end{pmatrix}$

Step 4: Finding $M^5$

$M^5 = M^4 \cdot M = \begin{pmatrix} 313 & 312 \\ 312 & 313 \end{pmatrix} \begin{pmatrix} 3 & 2 \\ 2 & 3 \end{pmatrix} = \begin{pmatrix} 1563 & 1562 \\ 1562 & 1563 \end{pmatrix}$

Step 5: Comparing with $f^5(x) = \frac{ax+b}{bx+a}$

$a = 1563, \quad b = 1562$

$\gcd(1563, 1562) = 1$

Step 6: Final Value

$a + b = 1563 + 1562$

$a + b = 3125$

Choose the correct answer:

Explore More