1
JEE Main 2018 (Online) 15th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
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
$$\left[ {\matrix{ {36} & { - 32} \cr 0 & 4 \cr } } \right]$$
2
JEE Main 2018 (Online) 15th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
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}
3
JEE Main 2017 (Online) 9th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
For two 3 × 3 matrices A and B, let A + B = 2BT and 3A + 2B = I3, where BT is the transpose of B and I3 is 3 × 3 identity matrix. Then :
A
5A + 10B = 2I3
B
10A + 5B = 3I3
C
B + 2A = I3
D
3A + 6B = 2I3
4
JEE Main 2017 (Online) 8th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
If

$$S = \left\{ {x \in \left[ {0,2\pi } \right]:\left| {\matrix{ 0 & {\cos x} & { - \sin x} \cr {\sin x} & 0 & {\cos x} \cr {\cos x} & {\sin x} & 0 \cr } } \right| = 0} \right\},$$

then $$\sum\limits_{x \in S} {\tan \left( {{\pi \over 3} + x} \right)} $$ is equal to :
A
$$4 + 2\sqrt 3 $$
B
$$ - 2 + \sqrt 3 $$
C
$$ - 2 - \sqrt 3 $$
D
$$-\,\,4 - 2\sqrt 3 $$
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