How do I solve CUET PG 2022 Mathematics questions?

Practice CUET PG 2022 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.

What is the difficulty level of CUET PG Mathematics questions?

CUET PG 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.

Are CUET PG previous year papers available for free?

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

Tip:A–D to answerE for explanationV for videoS to reveal answer

CUET PG 2022 — Mathematics PYQ

CUET PG | Mathematics | 2022

Let f: [2, ∞] → R be the function defined by $f (x) = x^{2} - 4 x + 5$ , then the range of $f$

Choose the correct answer:

(-∞, 0]

Explanation

Step 1: Express the function in vertex form

The function is a quadratic expression:

f(x) = x^2 - 4x + 5

We can complete the square to find the vertex:

f(x) = (x^2 - 4x + 4) + 1

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

Step 2: Analyze the behavior of the function

The expression $f(x) = (x - 2)^2 + 1$ is a parabola that opens upwards because the coefficient of $x^2$ is positive ( $1 > 0$ ).

Vertex: The vertex of the parabola is at $x = 2$ .
Domain: The given domain is $x \in [2, \infty)$ .

Step 3: Find the minimum and maximum values

1. Minimum Value:

Since the domain starts exactly at the $x$ -coordinate of the vertex ( $x = 2$ ), the function will take its minimum value at this point.

f(2) = (2 - 2)^2 + 1

f(2) = 0 + 1 = 1

2. Maximum Value:

As $x$ increases from $2$ towards $\infty$ , the term $(x - 2)^2$ increases indefinitely.

As $x \to \infty$ , $f(x) \to \infty$ .

Step 4: Determine the Rang

The function starts at its minimum value of $1$ and increases without bound. Therefore, the values of $f(x)$ cover the interval:

\text{Range} = [1, \infty)

Final Answer:

The range of the function $f$ is $[1, \infty)$ .