| Board | CBSE |
| Textbook | NCERT |
| Class | Class 12 |
| Subject | Computer Science |
| Chapter | CUET CS Chapter-Boolean Algebra |
| Chapter Name | Boolean Algebra |
| Category | CUET (Common University Entrance Test) UG |
MCQ-Based Questions for CUET Computer Science Chapter-Boolean Algebra
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Practice Questions for CUET Computer Science chapter-Boolean Algebra SET-1
Computer Science - MCQ on Boolean Algebra
Class XII
Q.1 The statement, which can take only two values, i.e., either true or false is called
a) tautological statement.
b) logical statement.
c) boolean statements.
d) relational statements.
Answer:
(b)
Explanation: A statement which can be classified as true or false without ambiguity, is known as a logical statement.
Q.2 The truth-values of logical statements are called
a) logical variables.
b) logical constants.
c) binary statement.
d) binary constants.
Answer:
(b)
Explanation: In symbolic logic, a logical constant of a language L is a symbol that has the same semantic value in all models of (the expressions of) L. Two important types of logical constants are logical connectives and quantifiers.
Q.3 Logical statement that is combined with the help of logical operators form
a) binary statement.
b) compound statement.
c) boolean statement.
d) switching statement.
Answer:
(b)
Explanation:A compound statement consists of zero or more statements enclosed in curly braces { }. Compound statements are commonly called "blocks."
Q.4 Speed with which an electronic switch can change from ON to OFF and vice-versa, is known as
a) switching speed.
b) running speed.
c) packet speed.
d) circuit speed.
Answer:
(a)
Explanation: Switching speed is the speed with which an electronic switch can change from ON to OFF and vice-versa. It is usually expressed in terms of the propagation delay time.
Q.5 The simplification of the following Boolean function is
F = y(wz’ + wz) + xy
a) y(w+x)
b) w(x+y)
c) x(w+y)
d) xy’+w
Answer:
(a)
Explanation: F = y(wz’ + wz) + xy
= yw(z+z’) + xy
= yw + xy
= y(w+x)
Q.6 The following property of the boolean algebra is called
(p+q)’ = p’q’
a) commutative law.
b) DeMorgan’s law.
c) associative law.
d) logical law.
Answer:
(b)
Explanation: In formal logic, De Morgan's laws are rules relating the logical operators "and" and "or" in terms of each other via negation, namely:
NOT (P OR Q) = (NOT P) AND (NOT Q)
NOT (P AND Q) = (NOT P) OR (NOT Q)
Q.7 The canonical SOP form of P+Q’R is
a) PQR + PQ’R + PQR’ + PQ’R’ + P’Q’R’
b) P’Q’R + PQ’R + PQR’ + PQ’R’ + P’Q’R’
c) PQ’R + PQ’R + PQR’ + PQ’R’ + P’Q’R’
d) PQR’ + PQ’R + PQR’ + PQ’R’ + P’Q’R’
Answer:
(a)
Explanation: P+Q’R
= P(Q+Q’)(R+R’)+Q’R(P+P’)
= (PQ + PQ’)(R+R’)+PQ’R + P’Q’R
= PQR + PQ’R + PQR’ +PQ’R’+P’Q’R
= PQR + PQ’R + PQR’ +PQ’R’ +P’Q’R’
Q.8 The canonical SOP form of P+QR’ is
a) P’QR + P’QR’ + P’Q’R + PQR’ +P’Q’R’
b) P’Q’R + P’QR’ + P’Q’R + PQR’ +P’Q’R’
c) P’QR + P’Q’R’ + P’Q’R + PQR’ +P’Q’R’
d) P’QR + P’QR’ + P’Q’R + P’QR’ +P’Q’R’
Answer:
(a)
Explanation: P+QR’
= P’[Q+Q’][R+R’] + QR’[P+P’]
= P’QR + P’QR’ + P’Q’R + P’Q’R’ + PQR’ + P’QR’
= P’QR + P’QR’ + P’Q’R + PQR’ + P’Q’R’
Q.9 The dual of the Boolean expression (B’+C).A is
a) B’C.A
b) B’C + A
c) BC + A’
d) B’C.A’
Answer:
(b)
Explanation:Changing (+) to (.) and vice versa and by replacing 0’s with 1’s and1’s with 0’s,the dual of the expression can be obtained.
Q.10 The dual of the Boolean expression A +B’C is
a) A.B’ + C
b) A+B’C
c) A’B’ +C
d) A+B+C’
Answer:
(a)
Explanation: Changing (+) to (.) and vice versa and by replacing 0’s with 1’s and 1’s with 0’s,the dual of the expression can be obtained.
Q.11 Seven inverters are cascaded one after the other. If the input is 1, output will be
a) 1
b) 0
c) no output.
d) Infinite.
Answer:
(b)
Explanation: In an inverter, output is always the reverse of the input. Therefore, when input is 1, the output will be 0.
Q.12 The dual of the boolean expression (x+y)(x’+z’)(y+z) is
a) x.y+x’z’+yz’
b) x.y+x’z’+y’z
c) x.y+x’z’+yz
d) x’.y+x’z’+yz
Answer:
(c)
Explanation: Changing (+) to (.) and vice versa and by replacing 0’s with 1’s and 1’s with 0’s,the dual of the expression can be obtained.
Q.13 The dual of the boolean expression X.X’ = 0 is
a) X+X=1
b) X+X’=0
c) X’+X’=1
d) X+X’=1
Answer:
(d)
Explanation: Changing (+) to (.) and vice versa and by replacing 0’s with 1’s and 1’s with 0’s,the dual of the expression can be obtained.
