1
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
$$\left[ {\matrix{ 1 & {2015} \cr 0 & 1 \cr } } \right]$$
2
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
3
JEE Main 2016 (Offline)
+4
-1
If $$A = \left[ {\matrix{ {5a} & { - b} \cr 3 & 2 \cr } } \right]$$ and $$A$$ adj $$A=A$$ $${A^T},$$ then $$5a+b$$ is equal to :
A
$$4$$
B
$$13$$
C
$$-1$$
D
$$5$$
4
JEE Main 2016 (Offline)
+4
-1

The system of linear equations

$$\matrix{ {x + \lambda y - z = 0} \cr {\lambda x - y - z = 0} \cr {x + y - \lambda z = 0} \cr }$$

has a non-trivial solution for :
A
infinitely many values of $$\lambda .$$
B
exactly one value of $$\lambda .$$
C
exactly two values of $$\lambda .$$
D
exactly three values of $$\lambda .$$
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