1
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
$$-{1 \over 4}$$
2
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
3
JEE Main 2019 (Online) 9th April Morning Slot
+4
-1
Let $$\alpha$$ and $$\beta$$ be the roots of the equation x2 + x + 1 = 0. Then for y $$\ne$$ 0 in R,
$$\left| {\matrix{ {y + 1} & \alpha & \beta \cr \alpha & {y + \beta } & 1 \cr \beta & 1 & {y + \alpha } \cr } } \right|$$\$ is equal to
A
y(y2 – 1)
B
y(y2 – 3)
C
y3
D
y3 – 1
4
JEE Main 2019 (Online) 9th April Morning Slot
+4
-1
If $$\left[ {\matrix{ 1 & 1 \cr 0 & 1 \cr } } \right]\left[ {\matrix{ 1 & 2 \cr 0 & 1 \cr } } \right]$$$$\left[ {\matrix{ 1 & 3 \cr 0 & 1 \cr } } \right]$$....$$\left[ {\matrix{ 1 & {n - 1} \cr 0 & 1 \cr } } \right] = \left[ {\matrix{ 1 & {78} \cr 0 & 1 \cr } } \right]$$,

then the inverse of $$\left[ {\matrix{ 1 & n \cr 0 & 1 \cr } } \right]$$ is
A
$$\left[ {\matrix{ 1 & { 0} \cr {12} & 1 \cr } } \right]$$
B
$$\left[ {\matrix{ 1 & { 0} \cr {13} & 1 \cr } } \right]$$
C
$$\left[ {\matrix{ 1 & { - 13} \cr 0 & 1 \cr } } \right]$$
D
$$\left[ {\matrix{ 1 & { - 12} \cr 0 & 1 \cr } } \right]$$
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