Mathematical foundation of Computer science
HNBGU BCA Previous Question Paper 201314
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If Q be the set of rational numbers and a function f:Q>Q be defined by f(x) = 2x+3, show that f is bijective. Find a formula that defines the inverse function.

Define a relation and a function. Give and example of a relation which is reflexive and transitive but not symmetric.



Show that the set N of all natural numbers is not a group with respect to addition.

Show that the set of all n, nth roots of unity forms a finite abelian group of order n with respect to multiplication



Decompose the following permutation into transposition:

1 2 3 4 5 6 7 6 5 2 4 3 1 7

1 2 3 4 5 6 7 8 3 1 4 7 2 5 8 6


If a group G has four elements, show that it must be abelian.



Five the two numeric functions and such that neither asymptotically dominates nor asymptotically dominates

Solve the recurrence relation a_{r}3a_{r1}+2a_{r2}=6, satisfying the initial conditions a_{0}=1 and a_{1}=4.



Solve the difference equation:
a_{r+2}2a_{r+1}+a_{r}=3r +5

If f is a homeomorphism of a group G into a group G’ with kernel K, then K is a normal subgroup of G.



Prove that each of the following is a tautology:
 [(p>q)^(q>r)]>(p>r)
 [p^(p>q)]>q


Write the form of the negation of each of the following:
 The corresponding sides of two triangles are equal if and only if the triangles are congruent.
 If the number x is less than 10, then there is a number y such that x^{2}+y^{2}100 is positive


If X be the set of factors of 12 and if ≤ be the relation divides, i.e., x ≤ y if and only if x  y. Draw the Hasse Diagram of (X,≤)

Prove that any right (left ) cosets of a subgroup are either disjoint or identical

Read Also:
 Computer Fundamental HNBGU BCA PYQ 2011
 Computer Fundamental HNBGU BCA PYQ 2012
 Computer Fundamental HNBGU BCA PYQ 2013
 Computer Fundamental HNBGU BCA PYQ 2016
 Computer Networks HNBGU BCA PYQ 2018
 Data Structure HNBGU BCA PYQ 2019
 General English HNBGU BCA PYQ 2016
 MFCS HNBGU BCA PYQ 2013
 MFCS HNBGU BCA PYQ 2016
 MFCS HNBGU BCA PYQ 2018
 Modern English HNBGU BCA PYQ 2018
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 Programming in C HNBGU BCA PYQ 2018