1
GATE CSE 2024 Set 1
MCQ (More than One Correct Answer)
+1
-0

Let A and B be two events in a probability space with $P(A) = 0.3$, $P(B) = 0.5$, and $P(A \cap B) = 0.1$. Which of the following statements is/are TRUE?

A

The two events A and B are independent.

B

$P(A \cup B) = 0.7$

C

$P(A \cap B^c) = 0.2$, where $B^c$ is the complement of the event B

D

$P(A^c \cap B^c) = 0.4$, where $A^c$ and $B^c$ are the complements of the events A and B respectively

2
GATE CSE 2024 Set 1
Numerical
+1
-0

Let $A$ and $B$ be non-empty finite sets such that there exist one-to-one and onto functions (i) from $A$ to $B$ and (ii) from $A \times A$ to $A \cup B$. The number of possible values of $|A|$ is _______

Your input ____
3
GATE CSE 2024 Set 1
Numerical
+1
-0

The number of spanning trees in a complete graph of 4 vertices labelled A, B, C, and D is __________

Your input ____
4
GATE CSE 2024 Set 1
MCQ (More than One Correct Answer)
+2
-0

Let A be any n x m matrix, where m > n. Which of the following statements is/are TRUE about the system of linear equations Ax = 0?

A

There exist at least m - n linearly independent solutions to this system

B

There exist m - n linearly independent vectors such that every solution is a linear combination of these vectors

C

There exists a non-zero solution in which at least m - n variables are 0

D

There exists a solution in which at least n variables are non-zero

EXAM MAP
Medical
NEETAIIMS
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Civil Services
UPSC Civil Service
Defence
NDA
Staff Selection Commission
SSC CGL Tier I
CBSE
Class 12