PPSC Lecturer Mathematics 2004
PPSC Lecturer Mathematics 2004
PPSC Lecturer Mathematics 2004
Prove that f is continuous if and only if f A f A , where A is closure of A . (12)
and let GL3 ¡ A M 3 ¡ : det A 0 . (10)
(b) Prove the following claims
(i) M 3 ¡ is a vector space of dimension 9 .
(ii) GL3 ¡ forms a non abelian group with centre consisting of non-zero scalar
matrices. (10)
Q 6: (a) A farmer has 50 ton of cattle which he can sell at a profit of Rs. 120 per ton. If
the cattle gain weight by 5 ton per week, but the profit falls by Rs. 4 per ton, when should
he sell the cattle to obtain the maximum profit? (10)
(b) Find the shortest distance between the lines
x a 2y 12z and x y 2a 6z 6a (10)
Q 7: (a) Prove that a monotonic increasing sequence which is bounded above, converges
to its least upper bound. (10)
(b) Discuss the existence of the Riemann integration over a closed interval a, b . (10)
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