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This particular Assignment references the syllabus chosen for the subject of Applied Science - Energy, for the January 2024 - July 2024 session. The code for the assignment is BEY-12 and it is often used by students who are enrolled in the BSCAEY Degree.
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Q.1 State whether the following statement are True or False and also give the reason in support of your answer.
a) Collection of intelligent students of IGNOU forms a set.
b) Following rule is a function from A to B
c) 
d) The negation of the following statement p is ¬p.
p: Longest chord of a circle is diameter
¬p: Diameter is the shortest chord of circle
e) Any term of an AP(except the first and last) is equal to half the sum of terms which are equidistant from it on both sides
Q.2 If the universal set is Ս = {1,2,3,4,5,6,7,9,10} and A = {2,3,6,7}, B= {4,6,8,9}, C= {6,7,8} are the subsets of Ս, then verify
a) De-Morgan’s Laws
b) Left distributive law
Q.3 Evaluate the following:
Q.4 a) If x,y,z be respectively the pth, qth and rth term of G.P., then evaluate (q-r) logx + (r-p) logy + (p-q) logz
b) The numbers a,b and c are between 2 and 18, such that, (i) their sum is 25, (ii) the number 2, a and b are consecutive terms of an A.P. and (iii) the number b,c and 18 are consecutive terms of a G.P. Find the values of a,b,c.
Q.5 a) For the statement p and q, consider the following compound statements:
A. {¬q ∧ (p→q)} → ¬p
B. {(p∨q) ∧ ¬p} → q
Then which of the following statement is correct:
(i) A is a tautology but not B
(ii) A and B both are not tautologies
(iii) A and B both are tautologies
(iv) B is a tautology but not A
b) Which of the following Boolean expression is a tautology?
(i) (p∧q) ∨ (p∨q)
(ii) (p∧q) ∨ (p→q)
(iii) (p∧q) ∧ (p→q)
(iv) (p∧q) → (p→q)
Q.6 Solve the following discrete difference equations:
a) Yt+2 + 12yt+1 + 30yt = 2 + 3t2
b) Yt+2 + 15yt+1 + 5yt = 1 + 6t + 13t2
Q.7
Q.8 Differentiate the following functions:
Q.9 Evaluate the following:
Q.10 Show that
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