MCQOPTIONS
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MCQOPTIONS
This section includes 57 Mcqs, each offering curated multiple-choice questions to sharpen your Mental Ability knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
On solving algebraic expression -38b⁄2, answer will be |
| A. | 19b |
| B. | −19b |
| C. | 56b |
| D. | −56b |
| Answer» C. 56b | |
| 2. |
If -4x + 5y is subtracted from 3x + 2y then answer will be |
| A. | x - 3y |
| B. | x + 3y |
| C. | 2x + 5y |
| D. | 3x + 6y |
| Answer» B. x + 3y | |
| 3. |
By factorizing expression 2bx + 4by - 3ax -6ay, answer must be |
| A. | (2b - 3a)(x + 2y) |
| B. | (2b + 3a)(x - 2y) |
| C. | (2a- 3b)(3x - 2y) |
| D. | (2a + 3b)(2x - 4y) |
| Answer» B. (2b + 3a)(x - 2y) | |
| 4. |
Answer of factorization of expression 4z(3a + 2b - 4c) + (3a + 2b - 4c) is |
| A. | (4z - 1)(3a - 2b -4c) |
| B. | (4z + 1)(3a + 2b -4c) |
| C. | (4z + 1) - (3a + 2b -4c) |
| D. | (4z + 1) + (3a + 2b -4c) |
| Answer» C. (4z + 1) - (3a + 2b -4c) | |
| 5. |
Which equation is equivalent to 5x −2 (7 x + = 1) 14 x? |
| A. | −9x + 2=14 x |
| B. | −9x + 1=14 x |
| C. | −9x − 2 =14 x |
| D. | 12x − 1 =14 x |
| Answer» D. 12x − 1 =14 x | |
| 6. |
What is the solution set of the inequality 5 − x + 4 ≤−3? |
| A. | − ≤2 x ≤6 |
| B. | − ≤ 12 x ≤ 4 |
| C. | x ≤−2 or x ≥6 |
| D. | x ≤−12 or x ≥ 4 |
| Answer» E. | |
| 7. |
What is the solution for this equation? 2x −3 = 5 |
| A. | x =−1 or x = 4 |
| B. | x =−1 or x = 3 |
| C. | x =−4 or x = 4 |
| D. | x =−4 or x = 3 |
| Answer» B. x =−1 or x = 3 | |
| 8. |
What is the multiplicative inverse of 1/2 ? |
| A. | -2 |
| B. | 2 |
| C. | -1/2 |
| D. | 1/2 |
| Answer» C. -1/2 | |
| 9. |
Which number does not have a reciprocal? |
| A. | -1 |
| B. | 0 |
| C. | 1 |
| D. | 1/1000 |
| Answer» C. 1 | |
| 10. |
√16 + 3√ 8 = |
| A. | 2 |
| B. | 4 |
| C. | 6 |
| D. | 8 |
| Answer» D. 8 | |
| 11. |
Is the equation 3(2 x−4) =−18 equivalent to 6x−12 =−18? |
| A. | Yes, the equations are equivalent by the Distributive Property of Multiplication over Addition. |
| B. | Yes, the equations are equivalent by the Commutative Property of Multiplication |
| C. | Yes, the equations are equivalent by the Associative Property of Multiplication. |
| D. | No, the equations are not equivalent. |
| Answer» B. Yes, the equations are equivalent by the Commutative Property of Multiplication | |
| 12. |
On solving 2p - 3q - 4r + 6r - 2q + p, answer will be |
| A. | 8q -5r |
| B. | 7p + 5r |
| C. | 3p - 5q + 2r |
| D. | 10p + 3q - 5r |
| Answer» D. 10p + 3q - 5r | |
| 13. |
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. |
| A. | L is a Poset |
| B. | L is a lattice |
| C. | L is a boolean algebra |
| D. | none of these |
| Answer» C. L is a boolean algebra | |
| 14. |
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 ≤ |
| A. | n ! |
| B. | 1 |
| C. | n |
| D. | n + 2 |
| Answer» B. 1 | |
| 15. |
The absorption law is defined as |
| A. | a * ( a ⊕ b ) = a |
| B. | a * ( a * b ) = b |
| C. | a * ( a ⊕ b ) = b |
| D. | a * ( a * b ) = a ⊕ b |
| Answer» B. a * ( a * b ) = b | |
| 16. |
Different partially ordered sets may be represented by the same Hasse diagram if they are |
| A. | same |
| B. | isomorphic |
| C. | order-isomorphic |
| D. | lattices with same order |
| Answer» D. lattices with same order | |
| 17. |
Principle of duality is defined as |
