1
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
2
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
$$\left[ {\matrix{ 1 & { - 12} \cr 0 & 1 \cr } } \right]$$
3
JEE Main 2019 (Online) 8th April Evening Slot
+4
-1
Let the number 2,b,c be in an A.P. and
A = $$\left[ {\matrix{ 1 & 1 & 1 \cr 2 & b & c \cr 4 & {{b^2}} & {{c^2}} \cr } } \right]$$. If det(A) $$\in$$ [2, 16], then c lies in the interval :
A
[2, 3)
B
[4, 6]
C
(2 + 23/4, 4)
D
[3, 2 + 23/4]
4
JEE Main 2019 (Online) 8th April Morning Slot
+4
-1
Let $$A = \left( {\matrix{ {\cos \alpha } & { - \sin \alpha } \cr {\sin \alpha } & {\cos \alpha } \cr } } \right)$$, ($$\alpha$$ $$\in$$ R)
such that $${A^{32}} = \left( {\matrix{ 0 & { - 1} \cr 1 & 0 \cr } } \right)$$ then a value of $$\alpha$$ is
A
0
B
$${\pi \over {16}}$$
C
$${\pi \over {32}}$$
D
$${\pi \over {64}}$$
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