1
JEE Main 2019 (Online) 10th April Morning Slot
+4
-1
If $${\Delta _1} = \left| {\matrix{ x & {\sin \theta } & {\cos \theta } \cr { - \sin \theta } & { - x} & 1 \cr {\cos \theta } & 1 & x \cr } } \right|$$ and
$${\Delta _2} = \left| {\matrix{ x & {\sin 2\theta } & {\cos 2\theta } \cr { - \sin 2\theta } & { - x} & 1 \cr {\cos 2\theta } & 1 & x \cr } } \right|$$, $$x \ne 0$$ ;

then for all $$\theta \in \left( {0,{\pi \over 2}} \right)$$ :
A
$${\Delta _1} - {\Delta _2}$$ = x (cos 2$$\theta$$ – cos 4$$\theta$$)
B
$${\Delta _1} + {\Delta _2}$$ = - 2x3
C
$${\Delta _1} + {\Delta _2}$$ = – 2(x3 + x –1)
D
$${\Delta _1} - {\Delta _2}$$ = - 2x3
2
JEE Main 2019 (Online) 10th April Morning Slot
+4
-1
If the system of linear equations
x + y + z = 5
x + 2y + 2z = 6
x + 3y + $$\lambda$$z = $$\mu$$, ($$\lambda$$, $$\mu$$ $$\in$$ R), has infinitely many solutions, then the value of $$\lambda$$ + $$\mu$$ is :
A
10
B
9
C
7
D
12
3
JEE Main 2019 (Online) 9th April Evening Slot
+4
-1
If the system of equations 2x + 3y – z = 0, x + ky – 2z = 0 and 2x – y + z = 0 has a non-trival solution (x, y, z), then $${x \over y} + {y \over z} + {z \over x} + k$$ is equal to :-
A
-4
B
$${3 \over 4}$$
C
$${1 \over 2}$$
D
$$-{1 \over 4}$$
4
JEE Main 2019 (Online) 9th April Evening Slot
+4
-1
The total number of matrices
$$A = \left( {\matrix{ 0 & {2y} & 1 \cr {2x} & y & { - 1} \cr {2x} & { - y} & 1 \cr } } \right)$$
(x, y $$\in$$ R,x $$\ne$$ y) for which ATA = 3I3 is :-
A
3
B
4
C
2
D
6
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