1
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
2
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
3
JEE Main 2022 (Online) 27th June Morning Shift
+4
-1

Let the system of linear equations
$$x + 2y + z = 2$$,
$$\alpha x + 3y - z = \alpha$$,
$$- \alpha x + y + 2z = - \alpha$$
be inconsistent. Then $$\alpha$$ is equal to :

A
$${5 \over 2}$$
B
$$-$$$${5 \over 2}$$
C
$${7 \over 2}$$
D
$$-$$$${7 \over 2}$$
4
JEE Main 2022 (Online) 26th June Evening Shift
+4
-1

If the system of equations

$$\alpha$$x + y + z = 5, x + 2y + 3z = 4, x + 3y + 5z = $$\beta$$

has infinitely many solutions, then the ordered pair ($$\alpha$$, $$\beta$$) is equal to :

A
(1, $$-$$3)
B
($$-$$1, 3)
C
(1, 3)
D
($$-$$1, $$-$$3)
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