1
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
2
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
3
JEE Advanced 2020 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2
Which of the following inequalities is/are TRUE?
A
$$\int_0^1 {x\cos xdx\, \ge \,{3 \over 8}}$$
B
$$\int_0^1 {x\sin xdx\, \ge \,{3 \over {10}}}$$
C
$$\int_0^1 {{x^2}\cos xdx\, \ge \,{1 \over 2}}$$
D
$$\int_0^1 {{x^2}\sin xdx\, \ge \,{2 \over 9}}$$
4
JEE Advanced 2020 Paper 1 Offline
Numerical
+4
-0
Let m be the minimum possible value of $${\log _3}({3^{{y_1}}} + {3^{{y_2}}} + {3^{{y_3}}})$$, where $${y_1},{y_2},{y_3}$$ are real numbers for which $${{y_1} + {y_2} + {y_3}}$$ = 9. Let M be the maximum possible value of $$({\log _3}{x_1} + {\log _3}{x_2} + {\log _3}{x_3})$$, where $${x_1},{x_2},{x_3}$$ are positive real numbers for which $${{x_1} + {x_2} + {x_3}}$$ = 9. Then the value of $${\log _2}({m^3}) + {\log _3}({M^2})$$ is ...........