1
JEE Main 2022 (Online) 28th June Morning Shift
+4
-1

If the system of linear equations

$$2x + 3y - z = - 2$$

$$x + y + z = 4$$

$$x - y + |\lambda |z = 4\lambda - 4$$

where, $$\lambda$$ $$\in$$ R, has no solution, then

A
$$\lambda$$ = 7
B
$$\lambda$$ = $$-$$7
C
$$\lambda$$ = 8
D
$$\lambda$$2 = 1
2
JEE Main 2022 (Online) 28th June Morning Shift
+4
-1

Let A be a matrix of order 3 $$\times$$ 3 and det (A) = 2. Then det (det (A) adj (5 adj (A3))) is equal to _____________.

A
512 $$\times$$ 106
B
256 $$\times$$ 106
C
1024 $$\times$$ 106
D
256 $$\times$$ 1011
3
JEE Main 2022 (Online) 27th June Evening Shift
+4
-1

Let $$f(x) = \left| {\matrix{ a & { - 1} & 0 \cr {ax} & a & { - 1} \cr {a{x^2}} & {ax} & a \cr } } \right|,\,a \in R$$. Then the sum of the squares of all the values of a, for which $$2f'(10) - f'(5) + 100 = 0$$, is

A
117
B
106
C
125
D
136
4
JEE Main 2022 (Online) 27th June Evening Shift
+4
-1

Let A and B be two 3 $$\times$$ 3 matrices such that $$AB = I$$ and $$|A| = {1 \over 8}$$. Then $$|adj\,(B\,adj(2A))|$$ is equal to

A
16
B
32
C
64
D
128
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