1
JEE Main 2019 (Online) 11th January Morning Slot
+4
-1
Let A = $$\left( {\matrix{ 0 & {2q} & r \cr p & q & { - r} \cr p & { - q} & r \cr } } \right).$$   If  AAT = I3,   then   $$\left| p \right|$$ is :
A
$${1 \over {\sqrt 2 }}$$
B
$${1 \over {\sqrt 5 }}$$
C
$${1 \over {\sqrt 6 }}$$
D
$${1 \over {\sqrt 3 }}$$
2
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
$$2\sqrt 3$$
3
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
4
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
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