For every prime number n, n + 2 is prime.
Which of the following prime number disproves the above statement.

• A) n=3
• B) n=11
• C) n=5
• D) n=7

If one event can occur in ${n_1}$ ways, a second event can occur in ${n_2}$ ways, a third event can occur in ${n_3}$ ways, how ways all of the events can occur in the order?

• A) ${n_1} + {n_2} + {n_3}$
• B) ${n_1}.{n_2}.{n_3}$
• C)
• D)

$${\text{The}}\,{\text{sequence}}\,1 + 2 + 3 + 4 - - - - - - + n\,{\text{is}}\,{\text{equal}}\,{\text{to}}\,\_\_\_\_\_\_\_\,.$$

• A) $$\frac{{{n^2}}}{2}$$
• B) $$\frac{{n\left( {n + 1} \right)}}{2}$$
• C) $$\frac{{n\left( {n + 1} \right)\left( {2n + 1} \right)}}{6}$$
• D) $$\frac{{{n^2}{{\left( {n + 1} \right)}^2}}}{4}$$

GCD of (8, 12) will be _____.

• A) 3
• B) 4
• C) 6
• D) 5

The factorial form of 9.8.7.6 is ______.

• A) 9!/4!
• B) 6!/5!
• C) 9!/5!
• D) 7!/6!

Number of combinations of 3-bit string that contain exactly three “0” is ……………….

• A) 6
• B) 7
• C) 1
• D) 8

To prove by mathematical induction basis step is _______.

• A) The proposition P(1) is true
• B) The proposition P(1) is false
• C)
• D)

P(0, 0)=________ ?

• A) 0
• B) 1
• C) 2
• D) Undefined

The predicate which describes the initial state is called the ---------- of the algorithm

• A) post-condition
• B) pre-condition
• C)
• D)

Number of ways the ‘7’ student can be divided into group of ‘3’ and ‘4’are ……………

• A) 35
• B) 120
• C) 50
• D) 210

The contrapositive of “5n + 2 is odd, then n is odd” is ………..

• A) “ if n is even then 5n + 2 is not even”
• B) “ if n is even then 5n + 2 is even”
• C) “ if n is not even then 5n + 2 is even”
• D) “ if n is not even then 5n + 2 is not even”

To prove by mathematical induction for 1+3+5+ ...+ (2n-1) = n^2 for all positive integers, the basis step is ------------

• A) 1+3+5+ ...+ (2k-1) = k^2
• B) 1+3+5+ ...+ (2(k+1)-1) = (k+1)^2
• C) LHS = p(1) = 2x1-1=1, RHS = 1^2 = 1
• D) 1+3+5+ ...+ (2n-1) = n^2

In how many ways can 6 people be seated on 6 available seats?

• A) 720
• B) 120
• C) 12
• D) 6

(-2)! = _________ ?

• A) 2
• B) -2
• C) Undefined
• D) 0

The set of prime numbers is -------------

• A) infinite set.
• B) finite set.
• C) continuous set.
• D) None of these.

There are 4 bus lines between X and Y; and 5 bus lines between Y and Z , the number of ways a person can travel from X to Z?

• A) 9
• B) 20
• C)
• D)

The sum of two irrational numbers must be an irrational number.

• A) True
• B) False
• C)
• D)

Proof by contraposition is based on the logical equivalence between a statement and its..... .

• A) none of these
• B) Inverse
• C) Converse
• D) contrapositive

P(n, 2)=90, Which of the followings is the value of n ?

• A) 90
• B) 45
• C) 15
• D) 10

In basis property the first iteration of the loop is solved for?

• A) I(k + 1)
• B) None
• C) I(k)
• D) I(0)