1
JEE Main 2017 (Online) 9th April Morning Slot
+4
-1
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
2
JEE Main 2017 (Online) 8th April Morning Slot
+4
-1
Let A be any 3 $$\times$$ 3 invertible matrix. Then which one of the following is not always true ?
A
adj (A) = $$\left| \right.$$A$$\left| \right.$$.A$$-$$1
B
adj (adj(A)) = $$\left| \right.$$A$$\left| \right.$$.A
C
adj (adj(A)) = $$\left| \right.$$A$$\left| \right.$$2.(adj(A))$$-$$1
D
adj (adj(A)) = $$\left| \, \right.$$A $$\left| \, \right.$$.(adj(A))$$-$$1
3
JEE Main 2017 (Online) 8th April Morning Slot
+4
-1
The number of real values of $$\lambda$$ for which the system of linear equations

2x + 4y $$-$$ $$\lambda$$z = 0

4x + $$\lambda$$y + 2z = 0

$$\lambda$$x + 2y + 2z = 0

has infinitely many solutions, is :
A
0
B
1
C
2
D
3
4
JEE Main 2017 (Online) 8th April Morning Slot
+4
-1
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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