If order matters and repetition is not allowed, then which counting method should be used in order to select 'k' elements from a total of 'n' elements?

• A) K-Permutation
• B) K-Sample
• C) K-Selection
• D) K-Combination

The sum of any rational number and any irrational number is irrational.

• A) False
• B) True
• C)
• D)

The rational number ‘2’ is the product of which of the two irrational numbers.

• A) √2, √2
• B) √2, √3
• C) √2, √5
• D) √2, √7

The predicate describing the final state is called ______.

• A) None
• B) post-condition of the algorithm
• C) pre-condition of the algorithm
• D) Input variables

A student can choose a computer project from one of the two lists. The two lists contain 12 and 18 possible projects, respectively.
How many possible projects are there to choose from ?

• A) 12
• B) 216
• C) 30
• D) 18

In division algorithm the pre-condition is?

• A) a is a nonnegative integer and d is a positive integer
• B) q and r are nonnegative integers
• C)
• D)

The last step of describing algorithms formally is?

• A) The output variable names.
• B) The name of the algorithm.
• C) An end statement.
• D) The input variable names.

A predicate is a sentence that contains a finite number of ----------------

• A) variables
• B) Constants
• C)
• D)

An integer n is prime number, if and only if
for all positive integers r and s, if n = rs then --------

• A) r > 1 or s > 1
• B) r = 1 or s = 1
• C) r < 1 or s < 1
• D) r = s

To prove by mathematical induction Inductive Step is ________.

• A) If P(k) is true then P(k - 1) is true for all integers k ≥ 1
• B) If P(k) is true then P(k + 1) is true for all integers k ≥ 1
• C)
• D)

The sum of two irrational numbers in general …………..

• A) may or may not be an irrational number
• B) none of these
• C) is always a rational number
• D) is always an irrational number

A box contains 5 different colored light bulbs. Which of the followings is the number of ordered samples of size 3 with replacement ?

• A) 243
• B) 8
• C) 15
• D) 125

The greatest common divisor (gcd) of two integers a and b is the largest integer that divides both a and b. It is called -------

• A) the Division Algorithm
• B) Pre-Condition of Algorithm
• C) the Euclidean Algorithm
• D) Post-Condition of Algorithm

----- is used to determine number of ordered or unordered arrangement of objects.

• A) Counting
• B) Algorithm
• C)
• D)

${\text{The}}\,{\text{sequence}}\,{1^3} + {2^3} + {3^3} + - - - - - - - + {n^3}\, = \,\_\_\_\_\_\_\_\,.$

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

The loop is correct if the four properties are true, one of the property is?

• A) Associativity
• B) Commutativity
• C) Eventual Falsity of Guard
• D) Transitivity

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 in which exactly one of the events can occur?

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

Which of the following statement is true according to the Division Algorithm?

• A) 17 = 5 x 4 - 3
• B) 17 = 5 x 1 + 12
• C) 17 = 5 x 3 + 2
• D) 17 = 5 x 5 - 8

Which of the following is not a rational number?

• A) 2
• B) 3.14
• C) √7
• D) 9/4

Which of the following is not a method to prove the mathematical statements?

• A) Permutation
• B) Mathematical induction
• C) Proof by contradiction
• D) Proof by contraposition