D.U. M.Sc Mathematics Admission Entrance Test Paper

Will you please provide the question paper of D.U. M.Sc Mathematics Admission Entrance Test ?

[Kiran Chandar]

Here is the list of few questions of D.U. M.Sc Mathematics Admission Entrance Test which you are looking for .

(1) How many elements are there in Z[i]=h3 + ii?
A) in
nite B) 3
C) 10 D)
nite but not 3 or 10.

(2) Let P be the set of all n n complex Hermitian matrices. Then P is a vector
space over the
led of
A) C B) R but not C
C) both R and C D) C but not R.

(3) Which one of the following is true?
A) There are in
nitely many one-one linear transformations from R4 to R3
B) The dimension of the vector space of all 3 3 skew-symmetric matrices over
the
eld of real numbers is 6
C) Let F be a
eld and A a
xed n n matrix over F. If T : Mn(F) ! Mn(F) is
a linear transformation such that T(B) = AB for every B 2 Mn(F), then the
characteristic polynomial for A is the same as the characteristic polynomial
for T
D) A two-dimensional vector space over a
eld with 2 elements has exactly 3
di
erent basis.

(4) Let V and W be vector spaces over a
led F. Let S : V ! W and T : W ! V be
linear transformations. Then which one of the following is true?
A) If ST is one-to-one, then S is one-to-one
B) If V = W and V is
nite-dimensional such that TS = I, then T is invertible
C) If dim V = 2 and dimW = 3, then ST is invertible
D) If TS is onto, then S is onto.








For more questions , here is the attachment

Will you provide me the sample paper of the Entrance Test of Delhi university for admission in M.Sc Mathematics course ?

[Quick Sam]

As you want I am here providing you sample paper of the Entrance Test of Delhi university for admission in M.Sc Mathematics course.

Sample paper :

Let a relation R be defined on the set of complex numbers C by ZRW to mean
Rc(Z)sRc(W) and Im{Z)::;Im(W). Then this relation R is
(1) reflexive and transitive but not symmetric
(2) symmetric and transitive but not reflexive
(3) reflexive and symmetric but not transitive
(4) symmetric but not reflexive and transitive

Let the relation R defined on the set A { 1, 2, 4, 6, ... } by x R Y iff x and y have a common
factor other than 1. Then the relation R is
(1) symmetric and reflexive but not transitive
(2) transitive and reflexive but not symmetric
(3) symmetric and transitive but not reflexive
(4) symmetric, transitive and reflexive

Which of the following statements is not true?
(1) Identity permutation is always a even permutation
(2) Product of two even permutations is an even permutation
(3) Inverse of an even permutation is a even permutation
(4) Product of one even permutation and one odd permutation is a even permutation


Solution of 235x =;: 54 (mod 7) is
235x 054 (mod 7) "" "" ~
(I) x ~ 12 (mod 7)
(3) x~5(mod7)
(2) x ~3 (mod 7)
(4) x. 4 (mod 7)

Order of a cyclic group and order of its generating element
(I) are equal
(2) order of first is greater than order of second
(3) order of first is less than order of second
(4) order of first is multiple of order of second


Which group is not Abelian?
(I) Every finite group of order less than 6
(2) Every cyclic group
(3) The multiplicative group of nth roots of unity
(4) The symmetric group Sn


Cayley theorem informs that any group originally is
(1) a Abelian group
(2) transformation group
(3) subgroup of transformation group
(4) symmetric group


If the characteristic values of a square matrix of third order are 4, 2, 3, then the value
of its determinant is
(I) 6 (2) 9 (3) 24 (4) 54


The system of equations 2x-y+3z=9, x+y+z=6, x-y+z=;2 has
(I) a unique non-zero solution (2) infinitely many solutions
(3) no solution (4) zero solution


The asymptotes of the curve x 3 +2x 2 y_xy2 _ 2y 3 +3xy+3y2 +x+l=O are
(I) y~x~I=O, y+x=O, 2y+x~I=O
(2) y+x~I=O, y+x=O, 2y~x+I=O
(3) y~x"I=O, y~x=O, x+2y~I=O
(4) y+x-l=O, y+x=O, x-2y+l=O



Which of the following statements is not true?
(I) Every sequentially compact metric space is compact
(2) A closed subset of a compact metric space is complete
(3) A compact metric space is not separable
(4) A totally bounded metric space is separable