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Q30 CSIR NET Dec 2023

Q29 CSIR NET DEC

Q31 CSIR Net dec 2023

Only connected sets in lower limit topology are singleton sets

A limit problem

Graph of a real valued function is a closed set.

Infinite root problem

Munkres Chapter 2 $17 question 2

If AUB=AUC and A∩B=A∩C then B=C

AA^{T}=BB^{T} implies A=BP where P is an orthogonal matrix

A way of proveing a set is an open set

Set theory result

(AUB)'=A'UB'

No trivial metric topology possible on a space with more than 1 element

GATE MA 2024 Complex analysis

GATE 2024 Mathematics GROUP THEORY Question

QID 523 15 UNIT 1 Linear Algebra CSIR NET MATHS

CSIR NET MATHEMATICAL SCIENCE Q6 QID 7044073 LINEAR ALGEBRA

CSIR NET 2023 Mathematical Science Q39 QUESTION ID 704062 Under Which conditions sequence converges.

Series 1\n! Converges or not?

Graph of a continuous function with a connected domain is a connected set.

Q35 Linear Algebra GATE mathematics 2023

Q18 GATE 2023 MATHEMATICS TOPOLOGY

Affine space is a closed space

A sum of an affine space and vector space affine + vector space

GATE 2023 Q12 TOPOLOGY

Inverse of A transpose

Q52 GATE MATH 2023

Q23 GATE FUNCTIONAL ANALYSIS 2023

Q34 GATE 2023 LINEAR ALGEBRA

Q44 GATE 2023 TOPOLOGY

Q38 GATE 2023 Functional Analysis

Q20 GATE 2023 MATHEMATICS FUNCTIONAL ANALYSIS

GATE MATHEMATICS FUNCTIONAL ANALYSIS 2023 Q32

Power of diagonalizable matrix is also diagonalizable

Q59 GATE MATH 2023

Eigenvectors of symmetric matrices are orthogonal to each other

Gate 2023 Mathematics Q14 Linear Algebra

N(A*)=orthagonal complement {R(A)}

Orthogonal complement of orthogonal complement of a singleton element

Trignometry identity in Complex Number

CSIR NET MATH 2023 704084 Group Theory

GATE MATHEMATICS 2023 Q56 FUNCTIONAL ANALYSIS

If real part of an analytic function f is constant then f itself a constant function

If Image of an analytic function f lies in a straight line then f is a constant map

Given f(z) is analytic then f(z)¯ is analytic iff f is a constant map

f(z) is analytic and |f(z)| is a constant then f(z) is a constant map

GATE MATHEMATICS 2023 Q60

Given f(z) is analytic then f(zˉ) is analytic iff f is a constant map.

Modulus of e^z

Let H be a subgroup of G such that x^2 lies in H for x in G then H is a normal subgroup of G

Kernel is a normal subgroup

SL(n,R ) is normal subgroup of GL(n,R)

KerA=KerA^T A

Orthogonal complement of a set in a Hilbert space is a closed subspace

If C_1 is subset of C_2 then d(x,C_2) is less than d(x,C_1)

Isometry implies orthogoality

Set of all orthogonal matrices is a compact set

Eigenvalues of Real orthogonal matrix are +1,-1