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

The value of $12 \int_{0}^{3} |x^2 - 3x + 2| dx$ is

Choose the correct answer:

Explanation

Step 1: Critical points nikalna

Modulus ke andar ka function $f(x) = x^2 - 3x + 2$ hai. Ise factorise karte hain:

x^2 - 3x + 2 = (x - 1)(x - 2)

Function ke signs:

$x \in [0, 1]$ par: Positive $(+)$
$x \in [1, 2]$ par: Negative $(-)$
$x \in [2, 3]$ par: Positive $(+)$

Step 2: Integral ko break karein

Modulus hatane ke liye hum limit ko teen parts mein divide karenge:

\int_{0}^{3} |x^2 - 3x + 2| dx = \int_{0}^{1} (x^2 - 3x + 2) dx - \int_{1}^{2} (x^2 - 3x + 2) dx + \int_{2}^{3} (x^2 - 3x + 2) dx

Step 3: Integration solve karein

$\int (x^2 - 3x + 2) dx = \frac{x^3}{3} - \frac{3x^2}{2} + 2x$

First Part $[0, 1]$ : $(\frac{1}{3} - \frac{3}{2} + 2) - (0) = \frac{2 - 9 + 12}{6} = \frac{5}{6}$
Second Part $[1, 2]$ : $(\frac{8}{3} - 6 + 4) - (\frac{5}{6}) = \frac{2}{3} - \frac{5}{6} = \frac{4 - 5}{6} = -\frac{1}{6}$ (Modulus ki wajah se ye $+1/6$ ho jayega)
Third Part $[2, 3]$ : $(9 - \frac{27}{2} + 6) - (\frac{2}{3}) = \frac{3}{2} - \frac{2}{3} = \frac{9 - 4}{6} = \frac{5}{6}$

Step 4: Total sum nikalna

Sum $= \frac{5}{6} - (-\frac{1}{6}) + \frac{5}{6} = \frac{5}{6} + \frac{1}{6} + \frac{5}{6} = \frac{11}{6}$

Step 5: Question ki value

Hume $12 \times \text{Integral}$ nikalna hai:

\text{Value} = 12 \times \frac{11}{6} = 2 \times 11 = 22

Final Answer:

Iska sahi jawab 22 hai.

Choose the correct answer:

Explore More