Highest current gain is obtained in common base configuration of an amplifier.

Bipolar junction transistor (BJT) is a voltage controlled device

Suppressor grid in pentode is kept at anode potential

Ideal current source has zero internal resistance.

Check whether the following graph is critical or not.

Draw the Ferrar graph of the following partitions:

i) 20 = 9+6+3+2

ii) 28 = 10+9+8+1

Also, write down the conjugate partitions of each of these partitions.

Express   in terms of [x]4 [ x]3 [x]2 and [x].

Find the generating function of the recurrence with initial conditions .

From a survey of 120 people, the following data was obtained: 90 owned a car, 35 owned a computer, 40 owned a house, 32 owned a car and a house, 21 owned a house and a computer, 26 owned a car and a computer, 17 owned all the three facilities.

i) How many people owned neither of the three.

ii) How many people owned only a car?

iii) How many people owned only a computer?

How many numbers form 0 to 999 (0 and 999 inclusive) are indivisible by 7 or 11?

If a planar graph has the degree sequence (2,2,2,3,4,4,5), how many faces will it have? Draw a planar graph with this degree sequence and the number of faces obtained to check your answer.

Use generating function to prove the identity

Find the general form of the solution to a linear homogeneous recurrence relation with constant coefficients for which the characteristic roots are 1,−2 and 3 with multiplicities 2,1 and 2, respectively. The relation also has a non-homogeneous part which is a linear combination of 3n and (−2) n

Write the expression   in conjunction normal form and disjunctive normal form

Consider the graph given below:

i) Write the degree sequence of the graph.

ii) Exhibit a cycle of length 9 in this graph.

iii) Does this have any complete graph as its subgraph? If yes, exhibit one

A die is rolled twice and the sum of the numbers that appear is observed. What is the probability that the sum is either a perfect square or a perfect cube?

If 5 points are chosen in a square of side 2cm, show that there will always be two points at a distance of at most √ 2cm

A bank pays you 4.5% interest per year. In addition, you receive ₹ 100 as bonus at the end of the year (after the interest is paid). Find a recurrence for the amount of money after n years if you invest ₹ 2000.

If the solution of the recurrence relation  is , then determine the values of α,β and

Write down the converse of each of the following statements: 

i) If p is a prime number and a and b are any two natural numbers and if p divides a or b, then p divides ab

ii) In a triangle .  then