| A. | all properties are unaltered when ≤ is replaced by ≥ other than 0 and 1 element. |
| B. | all properties are unaltered when ≤ is replaced by ≥ |
| C. | LUB becomes GLB |
| D. | ≤ is replaced by ≥ |
| Answer» B. all properties are unaltered when ≤ is replaced by ≥ | |
| 18. |
The less than relation, <, on reals is |
| A. | not a partial ordering because it is not anti- symmetric and not reflexive. |
| B. | not a partial ordering because it is not asymmetric and not reflexive |
| C. | a partial ordering since it is anti-symmetric and reflexive. |
| D. | a partial ordering since it is asymmetric and reflexive. |
| Answer» B. not a partial ordering because it is not asymmetric and not reflexive | |
| 19. |
If lattice (C ,≤) is a complemented chain, then |
| A. | |C|≤2 |
| B. | |C|≤1 |
| C. | |C| >1 |
| D. | C doesn't exist |
| Answer» B. |C|≤1 | |
| 20. |
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 |
| A. | 1 |
| B. | 3 |
| C. | 4 |
| D. | 7 |
| Answer» D. 7 | |
| 21. |
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 |
| A. | 1 |
| B. | 5 |
| C. | 15 |
| D. | 30 |
| Answer» E. | |
| 22. |
A self-complemented, distributive lattice is called |
| A. | Self dual lattice |
| B. | Complete lattice |
| C. | Modular lattice |
| D. | Boolean algebra |
| Answer» E. | |
| 23. |
Hasse diagrams are drawn for |
| A. | lattices |
| B. | boolean Algebra |
| C. | partially ordered sets |
| D. | none of these |
| Answer» E. | |
| 24. |
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 |
| A. | 1,5 |
| B. | 1,7 |
| C. | 1,3,5 |
| D. | None of these |
| Answer» B. 1,7 | |
| 25. |
In the group G = {2, 4, 6, 8) under multiplication modulo 10, the identity element is |
| A. | 2 |
| B. | 4 |
| C. | 6 |
| D. | 8 |
| Answer» E. | |
| 26. |
The set of all nth roots of unity under multiplication of complex numbers form a/an |
| A. | group |
| B. | abelian group |
| C. | semi group with identity |
| D. | commutative semigroups with identity |
| Answer» C. semi group with identity | |
| 27. |
Which of the following is TRUE ? |
| A. | Set of all matrices forms a group under multipication |
| B. | Set of all non-singular matrices forms a group under multiplication |
| C. | Set of all rational negative numbers forms a group under multiplication |
| D. | None of these |
| Answer» C. Set of all rational negative numbers forms a group under multiplication | |
| 28. |
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 |
| A. | 1 |
| B. | 3 |
| C. | 5 |
| D. | 7 |
| Answer» D. 7 | |
| 29. |
If A = (1, 2, 3, 4). Let ~= {(1, 2), (1, 3), (4, 2)}. Then ~ is |
| A. | reflexive |
| B. | transitive |
| C. | symmetric |
| D. | not anti-symmetric |
| Answer» C. symmetric | |
| 30. |
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 |
| A. | (7,11) |
| B. | (23,11) |
| C. | (32,40) |
| D. | (74,40) |
| Answer» E. | |
| 31. |
Some group (G, 0) is known to be abelian. Then which one of the following is TRUE for G ? |
| A. | G is of finite order |
| B. | g = g² for every g ∈ G |
| C. | g = g-1 for every g ∈ G |
| D. | (g o h)² = g²o h² for every g,h ∈ G |
| Answer» E. | |
| 32. |
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, *) ? |
| A. | (Z, *) is a group |
| B. | (Z, *) is a monoid |
| C. | (Z, *) is an abelian group |
| D. | None of these |
| Answer» E. | |
| 33. |
