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Summer 2015
|
PROGRAM
|
MCA(REVISED
FALL 2012)
|
|
SEMESTER
|
FIRST
|
|
SUBJECT
CODE & NAME
|
MCA1030-
FOUNDATION OF MATHEMATICS
|
|
CREDIT
|
4
|
|
BK
ID
|
B1646
|
|
MAX.
MARKS
|
60
|
Q1. State Leibnitz’s theorem. Find the nth derivative of(𝑥)= 𝑥2𝑒𝑎𝑥,
using Leibnitz theorem. [2+8] 10
Answer.
Leibnitz’s theorem
Statement: Let u(x) and v(x) be nth
order differentiable functions
Q2. Define Tautology and contradiction. Show that
a) (pV q) V (~ p) is a tautology.
b) (p^ q) ^ (~
p) is a contradiction [2+2+3+3] 10 marks
Answer.
a) A statement is said to be a tautology
if it is true for all logical possibilities. In other words, a statement is
called tautology if its truth value is T and only T in the last
column of its truth table.
Q3. State
Lagrange’s Theorem. Verify Lagrange’s mean value theorem for the function f(x)
= 3 x2 – 5x + 1 defined in interval [2, 5] [2+8] 10 marks
Answer.
Lagrange’s Theorem
Let f: [a,b] ->R be a
continuous function such that f: (a,b)->R is differentiable. Then, there
exists c ε (a,b) such that [f(b)-f(a)]/(b-a)
=f’(c).
Geometrical Interpretation
It states
Q4. Define
Negation. Write the negation of each of the following conjunctions:
a) Paris is in
France and London is in England.
b) 2 + 3 = 5 and 8
< 10. [2+8] 10 marks
Answer.
Negation
An assertion that a statement
fails or denial of a statement is called the negation of the statement. The
negation of a statement is generally formed by introducing the word “not” at
some proper place in the statement
Q5. Find the asymptote parallel to the coordinate axis of the following
curves
(i) (𝑥2+𝑦2)x−𝑎𝑦2=0
(ii) 𝑥2𝑦2−𝑎2(𝑥2+𝑦2)=0 [5+5] 10
marks
Answer.
Solution: (i) We have (𝑥2+𝑦2)x−𝑎𝑦2=0
Or
x3+(x-a)y2=0
Asymptote parallel to x – axis
are obtained by equating to zero the coefficient of the highest power of x.
Since
Q6. Define (i) Set (ii) Null Set (iii) Subset (iv) Power set (v) Union
set [5*2] 10 marks
Answer.
(i)
Set
A set is a well defined collection of
objects. The following points may be noted:
i) Objects, elements and members of a
set are synonymous terms.
ii) Sets are usually denoted by
capital letters A, B, C, X, Y, Z etc.
iii) The
Get fully solved assignment. Buy online from website
online store
or
plz drop a mail with your sub code
we will revert you within 2-3 hour or immediate
Charges rs
125/subject and rs 500/semester only.
if urgent then call us on 08791490301, 08273413412
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