1
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
2
JEE Main 2016 (Online) 10th April Morning Slot
+4
-1
If    A = $$\left[ {\matrix{ { - 4} & { - 1} \cr 3 & 1 \cr } } \right]$$,

then the determinant of the matrix (A2016 − 2A2015 − A2014) is :
A
2014
B
$$-$$ 175
C
2016
D
$$-$$ 25
3
JEE Main 2016 (Online) 9th April Morning Slot
+4
-1
If P = $$\left[ {\matrix{ {{{\sqrt 3 } \over 2}} & {{1 \over 2}} \cr { - {1 \over 2}} & {{{\sqrt 3 } \over 2}} \cr } } \right],A = \left[ {\matrix{ 1 & 1 \cr 0 & 1 \cr } } \right]\,\,\,$$

Q = PAPT, then PT Q2015 P is :
A
$$\left[ {\matrix{ 0 & {2015} \cr 0 & 0 \cr } } \right]$$
B
$$\left[ {\matrix{ {2015} & 1 \cr 0 & {2015} \cr } } \right]$$
C
$$\left[ {\matrix{ {2015} & 0 \cr 1 & {2015} \cr } } \right]$$
D
$$\left[ {\matrix{ 1 & {2015} \cr 0 & 1 \cr } } \right]$$
4
JEE Main 2016 (Online) 9th April Morning Slot
+4
-1
The number of distinct real roots of the equation,

$$\left| {\matrix{ {\cos x} & {\sin x} & {\sin x} \cr {\sin x} & {\cos x} & {\sin x} \cr {\sin x} & {\sin x} & {\cos x} \cr } } \right| = 0$$ in the interval $$\left[ { - {\pi \over 4},{\pi \over 4}} \right]$$ is :
A
4
B
3
C
2
D
1
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