NDA I 2022 Mathematics Previous Year Paper (10-Apr-2022)

Question 1

If $&Delta;_1 = \begin{vmatrix} 1 & p & q \ 1 & q & r \ 1 & r & p\end{vmatrix} \ \text{and} \ &Delta;_2 = \begin{vmatrix} 1 & 1 & 1 \ q & r & p \ r & p & q \end{vmatrix}$  where p &ne; q &ne; r, then &Delta; 1+ &Delta; 2is

Accepted Answer

always negative

Answer

0

Answer

always positive

Answer

positive if p, q, r are positive else negative

Question 2

If (a - b) (b - c) (c - a) = 2 and abc = 6, then what is the value of $\begin{vmatrix}a & b & c \ a^2 & b^2 & c^2 \ a^3 & b^3 & c^3 \end{vmatrix}?$

Accepted Answer

12

Answer

3

Answer

14

Answer

15

Question 3

Under which of the following conditions does the determinant $\begin{vmatrix}a & b & c \ b & c & a \ c & a & b\end{vmatrix}$  vanish?1. a + b + c = 02. a 3+ b 3+ c 3= 3abc3. a 2+ b 2+ c 2- ab - bc - ca = 0Select the correct answer using the code given below:

Accepted Answer

1, 2 and 3

Answer

1 and 2 only

Answer

2 and 3 only

Answer

1 and 3 only

Question 4

Consider the following in respect of the matrices:A = [m n], B = [-n -m] & $ C = \begin{bmatrix} m \ -m\end{bmatrix} $1. CA = CB2. AC = BC3. C(A + B) = CA + CBWhich of the above statements is/are correct?

Accepted Answer

2 and 3

Answer

1 only

Answer

2 only

Answer

1 and 2

Question 5

If $A = \begin{bmatrix} 2 \sin \theta & \cos \theta & 0 \ -2\cos \theta & \sin \theta & 0 \ -1 & 1 & 1 \end{bmatrix},$  then what is A(adj A) equal to?(where) I is the identity matrix.

Accepted Answer

2I

Answer

Null matrix

Answer

-I

Answer

I

NDA I 2022 Mathematics Previous Year Paper (10-Apr-2022)

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