1
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
$$-\,\,4 - 2\sqrt 3$$
2
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
$$\left[ {\matrix{ {72} & {-84} \cr {-63} & {51} \cr } } \right]$$
3
JEE Main 2017 (Offline)
+4
-1
If S is the set of distinct values of 'b' for which the following system of linear equations

x + y + z = 1
x + ay + z = 1
ax + by + z = 0

has no solution, then S is :
A
an empty set
B
an infinite set
C
a finite set containing two or more elements
D
a singleton
4
JEE Main 2016 (Online) 10th April Morning Slot
+4
-1
Let A be a 3 $$\times$$ 3 matrix such that A2 $$-$$ 5A + 7I = 0

Statement - I :

A$$-$$1 = $${1 \over 7}$$ (5I $$-$$ A).

Statement - II :

The polynomial A3 $$-$$ 2A2 $$-$$ 3A + I can be reduced to 5(A $$-$$ 4I).

Then :
A
Statement-I is true, but Statement-II is false.
B
Statement-I is false, but Statement-II is true.
C
Both the statements are true.
D
Both the statements are false
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