1 - (a - b)² =
a² - 2ab + b²
2 - (Z,*) is a group with a*b = a+b+1 ∀ a, b ∈Z. The inverse of a is
-a-2
3 - √16 + 3√ 8 =
6
4 - A partial order is deined on the set S = {x, a1, a2, a3,...... an, y} as x ≤ a i for all i and ai ≤ y for all i, where n ≥ 1. Number of total orders on the set S which contain partial order ≤
n !
5 - A self-complemented, distributive lattice is called
Boolean algebra
6 - A self-complemented, distributive lattice is called
Boolean algebra
7 - Answer of factorization of expression 4z(3a + 2b - 4c) + (3a + 2b - 4c) is
(4z + 1)(3a + 2b -4c)
8 - By factorizing expression 2bx + 4by - 3ax -6ay, answer must be
(2b - 3a)(x + 2y)
9 - Different partially ordered sets may be represented by the same Hasse diagram if they are
order-isomorphic
10 - Expand and simplfy (x - 5)(x + 4)
x² - x - 20
11 - Expand and simplfy (x - y)(x + y)
x² - y²
12 - Expand and simplify (x + y)³
x³ + 3xy(x + y) + y³
13 - Factorise -20x² - 9x + 20
(5 + 4x)(4 - 5x)
14 - Factorise x² + x - 72
(x - 8)(x + 9)
15 - Hasse diagrams are drawn for
none of these
16 - If (G, .) is a group such that (ab)- 1 = a-1b-1, ∀ a, b ∈ G, then G is a/an
abelian group
17 - If (G, .) is a group such that a2 = e, ∀a ∈ G, then G is
abelian group
18 - If (G, .) is a group, such that (ab)2 = a2 b2 ∀ a, b ∈ G, then G is a/an
abelian group
19 - If -4x + 5y is subtracted from 3x + 2y then answer will be
x - 3y
20 - If A = (1, 2, 3, 4). Let ~= {(1, 2), (1, 3), (4, 2)}. Then ~ is
transitive
21 - If a, b are positive integers, define a * b = a where ab = a (modulo 7), with this * operation, then inverse of 3 in group G (1, 2, 3, 4, 5, 6) is
5
22 - If R = {(1, 2),(2, 3),(3, 3)} be a relation defined on A= {1, 2, 3} then R . R (= R2) is
{(1, 3),(2, 3),(3, 3)}
23 - If the binary operation * is deined on a set of ordered pairs of real numbers as (a,b)*(c,d)=(ad+bc,bd) and is associative, then (1, 2)*(3, 5)*(3, 4) equals
(74,40)
24 - In the group G = {2, 4, 6, 8) under multiplication modulo 10, the identity element is
8
25 - Is the equation 3(2 x−4) =−18 equivalent to 6x−12 =−18?
Yes, the equations are equivalent by the Distributive Property of Multiplication over Addition.
26 - Let (Z, *) be an algebraic structure, where Z is the set of integers and the operation * is defined by n * m = maximum (n, m). Which of the following statements is TRUE for (Z, *) ?
None of these
27 - Let A be the set of all non-singular matrices over real numbers and let * be the matrix multiplication operator. Then
< A, * > is a group but not an abelian group
28 - Let D30 = {1, 2, 3, 4, 5, 6, 10, 15, 30} and relation I be partial ordering on D30. The all lower bounds of 10 and 15 respectively are
1,5
29 - Let D30 = {1, 2, 3, 5, 6, 10, 15, 30} and relation I be a partial ordering on D30. The lub of 10 and 15 respectively is
30
30 - Let G denoted the set of all n x n non-singular matrices with rational numbers as entries. Then under multiplication G is a/an
infinite, non abelian group
31 - Let L be a set with a relation R which is transitive, antisymmetric and reflexive and for any two elements a, b ∈ L. Let least upper bound lub (a, b) and the greatest lower bound glb (a, b) exist.
L is a lattice
32 - Let X = {2, 3, 6, 12, 24}, and ≤ be the partial order defined by X ≤ Y if X divides Y. Number of edges in the Hasse diagram of (X, ≤ ) is
4
33 - On solving 2p - 3q - 4r + 6r - 2q + p, answer will be
3p - 5q + 2r
34 - On solving algebraic expression -38b⁄2, answer will be
−19b
35 - Principle of duality is defined as
all properties are unaltered when ≤ is replaced by ≥ other than 0 and 1 element.
36 - Simplify (x - 9)(x + 10) ⁄ (x² - 81)
(x + 10) ⁄ (x + 9)
37 - Simplify 15ax² ⁄ 5x
3ax
38 - Simplify 5⁄2 ÷ 1⁄x
5x ⁄ 2
39 - Simplify a(c - b) - b(a - c)
ac - 2ab + bc
40 - Some group (G, 0) is known to be abelian. Then which one of the following is TRUE for G ?
(g o h)² = g²o h² for every g,h ∈ G
41 - The absorption law is defined as
a * ( a ⊕ b ) = a
42 - The banker's discount on a certain sum due 2 years hence is 11/10 of the true discount. 10 The rate percent is:
0.05
43 - The inverse of - i in the multiplicative group, {1, - 1, i , - i} is
i
44 - The less than relation, <, on reals is
not a partial ordering because it is not anti- symmetric and not reflexive.
45 - The set of all nth roots of unity under multiplication of complex numbers form a/an
abelian group
46 - The set of all real numbers under the usual multiplication operation is not a group since
zero has no inverse
47 - The set of integers Z with the binary operation "*" defined as a*b =a +b+ 1 for a, b ∈ Z, is a group. The identity element of this group is
-1
48 - What is the multiplicative inverse of 1/2 ?
2
49 - What is the solution for this equation? 2x −3 = 5
x =−1 or x = 4
50 - What is the solution set of the inequality 5 − x + 4 ≤−3?
x ≤−12 or x ≥ 4
51 - Which equation is equivalent to 5x −2 (7 x + = 1) 14 x?
−9x − 2 =14 x
52 - Which number does not have a reciprocal?
0
53 - Which of the following is TRUE ?
Set of all non-singular matrices forms a group under multiplication
54 - Which of the following statements is false ?
If R, R' are relexive relations in A, then R - R' is reflexive
55 - Which of the following statements is FALSE ?
The set of rational numbers form an abelian group under multiplication
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