y=sin³ x cos³ x

Evaluate

Evaluate 

b) 

a) 

Which of the following Boolean expression is a tautology?

(i) (p^q) v (pvq)

(ii) (p^q) v (p→q)

(iii) (p^q) ^ (p→q)

(iv) (p^q) → (p→q)

For the statement p and q, consider the following compound statements:

B. {(pvq)^-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

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.

If x,y,z be respectively the p^th, q^th and r^th term of G.P., then evaluate

(q-r) logx + (r-p) logy + (p-q) logz

b)

a) 

If the universal set is U = {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 U, then verify

a) De-Morgan's Laws

b) Left distributive law

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

Describe the simple vapour compression refrigeration cycle in detail.

Enumerate some of the desirable properties of refrigerants.

Describe a closed cycle gas turbine power plant and its characteristics with a neat sketch.

Differentiate, in detail between a four stroke and a two-stroke IC engine.

Derive the expression for efficiency in a Diesel cycle.

Enlist and explain the two primary classification of a condenser to be used in a power plant. Also, discuss steam surface condenser configuration.

Describe a velocity compounded impulse turbine with a neat sketch.