PPSC Lecturer Mathematics Solved Paper-2011

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Q.61  Let A = [0, 1] be a subset of R with Euclidean metric. Then interior of A is

(A) [0,1[

(B) ] 0,1[ 

(C) [0,1]

(D) ]0,1] 

Check Answer
b

62. Number of non-isomorphic groups of order 8 is

(A)  5

(B) 2

(C) 3

(D) 4

Check Answer
a

Q.63  Suppose a and c are real numbers, c> 0, and f is defined on [-1, 1] by  f(x)=\left\{\begin{matrix} x^a sin(x^{-c})\;\;\; (if\;x \neq 0) & \\ 0\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;(if\;x = 0) & \end{matrix}\right.    f is bounded if and only if

(A)  a>1+c

(B) a>2 +c

(C) a  \geq  1+c

(D) a  \geq  2+c

Check Answer
allll

 Q.64  Let M_{2,3} be a vector space of all 2 x 3 matrices over R. Then dimension of Hom(M_{2,3},R^{4})

(A) 12

(B) 6

(C) 8

(D)  24

Check Answer
d

Q.65   Let X = (a,b,c,d,e). Which one of the following classes of subsets of X is a topology on X. 

(A) T1= (X,{a), {a,b) {a,c}}

(B) T2= (X,{a,b,c), {a,b,d) {a,b,c,d}}

(C) T3= (X,{a), {a,b) {a,c,d), (a,b,c,d)} 

(D) T4 = {{a}, {a,b}, {a,c}}

Check Answer
c

Q.66   Let T= (X,{a), {a,b} {a,c,d),(a,b,c,d),{a,b,e}} be a topology on X= {a,b,c,d,e) and A = {a,b,c} be the subset of X. The interior of A is

(A) {a,b,c} 

(B)  {a,b}

(C) {a}

(D) {b,c}

Check Answer
b

Q.67  The value of sin( cos^{-1}\frac{\sqrt{3}}{2}   ) is

(A) \frac{\sqrt{3}}{2}

(B) \frac{1}{\sqrt 2}

(C) \frac{1}{2}

(D)  1

Check Answer
c

Q.68   The smallest field containing set of integers Z is

(A) Q(\sqrt{3})

(B) Q(\sqrt{6})

(C) Q(\sqrt{2})

(D)  Q

Check Answer
d

Q.69 Let R be the usual metric space. Then which of the following set is not closed. 

(A) set of integers

(B)  set of rational numbers

(C) [0, 1]

(D)  \left \{ 1,\frac{1}{2},\frac{1}{3},... \right \}

Check Answer
b,d Both are correct

Q.70 Let R be the usual metric space and Z be the set of integers. Then clouser of Z is

(A) Z

(B) set of rational numbers 

(C) set of real number R

(D) set of natural numbers

Check Answer
a

Q.71 A subspace A of a complete metric space X is complete if and only if A is

(A)  X

(B) open

(C) closed

(D) empty set

Check Answer
a

Q.72  A subset A of a topological space X is open if and only if A is

(A)  A is neighbourhood of each of its points

(B) A is neighbourhood of some of its points

(C) A contains all of its limit points

(D) A contains all of its boundary points

Check Answer
a

Q.73   Non-zero elements of a finite filed form__________group. 

(A) non-cyclic

(B) an abelian group but not cyclic

(C) non-abelian

(D) a cyclic

Check Answer
b

Q.74  Let R be the cofinite topology. Then R is a

(A)  T_0 \;but\; not\; T_1 

(B) T_1 \;but\; not\; T_2

(C) T_2 \;but\; not\; T_3

(D) T_3 \;but\; not\; T_1

Check Answer
b
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