1
JEE Main 2019 (Online) 10th January Evening Slot
+4
-1
Let A = $$\left[ {\matrix{ 2 & b & 1 \cr b & {{b^2} + 1} & b \cr 1 & b & 2 \cr } } \right]$$ where b > 0.

Then the minimum value of $${{\det \left( A \right)} \over b}$$ is -
A
$$\sqrt 3$$
B
$$-$$ $$2\sqrt 3$$
C
$$- \sqrt 3$$
D
$$2\sqrt 3$$
2
JEE Main 2019 (Online) 10th January Evening Slot
+4
-1
The number of values of $$\theta$$ $$\in$$ (0, $$\pi$$) for which the system of linear equations

x + 3y + 7z = 0

$$-$$ x + 4y + 7z = 0

(sin3$$\theta$$)x + (cos2$$\theta$$)y + 2z = 0.

has a non-trival solution, is -
A
two
B
one
C
four
D
three
3
JEE Main 2019 (Online) 10th January Morning Slot
+4
-1
If the system of equations

x + y + z = 5

x + 2y + 3z = 9

x + 3y + az = $$\beta$$

has infinitely many solutions, then $$\beta$$ $$-$$ $$\alpha$$ equals -
A
8
B
21
C
18
D
5
4
JEE Main 2019 (Online) 10th January Morning Slot
+4
-1
Let  d $$\in$$ R, and

$$A = \left[ {\matrix{ { - 2} & {4 + d} & {\left( {\sin \theta } \right) - 2} \cr 1 & {\left( {\sin \theta } \right) + 2} & d \cr 5 & {\left( {2\sin \theta } \right) - d} & {\left( { - \sin \theta } \right) + 2 + 2d} \cr } } \right],$$

$$\theta \in \left[ {0,2\pi } \right]$$ If the minimum value of det(A) is 8, then a value of d is -
A
$$-$$ 7
B
$$2\left( {\sqrt 2 + 2} \right)$$
C
$$-$$ 5
D
$$2\left( {\sqrt 2 + 1} \right)$$
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