MCQOPTIONS
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MCQOPTIONS
This section includes 379 Mcqs, each offering curated multiple-choice questions to sharpen your VITEEE knowledge and support exam preparation. Choose a topic below to get started.
| 101. |
A polygon with 25 sides can be triangulated into |
| A. | 23 |
| B. | 20 |
| C. | 22 |
| D. | 21 |
| Answer» B. 20 | |
| 102. |
A polygon with 12 sides can be triangulated into |
| A. | 7 |
| B. | 10 |
| C. | 5 |
| D. | 12 |
| Answer» C. 5 | |
| 103. |
What is the induction hypothesis assumption for the inequality m ! > 2m where m>=4? |
| A. | for m=k, k+1!>2k holds |
| B. | for m=k, k!>2k holds |
| C. | for m=k, k!>3k holds |
| D. | for m=k, k!>2k+1 holds |
| Answer» C. for m=k, k!>3k holds | |
| 104. |
For any positive integer m is divisible by 4. |
| A. | 5m2 + 2 |
| B. | 3m + 1 |
| C. | m2 + 3 |
| D. | m3 + 3m |
| Answer» E. | |
| 105. |
For any integer m>=3, the series 2+4+6+…+(4m) can be equivalent to |
| A. | m2+3 |
| B. | m+1 |
| C. | mm |
| D. | 3m2+4 |
| Answer» B. m+1 | |
| 106. |
For m = 1, 2, …, 4m+2 is a multiple ofis known as |
| A. | lemma |
| B. | corollary |
| C. | conjecture |
| D. | none of the mentioned |
| Answer» B. corollary | |
| 107. |
A proof that p → q is true based on the fact that q is true, such proofs are known as |
| A. | direct proof |
| B. | contrapositive proofs |
| C. | trivial proof |
| D. | proof by cases |
| Answer» D. proof by cases | |
| 108. |
A proof broken into distinct cases, where these cases cover all prospects, such proofs are known as |
| A. | direct proof |
| B. | contrapositive proofs |
| C. | vacuous proof |
| D. | proof by cases |
| Answer» D. proof by cases | |
| 109. |
A proof covering all the possible cases, such type of proofs are known as |
| A. | direct proof |
| B. | proof by contradiction |
| C. | vacuous proof |
| D. | exhaustive proof |
| Answer» E. | |
| 110. |
When to proof P→Q true, we proof P false, that type of proof is known as |
| A. | direct proof |
| B. | contrapositive proofs |
| C. | vacuous proof |
| D. | mathematical induction |
| Answer» D. mathematical induction | |
| 111. |
Let the statement be “If n is not an odd integer then square of n is not odd.”, then if P(n) is “n is an not an odd integer” and Q(n) is “(square of n) is not odd.” For direct proof we should prove |
| A. | ∀np ((n) → q(n)) |
| B. | ∃ np ((n) → q(n)) |
| C. | ∀n~(p ((n)) → q(n)) |
| D. | ∀np ((n) → ~(q(n))) |
| Answer» B. ∃ np ((n) → q(n)) | |
| 112. |
“Parul is out for a trip or it is not snowing” and “It is snowing or Raju is playing chess” imply that |
| A. | parul is out for trip |
| B. | raju is playing chess |
| C. | parul is out for a trip and raju is playing chess |
| D. | parul is out for a trip or raju is playing chess |
| Answer» E. | |
| 113. |
What rules of inference are used in this argument?“Jay is an awesome student. Jay is also a good dancer. Therefore, Jay is an awesome student and a good dancer.” |
| A. | conjunction |
| B. | modus ponens |
| C. | disjunctive syllogism |
| D. | simplification |
| Answer» B. modus ponens | |
| 114. |
What rules of inference are used in this argument?“It is either colder than Himalaya today or the pollution is harmful. It is hotter than Himalaya today. Therefore, the pollution is harmful.” |
| A. | conjunction |
| B. | modus ponens |
| C. | disjunctive syllogism |
| D. | hypothetical syllogism |
| Answer» D. hypothetical syllogism | |
| 115. |
What rules of inference are used in this argument?“All students in this science class has taken a course in physics” and “Marry is a student in this class” imply the conclusion “Marry has taken a course in physics.” |
| A. | universal instantiation |
| B. | universal generalization |
| C. | existential instantiation |
| D. | existential generalization |
| Answer» B. universal generalization | |
| 116. |
Find a counterexample of ∀x∀y(xy > y), where the domain for all variables consists of all integers. |
