Free Printable ANT-UNIT-1&II

1.

1. Which one is a commutative property.

a)

a∘b=b+a

b)

a∘b=b∘a

c)

a∘b=ab

2.

2. Which of the following statements are not true.

a)

For every group G, the inverse of each element of G is unique.

b)

For every group G, the identity of G is unique.

c)

For every group G, the inverse of each element of G is not unique

3.

3. For every group G, if a,b,c∈G and ab=ac, then b=c is called ----

a)

Associative

b)

Right cancellation

c)

Left cancellation

4.

4. If (G,∘)is a group such that

\left(ab\right)^2=a^2b^2

for all a,b∈G then G is an ---

a)

Sub group

b)

Abelian group

c)

Non-abelian group

5.

5.In the group G, the value of $b^{-1}a^{-1}$ is ----

a)

ab

b)

$\left(ab\right)^{-1}$

c)

$\left(ba\right)^{-1}$

6.

6. The inverse of -i in the multiplicative group {1,-1,i,-i} is

a)

i

b)

1

c)

-i

7.

7. The number of elements in a group is not finite is called

a)

Finite order

b)

Infinite order

c)

None of these

8.

8.When the function f is satisfies the condition one-to-one, onto and homomorphism is called---

a)

Monomorphism

b)

Epimorphism

c)

Isomorphism

9.

9. For any subset satisfies all the conditions of group means is called

a)

Group

b)

Subgroup

c)

Abelian group

10.

10. Which of the following condition is true.

a)

$z_4^*$ ={0,1,2,3}

b)

$z_4$ ={0,1,2,3,4}

c)

$z_5^*$ ={1,2,3,4}

11.

11. Which one is a correct statement?

a)

$f\left(e_G\right)=e^G$

b)

$f\left(e_G\right)=e_G$

c)

$f\left(e_G\right)=\left(e_H\right)$

12.

12 .When the homomorphism function is called isomorphism. If it is satisfies

a)

One-0ne

b)

Onto

c)

Both

13.

13. Every subgroup of a cyclic group is …..

a)

Group

b)

Cyclic

c)

Subgroup

14.

14.Find all the elements of order 10 in $\left(z_{15},+\right)$

a)

4, 8, 28, 32

b)

4, 12, 28, 36

c)

4, 12, 28

15.

15.Find all the elements in $U_6$

a)

{1, 4, 5}

b)

{1, 5}

c)

{1}

16.

16. Which one is a division algorithm

a)

s = qt + r

b)

q = r

c)

a = q -1

17.

17.Matrix multiplication is must satisfies ------

a)

Commutative Property

b)

Closure Property

c)

Associative Property

18.

18. Gcd of (5, 26) is

a)

5

b)

1

c)

4

19.

19.Find the order of $\pi_0$ if $\pi_0$ is identity permutation

a)

1

b)

0

c)

2

20.

20.When the function f is called a group homomorphism

a)

∀ a,b∈G ,f(a.b)=f(a)*f(b)

b)

∀ a,b∈G ,g(a.b)=g(a)*g(b)

c)

∀ a,b∈G ,f(a.b)=f(ba)

21.

21.Let R be a ring. The ring R is said to have ------- if for all a,b∈R, ab=z⇒a=z or b=z

a)

No proper divisors of zero

b)

Proper divisors of zero

c)

Both

22.

22. Let R be a ring. If ab=ba for all, a,b∈R, then R is called --------

a)

Associative Ring

b)

Commutative Ring

c)

Sub ring

23.

23. a + (b + c) = (a + b) + c is called ---------

a)

Associative law for *

b)

Distributive law

c)

Associative law for +

24.

24. The statement, “a is congruent to b modulo n” it is written as

a)

b = a + n

b)

a = b + kn

c)

None of the above

25.

25. What is the last digit in $3^{32}$

a)

1

b)

4

c)

7

26.

26. The divisor of 20 is -----

a)

{1, 2, 5, 10, 15, 20}

b)

{1, 10, 12, 20}

c)

{1, 2, 4, 5, 10,20}

27.

27. Whether the given pair of integers 68, 118 is congruent modulo 8.

a)

No

b)

Yes

28.

28. The integer 56 having ---- number of divisor.

a)

5

b)

6

c)

4

29.

29. Whether the given statement is true “ The additive inverse of each ring element is unique”.

a)

True

b)

False

30.

10. In any ring (R, +, .). The zero element z is ------

a)

Twice

b)

Unique

c)

None of the above

31.

31.For polynomials in F[x] every non-zero polynomial of ---- is irreducible

a)

degree ≥ 1

b)

degree ≤ 1

c)

degree ≥ 2

32.

A polynomial f(x)∈F[x] having its leading co-efficient 1 is called ----

a)

Monic

b)

Field

c)

Field

33.

33.How many monic polynomials in $Z_{7} [x]$ have degree 5 ?

a)

7

b)

c)

7^5

34.

34. Is S(x)=x2+1 is reducible in Z2[x]

a)

Yes

b)

No

35.

35. If ∣F∣=q and degree s(x)=n ,

then s(x)/F[x] contains …….. elements.

a)

$n^q$

b)

$q^n$

c)

Not defined

36.

36.The Division Algorithm is contains ---- parts.

a)

Two

b)

Three

c)

Infinite

37.

37.Find the quotient and remainder when the first integer is divided by the second (207, 15)

a)

q = -1, r = 2

b)

q = 13, r = 12

c)

q = 11, r = 15

38.

38.Find the positive factor of f(19)

a)

{1, 3, 19}

b)

{1, 19)

c)

{1, 19)

39.

39.25 div 5 = ---

a)

0

b)

5

c)

3

40.

40.Every non empty set of positive integers has a least number.

a)

The well ordering principle

b)

The pigeonhole principle

c)

The inclusion-Exclusion principle

41.

41.Let f(n) denote the number of positive factors of a positive integer n, Evaluate f(12)

a)

6

b)

4

c)

2

42.

42.The sum of any two odd integers is ---

a)

Odd

b)

Even

c)

Neither odd nor even

43.

43.The sum and the product of any two even integers are ---

a)

Even

b)

Odd

c)

None of these

44.

44.The product of any two odd integer is ---.

a)

Even

b)

Odd

c)

Either odd or even

45.

45.Whether it is true or false. Let a and b be positive integers such that a|b and b|a. Then a = b.

a)

False

b)

True

46.

46.Express 676 = ( )_eight.

a)

1244

b)

1145

c)

1028

47.

Find the number of ones in the binary representation of

2^5-1

a)

4

b)

5

c)

3

48.

48.Express (1101)₂ into octal integer.

a)

21

b)

19

c)

15

49.

Express 10110_two in base ten.

a)

21

b)

22

c)

20

50.

50.Find the positive integer of 1976. It is divisible by 13

a)

138

b)

136

c)

134

ANT-UNIT-1&II

Total questions: 50

Worksheet time: 50mins

Similar Resources on Wayground