1
JEE Advanced 2020 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2
Let M be a 3 $$\times$$ 3 invertible matrix with real entries and let I denote the 3 $$\times$$ 3 identity matrix. If M$$-$$1 = adj(adj M), then which of the following statements is/are ALWAYS TRUE?
A
M = I
B
det M = 1
C
M2 = I
D
(adj M)2 = I
2
JEE Advanced 2020 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2
Let S be the set of all complex numbers z
satisfying |z2 + z + 1| = 1. Then which of the following statements is/are TRUE?
A
$$\left| {z + {1 \over 2}} \right|$$ $$\le$$ $${{1 \over 2}}$$ for all z$$\in$$S
B
|z| $$\le$$ 2 for all z$$\in$$S
C
$$\left| {z + {1 \over 2}} \right|\, \ge {1 \over 2}$$ for all z$$\in$$S
D
The set S has exactly four elements
3
JEE Advanced 2020 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2
Let x, y and z be positive real numbers. Suppose x, y and z are the lengths of the sides of a triangle opposite to its angles X, Y, and Z, respectively. If

$$\tan {X \over 2} + \tan {Z \over 2} = {{2y} \over {x + y + z}}$$, then which of the following statements is/are TRUE?
A
2Y = X + Z
B
Y = X + Z
C
$$\tan {X \over 2}$$ = $${x \over {y + z}}$$
D
x2 + z2 $$-$$ y2 = xz
4
JEE Advanced 2020 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2
Let L1 and L2 be the following straight lines.

$${L_1}:{{x - 1} \over 1} = {y \over { - 1}} = {{z - 1} \over 3}$$ and $${L_2}:{{x - 1} \over { - 3}} = {y \over { - 1}} = {{z - 1} \over 1}$$.

Suppose the straight line

$$L:{{x - \alpha } \over l} = {{y - 1} \over m} = {{z - \gamma } \over { - 2}}$$

lies in the plane containing L1 and L2 and passes through the point of intersection of L1 and L2. If the line L bisects the acute angle between the lines L1 and L2, then which of the following statements is/are TRUE?
A
$$\alpha$$ $$-$$ $$\gamma$$ = 3
B
l + m = 2
C
$$\alpha$$ $$-$$ $$\gamma$$ = 1
D
l + m = 0
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