McqMate
These multiple-choice questions (MCQs) are designed to enhance your knowledge and understanding in the following areas: Computer Science Engineering (CSE) .
| 201. |
Let (A7, ⊗7)=({1, 2, 3, 4, 5, 6}, ⊗7) is a group. It has two sub groups X and Y. X={1, 3, 6}, Y={2, 3, 5}. What is the order of union of subgroups? |
| A. | 65 |
| B. | 5 |
| C. | 32 |
| D. | 18 |
| Answer» B. 5 | |
| 202. |
A relation (34 × 78) × 57 = 57 × (78 × 34) can have property. |
| A. | distributive |
| B. | associative |
| C. | commutative |
| D. | closure |
| Answer» B. associative | |
| 203. |
B1: ({0, 1, 2….(n-1)}, xm) where xn stands for “multiplication-modulo-n” and B2: ({0, 1, 2….n}, xn) where xn stands for “multiplication-modulo-m” are the two statements. Both B1 and B2 are considered to be |
| A. | groups |
| B. | semigroups |
| C. | subgroups |
| D. | associative subgroup |
| Answer» B. semigroups | |
| 204. |
If group G has 65 elements and it has two subgroups namely K and L with order 14 and 30. What can be order of K intersection L? |
| A. | 10 |
| B. | 42 |
| C. | 5 |
| D. | 35 |
| Answer» C. 5 | |
| 205. |
Consider the binary operations on X, a*b = a+b+4, for a, b ∈ X. It satisfies the properties of |
| A. | abelian group |
| B. | semigroup |
| C. | multiplicative group |
| D. | isomorphic group |
| Answer» A. abelian group | |
| 206. |
Let * be the binary operation on the rational number given by a*b=a+b+ab. Which of the following property does not exist for the group? |
| A. | closure property |
| B. | identity property |
| C. | symmetric property |
| D. | associative property |
| Answer» B. identity property | |
| 207. |
A group G, ({0}, +) under addition operation satisfies which of the following properties? |
| A. | identity, multiplicity and inverse |
| B. | closure, associativity, inverse and identity |
| C. | multiplicity, associativity and closure |
| D. | inverse and closure |
| Answer» B. closure, associativity, inverse and identity | |
| 208. |
If (M, *) is a cyclic group of order 73, then number of generator of G is equal to |
| A. | 89 |
| B. | 23 |
| C. | 72 |
| D. | 17 |
| Answer» C. 72 | |
| 209. |
The set of even natural numbers, {6, 8, 10, 12,..,} is closed under addition operation. Which of the following properties will it satisfy? |
| A. | closure property |
| B. | associative property |
| C. | symmetric property |
| D. | identity property |
| Answer» A. closure property | |
| 210. |
A non empty set A is termed as an algebraic structure |
| A. | with respect to binary operation * |
| B. | with respect to ternary operation ? |
| C. | with respect to binary operation + |
| D. | with respect to unary operation – |
| Answer» A. with respect to binary operation * | |
| 211. |
An algebraic structure is called a semigroup. |
| A. | (p, *) |
| B. | (q, +, *) |
| C. | (p, +) |
| D. | (+, *) |
| Answer» A. (p, *) | |
| 212. |
Condition for monoid is |
| A. | (a+e)=a |
| B. | (a*e)=(a+e) |
| C. | a=(a*(a+e) |
| D. | (a*e)=(e*a)=a |
| Answer» D. (a*e)=(e*a)=a | |
| 213. |
A monoid is called a group if |
| A. | (a*a)=a=(a+c) |
| B. | (a*c)=(a+c) |
| C. | (a+c)=a |
| D. | (a*c)=(c*a)=e |
| Answer» D. (a*c)=(c*a)=e | |
| 214. |
Matrix multiplication is a/an property. |
| A. | commutative |
| B. | associative |
| C. | additive |
| D. | disjunctive |
| Answer» B. associative | |
| 215. |
How many properties can be held by a group? |
| A. | 2 |
| B. | 3 |
| C. | 5 |
| D. | 4 |
| Answer» C. 5 | |
| 216. |
A cyclic group is always |
| A. | abelian group |
| B. | monoid |
| C. | semigroup |
| D. | subgroup |
| Answer» A. abelian group | |
| 217. |
{1, i, -i, -1} is |
| A. | a commutative subgroup |
| B. | a lattice |
| C. | a trivial group |
| D. | a monoid |
| Answer» C. a trivial group | |
| 218. |
Let K be a group with 8 elements. Let H be a subgroup of K and H<K. It is known that the size of H is at least 3. The size of H is |
| A. | semigroup |
| B. | subgroup |
