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

• 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]$$\frac{{n\left( {n + 1} \right)\left( {2n + 1} \right)}}{6}$$

If n is an odd integer then ‘3n+2’ is ………

• A) even
• B) either even or odd
• C) neither even nor odd
• D) odd

The sum of (6 − 7√2) and (6 + 7√2) is …………..

• A) 12-14√2)
• B) 12
• C) 2(6-7√2)
• D) 2(6+7√2)

If there are 5 different optional courses in English and 3
different optional courses in Maths. Choices for a student who wants to take one optional course _____?

• A) 7
• B) 8
• C) 9
• D) 5

If the guard G and the loop invariant I(k) are both true for an integer k ≥ 0 before an iteration of the loop, then I(k + 1) is?

• A) False
• B) True
• C)
• D)

The sum of two odd integers is ....

• A) even
• B) odd
• C)
• D)

Which of the following is not a rational number?

• A) 9/4
• B) 3.14
• C) 2
• D) √7

The factorial form of 9.8.7.6 is ______.

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

Proof by Contradiction is a/an........ method of proof.

• A) Direct
• B) Indirect
• C)
• D)

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 product of any two consecutive positive integers is divisible by 2.

• A) True
• B) False
• C)
• D)

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)

The sum of two integers is even when ……….

• A) one is zero and one is odd
• B) one is prime and one is composite
• C) one is even and one is odd
• D) both are even or both are odd

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

• A) 6
• B) 1
• C) 8
• D) 7

Proof by ……..uses the equivalence p →q ≡(p∧~q) →c

• A) contradiction
• B) superposition
• C) mathematical induction
• D) contraposition

If E(5)=5, then find arithmetic mean willl be

• A) 1
• B) 10
• C) 5
• D) 0

Which of the followings is correct option?

• A) C(n, 0) = 1
• B) C(n, n) = n
• C) C(n, k) + C(n, k + 1) = C(n, k + 1)
• D) C(n, k) = C(n + k, n – k)

$P(A|A) = ....................$

• A) 2
• B) 1
• C) 0
• D) None of these