1
JEE Main 2018 (Offline)
MCQ (Single Correct Answer)
+4
-1
If the system of linear equations

x + ky + 3z = 0
3x + ky - 2z = 0
2x + 4y - 3z = 0

has a non-zero solution (x, y, z), then $${{xz} \over {{y^2}}}$$ is equal to
A
30
B
-10
C
10
D
-30
2
JEE Main 2018 (Online) 15th April Evening Slot
MCQ (Single Correct Answer)
+4
-1
Suppose A is any 3$$\times$$ 3 non-singular matrix and ( A $$-$$ 3I) (A $$-$$ 5I) = O where I = I3 and O = O3. If $$\alpha$$A + $$\beta$$A-1 = 4I, then $$\alpha$$ + $$\beta$$ is equal to :
A
8
B
7
C
13
D
12
3
JEE Main 2018 (Online) 15th April Evening Slot
MCQ (Single Correct Answer)
+4
-1
If the system of linear equations
x + ay + z = 3
x + 2y + 2z = 6
x + 5y + 3z = b
has no solution, then :
A
a = $$-$$ 1,    b = 9
B
a = $$-$$ 1,    b $$\ne$$ 9
C
a $$\ne$$ $$-$$ 1,    b = 9
D
a = 1,    b $$\ne$$ 9
4
JEE Main 2018 (Online) 15th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
Let $$A$$ be a matrix such that $$A.\left[ {\matrix{ 1 & 2 \cr 0 & 3 \cr } } \right]$$ is a scalar matrix and |3A| = 108.
Then A2 equals :
A
$$\left[ {\matrix{ 4 & { - 32} \cr 0 & {36} \cr } } \right]$$
B
$$\left[ {\matrix{ {36} & 0 \cr { - 32} & 4 \cr } } \right]$$
C
$$\left[ {\matrix{ 4 & 0 \cr { - 32} & {36} \cr } } \right]$$
D
$$\left[ {\matrix{ {36} & { - 32} \cr 0 & 4 \cr } } \right]$$
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