JAMIA 2021 — Mathematics PYQ

Q: How do I solve JAMIA 2021 Mathematics questions?

Practice JAMIA 2021 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 JAMIA Mathematics questions?

JAMIA 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 JAMIA previous year papers available for free?

Yes. Mathem Solvex provides free access to JAMIA 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

JAMIA 2021 — Mathematics PYQ

JAMIA | Mathematics | 2021

Find the area bounded by the curve y $= ∣∣ x - 1∣ - 2∣$ with X-axis

Choose the correct answer:

Explanation

Step 1: Find the $x$ -intercepts

The bounded area lies where $y = 0$ :

||x - 1| - 2| = 0

|x - 1| - 2 = 0

|x - 1| = 2

x - 1 = 2 \implies x = 3

x - 1 = -2 \implies x = -1

The curve meets the $x$ -axis at $x = -1$ and $x = 3$ .

Step 2: Determine the Vertices

The function $y = ||x - 1| - 2|$ is a "W" shaped graph reflected above the $x$ -axis.

At $x = 1$ , $y = ||1 - 1| - 2| = |-2| = 2$ .
The inner absolute value $|x - 1| - 2$ equals zero at $x = 3$ and $x = -1$ .

Step 3: Setup the Integral

Since the function is non-negative ( $y \geq 0$ ) for all $x$ , the area $A$ is:

A = \int_{-1}^{3} ||x - 1| - 2| \, dx

Step 4: Break the Integral

By symmetry around $x = 1$ , we can calculate the area from $x = 1$ to $x = 3$ and double it:

A = 2 \int_{1}^{3} |(x - 1) - 2| \, dx

A = 2 \int_{1}^{3} |x - 3| \, dx

In the interval $[1, 3]$ , $(x - 3)$ is negative, so $|x - 3| = -(x - 3) = 3 - x$ :

A = 2 \int_{1}^{3} (3 - x) \, dx

A = 2 \left[ 3x - \frac{x^2}{2} \right]_{1}^{3}

A = 2 \left( \left[ 3(3) - \frac{3^2}{2} \right] - \left[ 3(1) - \frac{1^2}{2} \right] \right)

A = 2 \left( \left[ 9 - 4.5 \right] - \left[ 3 - 0.5 \right] \right)

A = 2 (4.5 - 2.5)

A = 2(2)

A = 4

Final Answer:

The area bounded by the curve is $4$ square units.