| A. | x = -1, y = 17 |
| B. | x = -2 y = 8 |
| C. | both x = -1, y = 17 and x = -2 y = 8 |
| D. | does not have any counter example |
| Answer» D. does not have any counter example | |
| 117. |
Let L(x, y) be the statement “x loves y,” where the domain for both x and y consists of all people in the world. Use quantifiers to express, “Joy is loved by everyone.” |
| A. | ∀x l(x, joy) |
| B. | ∀y l(joy,y) |
| C. | ∃y∀x l(x, y) |
| D. | ∃x ¬l(joy, x) |
| Answer» B. ∀y l(joy,y) | |
| 118. |
Let domain of m includes all students, P(m) be the statement “m spends more than 2 hours in playing polo”. Express ∀m ¬P (m) quantification in English. |
| A. | a student is there who spends more than 2 hours in playing polo |
| B. | there is a student who does not spend more than 2 hours in playing polo |
| C. | all students spends more than 2 hours in playing polo |
| D. | no student spends more than 2 hours in playing polo |
| Answer» E. | |
| 119. |
(p → r) ∨ (q → r) is logically equivalent to |
| A. | (p ∧ q) ∨ r |
| B. | (p ∨ q) → r |
| C. | (p ∧ q) → r |
| D. | (p → q) → r |
| Answer» D. (p → q) → r | |
| 120. |
(p → q) ∧ (p → r) is logically equivalent to |
| A. | p → (q ∧ r) |
| B. | p → (q ∨ r) |
| C. | p ∧ (q ∨ r) |
| D. | p ∨ (q ∧ r) |
| Answer» B. p → (q ∨ r) | |
| 121. |
p ↔ q is logically equivalent to |
| A. | (p → q) → (q → p) |
| B. | (p → q) ∨ (q → p) |
| C. | (p → q) ∧ (q → p) |
| D. | (p ∧ q) → (q ∧ p) |
| Answer» D. (p ∧ q) → (q ∧ p) | |
| 122. |
¬ (p ↔ q) is logically equivalent to |
| A. | q↔p |
| B. | p↔¬q |
| C. | ¬p↔¬q |
| D. | ¬q↔¬p |
| Answer» C. ¬p↔¬q | |
| 123. |
p ∨ q is logically equivalent to |
| A. | ¬q → ¬p |
| B. | q → p |
| C. | ¬p → ¬q |
| D. | ¬p → q |
| Answer» E. | |
| 124. |
p → q is logically equivalent to |
| A. | ¬p ∨ ¬q |
| B. | p ∨ ¬q |
| C. | ¬p ∨ q |
| D. | ¬p ∧ q |
| Answer» D. ¬p ∧ q | |
| 125. |
The compound propositions p and q are called logically equivalent if is a tautology. |
| A. | p ↔ q |
| B. | p → q |
| C. | ¬ (p ∨ q) |
| D. | ¬p ∨ ¬q |
| Answer» B. p → q | |
| 126. |
Let P: If Sahil bowls, Saurabh hits a century.; Q: If Raju bowls, Sahil gets out on first ball. Now if P is true and Q is false then which of the following can be true? |
| A. | raju bowled and sahil got out on first ball |
| B. | raju did not bowled |
| C. | sahil bowled and saurabh hits a century |
| D. | sahil bowled and saurabh got out |
| Answer» D. sahil bowled and saurabh got out | |
| 127. |
Let p: I will get a job, q: I pass the exam, then the statement form: I will get a job only if I pass the exam, in symbolic from is |
| A. | p → q |
| B. | p ˄ q |
| C. | q → p |
| D. | p ˄ q |
| Answer» B. p ˄ q | |
| 128. |
The less than relation < on real is __________. |
| A. | a partial ordering since it is asymmetric and reflexive |
| B. | a partial ordering since it is anti-symmetric and reflexive |
| C. | not a partial ordering since it is not asymmetric and not reflexive |
| D. | not a partial ordering since it is not anti-symmetric and not reflexive |
| Answer» E. | |
| 129. |
A graph that has neither self loops nor parallel edges is called_____graph. |
| A. | regular |
| B. | simple |
| C. | complete |
| Answer» C. complete | |
| 130. |
Let A and B be two sets in the same universal set. Then A – B = |
| A. | a b |
| B. | a b |
| C. | a b |
| D. | none of these |
| Answer» D. none of these | |
| 131. |
Which of the following is Absorption Law? |
| A. | a*a <=>a |
| B. | a+(a*b)<=> a |
| C. | a*b <=>a*a |
| D. | (a*b)*c <=>a*(b*c) |
| Answer» C. a*b <=>a*a | |
| 132. |
The set difference of the set A with null set is ________. |
| A. | a |
| B. | |
| C. | u |
| Answer» B. | |
| 133. |
Two vertices which are incident with the common edge are called______________vertices. |
| A. | distinct |
| B. | directed |
| C. | adjacent |
| D. | loops |
| Answer» D. loops | |
| 134. |
