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ASSIGNMENT
PROGRAM MCA(REVISED FALL 2012)
SEMESTER FIRST
SUBJECT CODE & NAME MCA1030- FOUNDATION OF MATHEMATICS
CREDIT 4
BK ID B1646
MAX.MARKS 60
Note: Answer all questions. Kindly note that answers for 10 marks questions should be approximately
of 400 words. Each question is followed by evaluation scheme.
Q.1 State Leibnitz’s theorem. Find the nth derivative of𝑦(𝑥)= 𝑥2
𝑒 𝑎𝑥, using Leibnitz theorem.
Answer: - Leibniz's rule for differentiation under the integral sign, named after Gottfried Leibniz, tells us
that if we have an integral of the form
Then for x in (x0, x1) the derivative of this integral is thus expressible
Provided that f and its partial derivative f(x) are both continuous over a region in the form [x0, x1] × [y0,
y1].Thus under certain conditions, one may interchange the integral and partial differential operators.
This important result is particularly useful in
Q.2 Define Tautology and contradiction. Show that
a) (p q)  (~ p) is a tautology.
b) (p q) (~ p) is a contradiction
Answer: - Tautology: - A proposition which is always true is called a tautology. The column of a
tautology in a truth table contains only T's. For example, if is a proposition, then is a tautology. We could

2. have used tautologies for proving all the previous laws; just add an extra column to each truth table,
corresponding to the specific logical equivalence and check that this column
Q.3 State Lagrange’s Theorem. Verify Lagrange’s mean value theorem for the function
f(x) = 3 x2
– 5x + 1 defined in interval [2, 5]
Answer: - Suppose f is a function defined on a closed interval [a,b] (with a<b ) such that the following
two conditions hold:
Q.4 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.
Answer: - Negation: - The action or logical operation of negating or making negative b : a negative
statement, judgment, or doctrine; especially : a logical proposition formed by asserting the falsity of a
given proposition .
 Negation refers to contradiction and not to a contrary statement.
 We should be very careful while writing



Q.5 Find the asymptote parallel to the coordinate axis of the following curves
(i) (𝑥2
+𝑦2
)𝑥−𝑎𝑦2
=0
(ii) 𝑥2
𝑦2
−𝑎2
(𝑥2
+𝑦2
)=0
Answer: - (I) (𝑥2
+𝑦2
)𝑥−𝑎𝑦2
=0
F(x) = (𝑥2
+𝑦2
)𝑥−𝑎𝑦2
(b ) 𝑥2 𝑦2− 𝑎2( 𝑥2+ 𝑦2)=0

3. Q.6 Define (I) Set (ii) Null Set (iii) Subset (iv) Power set (v)Union set
Answer: - Set: - In everyday life, we have to deal with the collections of objects of one kind or the other.
 The collection of even natural numbers less than 12 i.e., of the numbers 2,4,6,8, and 10.
 The collection of vowels in the English alphabet, i.e., of the letters a ,e ,i ,o , u.
 The collection of all students of class MCA 1st semester of your college.
 In each of the above collections, it is
Dear students get fully solved SMU MBA Spring 2014 assignments
Send your semester & Specialization name to our mail id :
“ help.mbaassignments@gmail.com ”
or
Call us at : 08263069601