1
JEE Advanced 2021 Paper 1 Online
+3
-1
The area of the region

$$\left\{ {\matrix{ {(x,y):0 \le x \le {9 \over 4},} & {0 \le y \le 1,} & {x \ge 3y,} & {x + y \ge 2} \cr } } \right\}$$ is
A
$${{11} \over {32}}$$
B
$${{35} \over {96}}$$
C
$${{37} \over {96}}$$
D
$${{13} \over {32}}$$
2
JEE Advanced 2021 Paper 1 Online
+3
-1
Consider three sets E1 = {1, 2, 3}, F1 = {1, 3, 4} and G1 = {2, 3, 4, 5}. Two elements are chosen at random, without replacement, from the set E1, and let S1 denote the set of these chosen elements. Let E2 = E1 $$-$$ S1 and F2 = F1 $$\cup$$ S1. Now two elements are chosen at random, without replacement, from the set F2 and let S2 denote the set of these chosen elements.

Let G2 = G1 $$\cup$$ S2. Finally, two elements are chosen at random, without replacement, from the set G2 and let S3 denote the set of these chosen elements.

Let E3 = E2 $$\cup$$ S3. Given that E1 = E3, let p be the conditional probability of the event S1 = {1, 2}. Then the value of p is
A
$${1 \over 5}$$
B
$${3 \over 5}$$
C
$${1 \over 2}$$
D
$${2 \over 5}$$
3
JEE Advanced 2021 Paper 1 Online
+3
-1
Let $$\theta$$1, $$\theta$$2, ........, $$\theta$$10 = 2$$\pi$$. Define the complex numbers z1 = ei$$\theta$$1, zk = zk $$-$$ 1ei$$\theta$$k for k = 2, 3, ......., 10, where i = $$\sqrt { - 1}$$. Consider the statements P and Q given below :

$$P:\left| {{z_2} - {z_1}} \right| + \left| {{z_3} - {z_2}} \right| + ..... + \left| {{z_{10}} - {z_9}} \right| + \left| {{z_1} - {z_{10}}} \right| \le 2\pi$$

$$Q:\left| {z_2^2 - z_1^2} \right| + \left| {z_3^2 - z_2^2} \right| + .... + \left| {z_{10}^2 - z_9^2} \right| + \left| {z_1^2 - z_{10}^2} \right| \le 4\pi$$

Then,
A
P is TRUE and Q is FALSE
B
Q is TRUE and P is FALSE
C
both P and Q are TRUE
D
both P and Q are FALSE
4
JEE Advanced 2021 Paper 1 Online
Numerical
+2
-0
Three numbers are chosen at random, one after another with replacement, from the set S = {1, 2, 3, ......, 100}. Let p1 be the probability that the maximum of chosen numbers is at least 81 and p2 be the probability that the minimum of chosen numbers is at most 40.

The value of $${{625} \over 4}{p_1}$$ is ___________.