1
JEE Main 2019 (Online) 10th January Morning Slot
+4
-1
If the system of equations

x + y + z = 5

x + 2y + 3z = 9

x + 3y + az = $$\beta$$

has infinitely many solutions, then $$\beta$$ $$-$$ $$\alpha$$ equals -
A
8
B
21
C
18
D
5
2
JEE Main 2019 (Online) 10th January Morning Slot
+4
-1
Let  d $$\in$$ R, and

$$A = \left[ {\matrix{ { - 2} & {4 + d} & {\left( {\sin \theta } \right) - 2} \cr 1 & {\left( {\sin \theta } \right) + 2} & d \cr 5 & {\left( {2\sin \theta } \right) - d} & {\left( { - \sin \theta } \right) + 2 + 2d} \cr } } \right],$$

$$\theta \in \left[ {0,2\pi } \right]$$ If the minimum value of det(A) is 8, then a value of d is -
A
$$-$$ 7
B
$$2\left( {\sqrt 2 + 2} \right)$$
C
$$-$$ 5
D
$$2\left( {\sqrt 2 + 1} \right)$$
3
JEE Main 2019 (Online) 9th January Evening Slot
+4
-1
If the system of linear equations
x $$-$$ 4y + 7z = g
3y $$-$$ 5z = h
$$-$$2x + 5y $$-$$ 9z = k
is consistent, then :
A
g + 2h + k = 0
B
g + h + 2k = 0
C
2g + h + k = 0
D
g + h + k = 0
4
JEE Main 2019 (Online) 9th January Evening Slot
+4
-1
If   $$A = \left[ {\matrix{ {{e^t}} & {{e^{ - t}}\cos t} & {{e^{ - t}}\sin t} \cr {{e^t}} & { - {e^{ - t}}\cos t - {e^{ - t}}\sin t} & { - {e^{ - t}}\sin t + {e^{ - t}}co{\mathop{\rm s}\nolimits} t} \cr {{e^t}} & {2{e^{ - t}}\sin t} & { - 2{e^{ - t}}\cos t} \cr } } \right]$$

then A is :
A
invertible for all t$$\in$$R.
B
invertible only if t $$=$$ $$\pi$$
C
not invertible for any t$$\in$$R
D
invertible only if t $$=$$ $${\pi \over 2}$$.
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