Test Index

IIT JEE Advanced 2006 Paper 1

Paragraph Type

This section contains 4 paragraphs. Based on each paragraph, there are 3 questions. Each of these questions has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct.

Paragraph for Questions 101–103:

A =

\begin{bmatrix} 1 & 0 & 0 \\ 2 & 1 & 0 \\ 3 & 2 & 1 \end{bmatrix}

, if

U_1, U_2

and

U_3

are column matrix satisfying

AU_1

\begin{bmatrix} 1 \\ 0 \\ 0 \end{bmatrix}

AU_2

\begin{bmatrix} 2 \\ 3 \\ 0 \end{bmatrix}

AU_3

\begin{bmatrix} 2 \\ 3 \\ 1 \end{bmatrix}

and U is a 3 × 3 matrix whose column are

U_1, U_2, U_3

, then answer the following questions.

Section: Mathematics

Question : 103 of 120

Marks: +1, -0

The value of

\begin{bmatrix} 3 & 2 & 0 \end{bmatrix} \cup \begin{bmatrix} 3 \\ 2 \\ 0 \end{bmatrix}

[JEE Adv 2006 P1]

[5]
$\left[ \frac{5}{2} \right]$
[4]
$\left[ \frac{3}{2} \right]$

Validate

Solution:

We have

\begin{bmatrix} 3 & 2 & 0 \end{bmatrix} \begin{bmatrix} 1 & 2 & 2 \\ -2 & -1 & -1 \\ 1 & -4 & -3 \end{bmatrix} \begin{bmatrix} 3 \\ 2 \\ 0 \end{bmatrix}

\begin{bmatrix} 3 & 2 & 0 \end{bmatrix} \begin{bmatrix} 7 \\ -8 \\ -5 \end{bmatrix}

= [21 – 16] = [5]

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