| C. | cyclic group |
| D. | abelian group |
| Answer» C. cyclic group | |
| 219. |
is not necessarily a property of a Group. |
| A. | commutativity |
| B. | existence of inverse for every element |
| C. | existence of identity |
| D. | associativity |
| Answer» A. commutativity | |
| 220. |
A group of rational numbers is an example of |
| A. | a subgroup of a group of integers |
| B. | a subgroup of a group of real numbers |
| C. | a subgroup of a group of irrational numbers |
| D. | a subgroup of a group of complex numbers |
| Answer» B. a subgroup of a group of real numbers | |
| 221. |
Intersection of subgroups is a |
| A. | group |
| B. | subgroup |
| C. | semigroup |
| D. | cyclic group |
| Answer» B. subgroup | |
| 222. |
What is a circle group? |
| A. | a subgroup complex numbers having magnitude 1 of the group of nonzero complex elements |
| B. | a subgroup rational numbers having magnitude 2 of the group of real elements |
| C. | a subgroup irrational numbers having magnitude 2 of the group of nonzero complex elements |
| D. | a subgroup complex numbers having magnitude 1 of the group of whole numbers |
| Answer» A. a subgroup complex numbers having magnitude 1 of the group of nonzero complex elements | |
| 223. |
A normal subgroup is |
| A. | a subgroup under multiplication by the elements of the group |
| B. | an invariant under closure by the elements of that group |
| C. | a monoid with same number of elements of the original group |
| D. | an invariant equipped with conjugation by the elements of original group |
| Answer» D. an invariant equipped with conjugation by the elements of original group | |
| 224. |
Two groups are isomorphic if and only if is existed between them. |
| A. | homomorphism |
| B. | endomorphism |
| C. | isomorphism |
| D. | association |
| Answer» C. isomorphism | |
| 225. |
a * H is a set of coset. |
| A. | right |
| B. | left |
| C. | sub |
| D. | semi |
| Answer» B. left | |
| 226. |
a * H = H * a relation holds if |
| A. | h is semigroup of an abelian group |
| B. | h is monoid of a group |
| C. | h is a cyclic group |
| D. | h is subgroup of an abelian group |
| Answer» D. h is subgroup of an abelian group | |
| 227. |
Lagrange’s theorem specifies |
| A. | the order of semigroup is finite |
| B. | the order of the subgroup divides the order of the finite group |
| C. | the order of an abelian group is infinite |
| D. | the order of the semigroup is added to the order of the group |
| Answer» B. the order of the subgroup divides the order of the finite group | |
| 228. |
A function is defined by f(x)=2x and f(x + y) = f(x) + f(y) is called |
| A. | isomorphic |
| B. | homomorphic |
| C. | cyclic group |
| D. | heteromorphic |
| Answer» A. isomorphic | |
| 229. |
An isomorphism of a group onto itself is called |
| A. | homomorphism |
| B. | heteromorphism |
| C. | epimorphism |
| D. | automorphism |
| Answer» D. automorphism | |
| 230. |
The elements of a vector space form a/an under vector addition. |
| A. | abelian group |
| B. | commutative group |
| C. | associative group |
| D. | semigroup |
| Answer» A. abelian group | |
| 231. |
A set of representatives of all the cosets is called |
| A. | transitive |
| B. | reversal |
| C. | equivalent |
| D. | transversal |
| Answer» D. transversal | |
| 232. |
Which of the following statement is true? |
| A. | the set of all rational negative numbers forms a group under multiplication |
| B. | the set of all matrices forms a group under multiplication |
| C. | the set of all non-singular matrices forms a group under multiplication |
| D. | the set of matrices forms a subgroup under multiplication |
| Answer» C. the set of all non-singular matrices forms a group under multiplication | |
| 233. |
How many different non-isomorphic Abelian groups of order 8 are there? |
| A. | 5 |
| B. | 4 |
| C. | 2 |
| D. | 3 |
| Answer» C. 2 | |
| 234. |
Consider the set B* of all strings over the alphabet set B = {0, 1} with the concatenation operator for strings |
