In how many ways a student can choose one of each of the courses when he is offered 3 mathematics courses, 4 literature courses and 2 history courses.

• A) 288
• B) 14
• C) 9
• D) 24

(n-2)!/(n-2)=_________ ?

• A) (n-1)!
• B) (n-2)!
• C) (n-3)!
• D) (n-2)(n-3)!

${\text{If}}\,n\,{\text{is}}\,{\text{any}}\,{\text{positive}}\,{\text{integer}}\,{\text{then}}\,{2^n} \geqslant 2\left( {n + 1} \right)\,{\text{is}}\,{\text{true}}\,{\text{for}}\,{\text{all}}\,\,\_\_\_\_\_\_\_\_\,.$

• A) $n \geqslant 3$
• B) $n \leqslant 3$
• C) $n > 3$
• D) $n < 3$

In a city, the bus route numbers consist of a natural number less than 20, followed by one of the letters A,B,C,D,E and F. How many different bus routes are possible?

• A) 20!
• B) 114
• C) 26
• D) 120

${\text{If}}\,n\,{\text{is}}\,{\text{any}}\,{\text{positive}}\,{\text{integer}}\,{\text{then}}\,{\text{the}}\,{\text{sequence}}\,3 + 6 + 9 + - - - - - - + 3n\, = \,\,\_\_\_\_\_\_\_\,.$

• A) $\frac{{{n^2}{{\left( {n + 1} \right)}^2}}}{4}$
• B) $\frac{{3n\left( {n + 1} \right)}}{2}$
• C) $$3n(n + 1)$$
• D) $\frac{{2n\left( {n + 1} \right)}}{3}$

In the Direct Proof, we show that if the statement p is true, then the statement q is ----------

• A) not necessarily true.
• B) true
• C) false
• D) opposite to p

A proof by contraposition is based on the logical equivalence between a statement and its………..

• A) contrapositive
• B) none of these
• C) converse
• D) inverse

GCD of (330,156) is?

• A) 6
• B) 12
• C) 5
• D) 8

For all positive real numbers a and b, if a < b, then -----------

• A) a^2 = b^2
• B) a^2 > b^2
• C) a^2 < b^2
• D) None of these.

How many 4-bit string contain at least one “1”

• A) 14
• B) 16
• C) 15
• D) 12

How many multiples of 5 are there from 10 to 75?

• A) 14
• B) 15
• C) 20
• D) 10

Algorithm is a more general term in that the term ---- refers to a particular programming language.

• A) None
• B) Information
• C) Task
• D) Program

A bit string is a sequence of 0’s and 1’s.

• A) True
• B) False
• C)
• D)

An integer n is a perfect square if and only if ---------- for some integer k.

• A) n = k^3
• B) n = k^2
• C) n = square-root of k
• D) n = 2k

Sum rule in terms of sets, involves which set operation?

• A) Intersection
• B) Union
• C)
• D)

There are three bus lines between A and B, and two bus lines between B and C.
Find the number of ways a person can travel round trip by bus from A to C by way of B ?

• A) 5
• B) 36
• C) 6
• D) 10

While proofing by contradiction the equivalence ………..is used.

• A) p →q ≡(~p∧~q) →c
• B) ~p →q ≡(p∧~q) →c
• C) p →~q ≡(p∧~q) →c
• D) p →q ≡(p∧~q) →c

$${\text{The}}\,{\text{statement}}\,{3^n} < n!\,{\text{is}}\,{\text{true}}\,{\text{when}}\,\_\_\_\_\_\_\,.$$

• A) $$n > 6$$
• B) $$n = 6$$
• C) $$n = 2$$
• D) $$n = 4$$

While proofing by contraposition the equivalence ………..is used.

• A) ~p →~q≡ ~q→~p
• B) p →~q≡ ~q→~p
• C) p →q≡ ~q→~p
• D) ~p →q≡ ~q→~p

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

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