CUET PG 2023 — Mathematics PYQ

Q: How do I solve CUET PG 2023 Mathematics questions?

Practice CUET PG 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 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.

Q: 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.

Question

CUET PG 2023 — Mathematics PYQ

CUET PG | Mathematics | 2023

$a = 2 \hat{i} + 2 \hat{j} + 3 \hat{k}, b = - \hat{i} + 2 \hat{j} + \hat{k}$ and $c = 3 \hat{i} + \hat{j}$ are such that $a + y b$ is perpendicular to $c$ then determine the value of $y$ ?

Choose the correct answer:

Explanation

Step 1: Find the vector $\vec{a} + y\vec{b}$

Given:

$\vec{a} = 2\hat{i} + 2\hat{j} + 3\hat{k}$
$\vec{b} = -\hat{i} + 2\hat{j} + \hat{k}$

Adding them with the scalar $y$ :

\vec{a} + y\vec{b} = (2\hat{i} + 2\hat{j} + 3\hat{k}) + y(-\hat{i} + 2\hat{j} + \hat{k})

\vec{a} + y\vec{b} = (2 - y)\hat{i} + (2 + 2y)\hat{j} + (3 + y)\hat{k}

Step 2: Set the Dot Product with $\vec{c}$ to Zero

Since $(\vec{a} + y\vec{b}) \perp \vec{c}$ , we have:

(\vec{a} + y\vec{b}) \cdot \vec{c} = 0

Given $\vec{c} = 3\hat{i} + \hat{j} + 0\hat{k}$ , we substitute the components:

[(2 - y)\hat{i} + (2 + 2y)\hat{j} + (3 + y)\hat{k}] \cdot [3\hat{i} + 1\hat{j} + 0\hat{k}] = 0

Multiplying corresponding components:

3(2 - y) + 1(2 + 2y) + 0(3 + y) = 0

Step 3: Solve for $y$

Expand the equation:

6 - 3y + 2 + 2y = 0

Combine the like terms:

8 - y = 0

y = 8

Answer: The value of $y$ is 8.

Choose the correct answer:

Explore More