1
JEE Main 2018 (Online) 15th April Evening Slot
+4
-1
Suppose A is any 3$$\times$$ 3 nonsingular matrx 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
2
JEE Main 2018 (Online) 15th April Evening Slot
+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
3
JEE Main 2018 (Online) 15th April Morning Slot
+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
$$\left[ {\matrix{ {36} & { - 32} \cr 0 & 4 \cr } } \right]$$
4
JEE Main 2018 (Online) 15th April Morning Slot
+4
-1
Let S be the set of all real values of k for which the systemof linear equations
x + y + z = 2
2x + y $$-$$ z = 3
3x + 2y + kz = 4
has a unique solution. Then S is :
A
an empty set
B
equal to {0}
C
equal to R
D
equal to R $$-$$ {0}
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