1
NDA Mathematics 1st September 2024
MCQ (Single Correct Answer)
+2.5
-0.833
Change Language

Consider the following in respect of the matrices  $\rm P=\begin{bmatrix}0&c&-b\\\ -c&0&a\\\ b&-a&0\end{bmatrix}\ and\ \rm Q=\begin{bmatrix}a^2&ab&ac\\\ ab&b^2&bc\\\ ac&bc&c^2\end{bmatrix}$

I. PQ is a null matrix. 

II. QP is an identity matrix of order 3. 

III. PQ = QP

Which of the above is/are correct? 

1
I only 
2
II only
3
I and III
4
II and III
2
NDA Mathematics 1st September 2024
MCQ (Single Correct Answer)
+2.5
-0.833
Change Language

Direction : Consider the following for the items that follow :  

Let $\rm A=\begin{bmatrix}3&-3&4\\\ 2&-3&4\\\ 0&-1&1\end{bmatrix}$

What is A(adj A) equal to?  
1
$\rm \begin{bmatrix}5&0&0\\\ 0&5&0\\\ 0&0&5\end{bmatrix}$
2
$\rm \begin{bmatrix}2&0&0\\\ 0&2&0\\\ 0&0&2\end{bmatrix}$
3
$\rm \begin{bmatrix}1/2&0&0\\\ 0&1/2&0\\\ 0&0&1/2\end{bmatrix}$
4
$\rm \begin{bmatrix}1&0&0\\\ 0&1&0\\\ 0&0&1\end{bmatrix}$
3
NDA Mathematics 1st September 2024
MCQ (Single Correct Answer)
+2.5
-0.833
Change Language

Direction : Consider the following for the items that follow :  

Let $\rm A=\begin{bmatrix}3&-3&4\\\ 2&-3&4\\\ 0&-1&1\end{bmatrix}$

What is A-1 equal to?  
1
$\rm \begin{bmatrix}1&-1&0\\\ -2&3&-4\\\ -2&3&-3\end{bmatrix}$
2
$\rm \begin{bmatrix}1/2&-1/2&0\\\ -1&3/2&-2\\\ -1&3/2&-3/2\end{bmatrix}$
3
$\rm \begin{bmatrix}2&-2&0\\\ -4&6&-8\\\ -4&6&-6\end{bmatrix}$
4
$\rm \begin{bmatrix}1/5&-1/5&0\\\ -2/5&3/5&-4/5\\\ -2/5&3/5&-3/5\end{bmatrix}$
4
NDA Mathematics 21 April 2024
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language

Let $A$ and $B$ be matrices of order $3 \times 3$. If $|A| = \frac{1}{2 \sqrt{2}}$ and $|B| = \frac{1}{729}$, then what is the value of $|2B(adj(3A))|$?

A

27

B

$\frac{-27}{2\sqrt{2}}$

C

$\frac{27}{2}$

D

1

EXAM MAP
Medical
NEETAIIMS
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Civil Services
UPSC Civil Service
Defence
NDA
Staff Selection Commission
SSC CGL Tier I
CBSE
Class 12