1
BITSAT 2024
MCQ (Single Correct Answer)
+3
-1
If $ A=\frac{1}{3}\left[\begin{array}{ccc}1 & 2 & 2 \\ 2 & 1 & -2 \\ a & 2 & b\end{array}\right] $ is an orthogonal matrix, then
A
$ a=-2, b=-1 $
B
$ a=2, b=1 $
C
$ a=2, b=-1 $
D
$ a=-2, b=1 $
2
BITSAT 2024
MCQ (Single Correct Answer)
+3
-1
Suppose $ p, q, r \neq 0 $ and system of equation $ (p+a) x+b y+c z=0 $, $ a x+(q+b) y+c z=0 $, $ a x+b y+(r+c) z=0 $, has a non-trivial solution, then the value of $ \frac{a}{p}+\frac{b}{q}+\frac{c}{r} $ is
A
-1
B
0
C
1
D
2
3
BITSAT 2024
MCQ (Single Correct Answer)
+3
-1
If matrix $ A=\left[\begin{array}{ccc}3 & -2 & 4 \\ 1 & 2 & -1 \\ 0 & 1 & 1\end{array}\right] $ and $ A^{-1}=\frac{1}{k} \operatorname{adj}(A) $,
A
7
B
-7
C
15
D
-11
4
BITSAT 2023
MCQ (Single Correct Answer)
+3
-1

If the system of linear equation $$3 x-2 y+z=2, 4 x-3 y+3 z=-5$$ and $$7 x-5 y+\lambda z=9$$ has no solution, then $$\lambda$$ equals to

A
4
B
5
C
6
D
7
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