1
BITSAT 2023
+3
-1

If $$a, b, c$$ are non-zero real numbers and if the system of equations $$(a-1) x-y-z=0, -x+(b-1) y-z=0,-x-y+(c-1) z=0$$ has a non-trivial solution, then $$a b+b c+c a$$ equals to

A
$$a b c$$
B
$$a+b+c$$
C
1
D
$$-1$$
2
BITSAT 2022
+3
-1

Given 2x $$-$$ y + 2z = 2, x $$-$$ 2y - z = $$-$$4, x + y + $$\lambda$$z = 4, then the value of $$\lambda$$ such that the given system of equation has no solution is

A
$$-$$3
B
1
C
0
D
3
3
BITSAT 2022
+3
-1

Let $$A = \left[ {\matrix{ 1 & { - 1} & 1 \cr 2 & 1 & { - 3} \cr 1 & 1 & 1 \cr } } \right]$$ and $$10B = \left[ {\matrix{ 4 & 2 & 2 \cr { - 5} & 0 & \alpha \cr 1 & { - 2} & 3 \cr } } \right]$$

If B is the inverse of A, then the value of $$\alpha$$ is

A
4
B
$$-$$4
C
3
D
5
4
BITSAT 2022
+3
-1

If $$\left[ {\matrix{ 1 & { - \tan \theta } \cr {\tan \theta } & 1 \cr } } \right]{\left[ {\matrix{ 1 & {\tan \theta } \cr { - \tan \theta } & 1 \cr } } \right]^{ - 1}} = \left[ {\matrix{ a & { - b} \cr b & a \cr } } \right]$$, then

A
a = 1, b = 1
B
$$a = \sin 2\theta ,b = \cos 2\theta$$
C
$$a = \cos 2\theta ,b = \sin 2\theta$$
D
None of these
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