Let A be the set of all non-singular matrices over real numbers and let * be the matrix multiplication operator. Then |
| A. | < A, * > is a monoid but not a group |
| B. | < A, * > is a group but not an abelian group |
| C. | < A, * > is a semi group but not a monoid |
| D. | A is closed under * but < A, * > is not a semi group |
| Answer» C. < A, * > is a semi group but not a monoid | |
| 34. |
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 |
| A. | subgroup |
| B. | ininite, abelian |
| C. | finite abelian group |
| D. | infinite, non abelian group |
| Answer» E. | |
| 35. |
(Z,*) is a group with a*b = a+b+1 ∀ a, b ∈Z. The inverse of a is |
| A. | 0 |
| B. | -2 |
| C. | a-2 |
| D. | -a-2 |
| Answer» E. | |
| 36. |
If (G, .) is a group, such that (ab)2 = a2 b2 ∀ a, b ∈ G, then G is a/an |
| A. | abelian group |
| B. | non-abelian group |
| C. | commutative semi group |
| D. | none of these |
| Answer» B. non-abelian group | |
| 37. |
Which of the following statements is false ? |
| A. | If R is relexive, then R ∩ R-1 ≠ φ |
| B. | R ∩ R-1 ≠ φ =>R is anti-symmetric. |
| C. | If R, R' are relexive relations in A, then R - R' is reflexive |
| D. | If R, R' are equivalence relations in a set A, then R ∩ R' is also an equivalence relation in A |
| Answer» D. If R, R' are equivalence relations in a set A, then R ∩ R' is also an equivalence relation in A | |
| 38. |
If R = {(1, 2),(2, 3),(3, 3)} be a relation defined on A= {1, 2, 3} then R . R (= R2) is |
| A. | {(1, 2),(1, 3),(3, 3)} |
| B. | {(1, 3),(2, 3),(3, 3)} |
| C. | {(2, 1),(1, 3),(2, 3)} |
| D. | R itself |
| Answer» C. {(2, 1),(1, 3),(2, 3)} | |
| 39. |
Simplify (x - 9)(x + 10) ⁄ (x² - 81) |
| A. | (x + 10) ⁄ (x - 9) |
| B. | (x + 10) ⁄ (x + 9) |
| C. | (x² + x - 90) ⁄ (x² - 81) |
| D. | None of above |
| Answer» C. (x² + x - 90) ⁄ (x² - 81) | |
| 40. |
Expand and simplify (x + y)³ |
| A. | x³ - y³ |
| B. | x³ + y³ |
| C. | x³ + 3xy(x - y) + y³ |
| D. | x³ + 3xy(x + y) + y³ |
| Answer» E. | |
| 41. |
Factorise -20x² - 9x + 20 |
| A. | (5 - 4x)(4 - 5x) |
| B. | (5 - 4x)(4 + 5x) |
| C. | (5 + 4x)(4 - 5x) |
| D. | (5 + 4x)(4 + 5x) |
| Answer» D. (5 + 4x)(4 + 5x) | |
| 42. |
Factorise x² + x - 72 |
| A. | (x + 8)(x - 9) |
| B. | (x - 8)(x + 9) |
| C. | (x - ?72)² |
| D. | (x - ?72)(x + ?72) |
| Answer» C. (x - ?72)² | |
| 43. |
(a - b)² = |
| A. | a² + b² |
| B. | a² - b² |
| C. | a² + 2ab + b² |
| D. | a² - 2ab + b² |
| Answer» E. | |
| 44. |
Expand and simplfy (x - y)(x + y) |
| A. | x² - y² |
| B. | x² + y² |
| C. | x²- 2xy + y² |
| D. | x² + 2xy + y² |
| Answer» B. x² + y² | |
| 45. |
Expand and simplfy (x - 5)(x + 4) |
| A. | x² - x - 1 |
| B. | x² - x - 9 |
| C. | x² - x - 20 |
| D. | x² + 9x - 20 |
| Answer» D. x² + 9x - 20 | |
| 46. |
Simplify a(c - b) - b(a - c) |
| A. | ac + bc |
| B. | ac - 2ab - bc |
| C. | ac - 2ab + bc |
| D. | ac + 2ab + bc |
| Answer» D. ac + 2ab + bc | |
| 47. |
Simplify 5⁄2 ÷ 1⁄x |
| A. | 2x ⁄ 5 |
| B. | 5x ⁄ 2 |
| C. | 5 ⁄ 2x |
| D. | 2 ⁄ 5x |
| Answer» C. 5 ⁄ 2x | |
| 48. |
Simplify 15ax² ⁄ 5x |
| A. | 3ax |
| B. | 3ax² |
| C. | 5ax |
| D. | 5ax² |
| Answer» B. 3ax² | |
| 49. |
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 |
| A. | -1 |
| B. | 0 |
| C. | 1 |
| D. | 2 |
| Answer» B. 0 | |
| 50. |
The inverse of - i in the multiplicative group, {1, - 1, i , - i} is |
| A. | -1 |
| B. | 1 |
| C. | -i |
| D. | i |
| Answer» E. | |