1
NDA Mathematics 10 April 2022
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language
If $Δ_1 = \begin{vmatrix} 1 & p & q \\ 1 & q & r \\ 1 & r & p\end{vmatrix} \ \text{and} \ Δ_2 = \begin{vmatrix} 1 & 1 & 1 \\ q & r & p \\ r & p & q \end{vmatrix}$ where p ≠ q ≠ r, then Δ1 + Δ2 is
A
0
B
always positive
C
always negative
D
positive if p, q, r are positive else negative
2
NDA Mathematics 10 April 2022
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language
If (a - b) (b - c) (c - a) = 2 and abc = 6, then what is the value of $\begin{vmatrix}a & b & c \\ a^2 & b^2 & c^2 \\ a^3 & b^3 & c^3 \end{vmatrix}?$
A
3
B
12
C
14
D
15
3
NDA Mathematics 10 April 2022
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language

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 = 0

2. a3 + b3 + c3 = 3abc

3. a2 + b2 + c2 - ab - bc - ca = 0

Select the correct answer using the code given below:

A
1 and 2 only
B
2 and 3 only
C
1 and 3 only
D
1, 2 and 3
4
NDA Mathematics 10 April 2022
MCQ (Single Correct Answer)
+2.5
-0.83
Change Language
For what value of k is the matrix $\begin{bmatrix} 2\cos 2\theta & 2\cos 2\theta & 6 \\ 1 -2 \sin^2\theta & 2 \cos^2\theta -1 & 3 \\ k & 2k & 1 \end{bmatrix}$ singular?
A
0 only
B
1 only
C
2 only
D
Any real value
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