Let a relation R in the set R of real numbers be defined as (a, b) Î R if and only if 1 + ab > 0 for all a, bÎR. The relation R is |
| A. | reflexive and symmetric |
| B. | symmetric and transitive |
| C. | only transitive |
| D. | an equivalence relation |
| Answer» B. symmetric and transitive | |
| 135. |
The NAND statement is a combination of ______. |
| A. | NOT and AND |
| B. | NOT and OR |
| C. | AND and OR |
| D. | NOT or OR |
| Answer» B. NOT and OR | |
| 136. |
Using Induction Principle if 13 = 1, 23 = 3 + 5, 33 = 7 + 9 + 11, then |
| A. | 43= 15 + 17 + 19 + 21 |
| B. | 43= 11 + 13 + 15 + 17 + 19 |
| C. | 43 = 13 + 15 + 17 + 19 |
| D. | 43 = 13 + 15 + 17 + 19 + 21 |
| Answer» D. 43 = 13 + 15 + 17 + 19 + 21 | |
| 137. |
Let P: If Sahil bowls, Saurabh hits a century.; Q: If Raju bowls, Sahil gets out on first ball. Now if P istrue and Q is false then which of the following can be true? |
| A. | Raju bowled and Sahil got out on first ball |
| B. | Raju did not bowled |
| C. | Sahil bowled and Saurabh hits a century |
| D. | Sahil bowled and Saurabh got out |
| Answer» D. Sahil bowled and Saurabh got out | |
| 138. |
(p ˄ (p → q )) → q is logically equivalent to |
| A. | p ˅ q |
| B. | (p ˄ q) ˅ (~ p˄ ~q) |
| C. | tautology |
| D. | (~ p ˅ q) ˄ (p ˅ q) |
| Answer» D. (~ p ˅ q) ˄ (p ˅ q) | |
| 139. |
To prove the statement P is tautologically equivalent to the statement Q, it is enough toprove that _______. |
| A. | P conditional Q is a contradiction |
| B. | P conditional Q is a tautology |
| C. | P biconditional Q is a contradiction |
| D. | P biconditional Q is a tautology |
| Answer» E. | |
| 140. |
A directed complete graph of n vertices contains __________. |
| A. | one arrow between each pair of distinct vertices |
| B. | two arrows between each pair of distinct vertices |
| C. | n-1 arrows between each pair of distinct vertices |
| D. | path between every two distinct vertices |
| Answer» B. two arrows between each pair of distinct vertices | |
| 141. |
The grammar G ={{S},{0,1},P,S}} where P={S tends to 0S1 , S tends to S1} is a ________. |
| A. | recursively enumerable grammar. |
| B. | regular grammar |
| C. | context sensitive grammar |
| D. | context free grammar |
| Answer» E. | |
| 142. |
The production S tends to aB is of the type ________grammar. |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | all the above |
| Answer» E. | |
| 143. |
The production S tends to A is of the type _____grammar. |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | all the above |
| Answer» B. 1 | |
| 144. |
If R= {(x, 2x)} and S= {(x, 5x)} then R composition S=____. |
| A. | {(x, 4x)} |
| B. | {(x, 2x)} |
| C. | {(x, 8x)} |
| D. | {(x, 10x)} |
| Answer» E. | |
| 145. |
The bit strings for the sets are 1111100000 and 1010101010. The union of these sets is ____________. |
| A. | 1010100000 |
| B. | 1010101101 |
| C. | 1111111100 |
| D. | 1111101010 |
| Answer» E. | |
| 146. |
If R is reflexive, symmetric and transitive then the relation is said to be ________. |
| A. | Binary relation |
| B. | Compatibility relation |
| C. | Equivalence relation |
| D. | Partial order relation |
| Answer» D. Partial order relation | |
| 147. |
If a relation is reflexive then in the graph of a relation there must be a loop at _____. |
| A. | each node |
| B. | only first node |
| C. | any two nodes |
| D. | only first and last nodes |
| Answer» B. only first node | |
| 148. |
If (∼ p → r) ˄ (p ↔ q) is T and r is F, then truth values of p and q are: |
| A. | p is t, q is t |
| B. | p is t, q is f |
| C. | p is f, q is f |
| D. | p is f, q is t |
| Answer» B. p is t, q is f | |
| 149. |
The number of letters in a word is called ________. |
| A. | length |
| B. | string |
| C. | syntax |
| D. | alphabet |
| Answer» B. string | |
| 150. |
(P->Q)-> (^Q) is __________. |
| A. | not a well formed formula |
| B. | tautology |
| C. | contradiction |
| D. | well formed formula |
| Answer» B. tautology | |