1
JEE Main 2019 (Online) 11th January Morning Slot
+4
-1
If the system of linear equations
2x + 2y + 3z = a
3x – y + 5z = b
x – 3y + 2z = c
where a, b, c are non zero real numbers, has more one solution, then :
A
b – c – a = 0
B
a + b + c = 0
C
b – c + a = 0
D
b + c – a = 0
2
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
$${1 \over {\sqrt 3 }}$$
3
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
$$2\sqrt 3$$
4
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
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