| A. | does not form a group |
| B. | does not have the right identity element |
| C. | forms a non-commutative group |
| D. | forms a group if the empty string is removed from |
| Answer» A. does not form a group | |
| 235. |
All groups satisfy properties |
| A. | g-i to g-v |
| B. | g-i to g-iv |
| C. | g-i to r-v |
| D. | r-i to r-v |
| Answer» B. g-i to g-iv | |
| 236. |
An Abelian Group satisfies the properties |
| A. | g-i to g-v |
| B. | g-i to r-iv |
| C. | g-i to r-v |
| D. | r-i to r-v |
| Answer» A. g-i to g-v | |
| 237. |
A Ring satisfies the properties |
| A. | r-i to r-v |
| B. | g-i to g-iv |
| C. | g-i to r-v |
| D. | g-i to r-iii |
| Answer» D. g-i to r-iii | |
| 238. |
A Ring is said to be commutative if it also satisfies the property |
| A. | r-vi |
| B. | r-v |
| C. | r-vii |
| D. | r-iv |
| Answer» D. r-iv | |
| 239. |
An ‘Integral Domain’ satisfies the properties |
| A. | g-i to g-iii |
| B. | g-i to r-v |
| C. | g-i to r-vi |
| D. | g-i to r-iii |
| Answer» C. g-i to r-vi | |
| 240. |
a.(b.c) = (a.b).c is the representation for which property? |
| A. | g-ii |
| B. | g-iii |
| C. | r-ii |
| D. | r-iii |
| Answer» A. g-ii | |
| 241. |
a(b+c) = ac+bc is the representation for which property? |
| A. | g-ii |
| B. | g-iii |
| C. | r-ii |
| D. | r-iii |
| Answer» D. r-iii | |
| 242. |
For the group Sn of all permutations of n distinct symbols, what is the number of elements in Sn? |
| A. | n |
| B. | n-1 |
| C. | 2n |
| D. | n! |
| Answer» D. n! | |
| 243. |
Does the set of residue classes (mod 3) form a group with respect to modular addition? |
| A. | yes |
| B. | no |
| C. | can’t say |
| D. | insufficient data |
| Answer» A. yes | |
| 244. |
Does the set of residue classes (mod 3) form a group with respect to modular addition? |
| A. | yes |
| B. | no |
| C. | can’t say |
| D. | insufficient data |
| Answer» B. no | |
| 245. |
The less-than relation, <, on a set of real numbers is |
| A. | not a partial ordering because it is not asymmetric and irreflexive equals antisymmetric |
| B. | a partial ordering since it is asymmetric and reflexive |
| C. | a partial ordering since it is antisymmetric and reflexive |
| D. | not a partial ordering because it is not antisymmetric and reflexive |
| Answer» A. not a partial ordering because it is not asymmetric and irreflexive equals antisymmetric | |
| 246. |
If the longest chain in a partial order is of length l, then the partial order can be written as disjoint antichains. |
| A. | l2 |
| B. | l+1 |
| C. | l |
| D. | ll |
| Answer» C. l | |
| 247. |
Suppose X = {a, b, c, d} and π1 is the partition of X, π1 = {{a, b, c}, d}. The number of ordered pairs of the equivalence relations induced by |
| A. | 15 |
| B. | 10 |
| C. | 34 |
| D. | 5 |
| Answer» B. 10 | |
| 248. |
The inclusion of sets into R = {{1, 2}, {1, 2, 3}, {1, 3, 5}, {1, 2, 4}, {1, 2, 3, 4, 5}} is necessary and sufficient to make R a complete lattice under the partial order defined by set containment. |
| A. | {1}, {2, 4} |
| B. | {1}, {1, 2, 3} |
| C. | {1} |
| D. | {1}, {1, 3}, {1, 2, 3, 4}, {1, 2, 3, 5} |
| Answer» C. {1} | |
| 249. |
Consider the set N* of finite sequences of natural numbers with a denoting that sequence a is a prefix of sequence b. Then, which of the following is true? |
| A. | every non-empty subset of has a greatest lower bound |
| B. | it is uncountable |
| C. | every non-empty finite subset of has a least upper bound |
| D. | every non-empty subset of has a least upper bound |
| Answer» A. every non-empty subset of has a greatest lower bound | |
| 250. |
A partial order ≤ is defined on the set S = {x, b1, b2, … bn, y} as x ≤ bi for all i and bi ≤ y for all i, where n ≥ 1. The number of total orders on the set S which contain the partial order ≤ is |
| A. | n+4 |
| B. | n2 |
| C. | n! |
| D. | 3 |
| Answer» C. n! | |
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