1
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
2
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
3
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
$$-\,\,4 - 2\sqrt 3$$
4
JEE Main 2017 (Offline)
+4
-1
If $$A = \left[ {\matrix{ 2 & { - 3} \cr { - 4} & 1 \cr } } \right]$$,

then adj(3A2 + 12A) is equal to
A
$$\left[ {\matrix{ {51} & {63} \cr {84} & {72} \cr } } \right]$$
B
$$\left[ {\matrix{ {51} & {84} \cr {63} & {72} \cr } } \right]$$
C
$$\left[ {\matrix{ {72} & {-63} \cr {-84} & {51} \cr } } \right]$$
D
$$\left[ {\matrix{ {72} & {-84} \cr {-63} & {51} \cr } } \right]$$
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