1
JEE Main 2023 (Online) 24th January Morning Shift
+4
-1 Let N denote the number that turns up when a fair die is rolled. If the probability that the system of equations

$$x + y + z = 1$$

$$2x + \mathrm{N}y + 2z = 2$$

$$3x + 3y + \mathrm{N}z = 3$$

has unique solution is $${k \over 6}$$, then the sum of value of k and all possible values of N is

A
18
B
21
C
20
D
19
2
JEE Main 2023 (Online) 24th January Morning Shift
+4
-1 Let $$\Omega$$ be the sample space and $$\mathrm{A \subseteq \Omega}$$ be an event.

Given below are two statements :

(S1) : If P(A) = 0, then A = $$\phi$$

(S2) : If P(A) = 1, then A = $$\Omega$$

Then

A
both (S1) and (S2) are true
B
both (S1) and (S2) are false
C
only (S2) is true
D
only (S1) is true
3
JEE Main 2022 (Online) 29th July Evening Shift
+4
-1 Bag I contains 3 red, 4 black and 3 white balls and Bag II contains 2 red, 5 black and 2 white balls. One ball is transferred from Bag I to Bag II and then a ball is drawn from Bag II. The ball so drawn is found to be black in colour. Then the probability, that the transferred ball is red, is:

A
$$\frac{4}{9}$$
B
$$\frac{5}{18}$$
C
$$\frac{1}{6}$$
D
$$\frac{3}{10}$$
4
JEE Main 2022 (Online) 29th July Morning Shift
+4
-1 Let $$S=\{1,2,3, \ldots, 2022\}$$. Then the probability, that a randomly chosen number n from the set S such that $$\mathrm{HCF}\,(\mathrm{n}, 2022)=1$$, is :

A
$$\frac{128}{1011}$$
B
$$\frac{166}{1011}$$
C
$$\frac{127}{337}$$
D
$$\frac{112}{337}$$
JEE Main Subjects
Physics
Mechanics
Electricity
Optics
Modern Physics
Chemistry
Physical Chemistry
Inorganic Chemistry
Organic Chemistry
Mathematics
Algebra
Trigonometry
Coordinate Geometry
Calculus
EXAM MAP
Joint Entrance Examination