Q.14 NAND and NOR are universal gates because
a) these gates were the first to develop.
b) these gates are combination of NOT, AND, OR gates.
c) any circuit diagram is possible using these two gates.
d) these gates follow distributive law.
Answer:
(c)
Explanation: NAND and NOR are functionally complete gates, i.e., any gate can be formed using these two gates.
Q.15 The idempotent law states
a) X+X = X’ and X.X = X
b) X+X = X and X.X = X
c) X+X = X and X.X = X’
d) X+X = X’ and X.X = X’
Answer:
(b)
Explanation: If X = 1 then
X + X = 1 + 1 = 1 = X
X.X = 1.1 = 1 = X
Q.16 The absorption law states
a) X + X.Y = X
b) X + X’.Y = X
c) X + X.Y’ = X
d) X + X.Y = X’
Answer:
(a)
Explanation: The expression can be proved with the help of truth table. The values of X and X+XY are the same and this law is known as absorption law.
Q.17 The involution law states that
a) (X’)’ = X’
b) (X’) = X
c) (X)’ = X
d) (X’)’ = X
Answer:
(c)
Explanation: If X = 1 then
X’ = 0
(X’)’ = 1 = X
Q.18 The difference between the distributive laws of Boolean algebra and the distributive laws of ordinary algebra is
a) first distributive law of Boolean algebra is not available in the ordinary algebra.
b) first idempotent law of Boolean algebra is not available in the ordinary algebra.
c) second distributive law of Boolean algebra is not available in the ordinary algebra.
d) first commutative law of Boolean algebra is not available in the ordinary algebra.
Answer:
(c)
Explanation: The distributive law states that: X.(Y+Z) = X.Y +X.Z and X+Y.Z = (X+Y).(X+Z).The second distributive law of the Boolean algebra is not available in the ordinary algebra.
Q.19 The purpose of Karnaugh maps is
a) to maximize the boolean expression.
b) to correct the boolean expression.
c) to verify the boolean expression.
d) to minimize the Boolean expression.
Answer:
(d)
Explanation: The Karnaugh map, also known as a Veitch diagram, is a tool to facilitate the simplification of boolean algebra integrated circuit expressions.
Q.20 The number of rows in the truth table of a logic system having n input binary variable, is
a) nn
b) 2n
c) 10n
d) 22n
Answer:
(b)
Explanation: The number of rows in the truth table is 2n ,i.e., 2 raise to the power of input binary variable.
Q.21 When we pass 1001100 to NOT gate, the output is
a) 1110011
b) 1111000
c) 0110011
d) 0010111
Answer:
(c)
Explanation: The output of the NOT gate is always the reverse of the input. Here, 1 will be replaced by 0 and 0 will be replaced by 1.
Q.22 The difference between the boolean variable and the algebraic variable is
a) processing is fast in boolean variable.
b) boolean variable is easy to use.
c) boolean variable takes two values.
d) boolean variables are more widely used.
Answer:
(c)
Explanation: In the ordinary algebra, the variables can take any value like 1,2,3, etc. but the boolean variables can take only two values 0 and 1.
Q.23 The complement of A(B+C)(C+D’) is
a) A+C’+C’D
b) A’+B’C+C’D
c) A+B’C’+C’D’
d) A’+B’C’+C’D
Answer:
(d)
Explanation: [A(B+C)(C+D’)]’ = A’ + (B+C)’ + (C + D’)’ = A’ + B’C’ + C’D
Q.24 The purpose of reducing the switching functions to the minimal form is
a) to enhance the output.
b) to carry the calculations.
c) to reduce the cost.
d) to attract the users.
Answer:
(c)
Explanation: The main purpose is to reduce the number of gates required to build that function. Reduction of the gates reduces the cost of the circuit.
Q.25 The POS form of xy + x’z is
a) ((x’+y’)(x+z’))’
b) ((x’+y’)(x+z’))
c) ((x’+y’)(x+z))’
d) ((x’+y)(x+z’))’
Answer:
(a)
Explanation: (xy +x’z) = (xy +x’z)’ = ((xy)’.(x’z)’)’ = ((x’ + y’)(x + z’))’
Q.26 The dual of (x + y’) is
a) x’y’
b) x’+y
c) x’y
d) xy’
Answer:
(d)
Explanation: Changing (+) to (.) and vice versa and by replacing 0’s with 1’s and1’s with 0’s,the dual of the expression can be obtained.
Computer Science - MCQ on Boolean Algebra
Practice Questions for CUET Computer Science chapter-Boolean Algebra SET-2
Q.1 Boolean algebra, which is used to solve logic problems, is also known as
a) logic algebra.
b) symbolic algebra.
c) George Boole algebra.
d) switching algebra.
Answer:
(d)
Explanation: It is so called because logic problems are binary decisions and Boolean algebra deals with these binary values.
Q.2 The number of types of logic gates are
a) two.
b) three.
c) four.
d) infinite.
Answer:
(b)
Explanation: Three types of logic gates are- “Not gate”, “OR gate” and “AND gate”.
Q.3 The logic gate, whose output is high when all the input are high, is
a) AND gate.
b) OR gate.
c) NOT gate
d) NAND gate.
Answer:
(a)
Explanation: The AND gate can have two or more than two inputs and produces an output signal. When all the inputs are 1, then the output is also 1 otherwise output is 0 only.
Q.4 The group of wires carrying digital signals is
a) gate.
b) quad.
c) redundant group.
d) bus.
Answer:
(d)
Explanation: The bus carries signals, which are in the form of 0’s and 1’s.
Q.5 A graphical display of fundamental products in a truth table is known as
a) maxterm.
b) minterm.
c) non-canonical expression.
d) veitch diagram.
Answer:
(d)
Explanation: Veitch diagram is also known as karnaugh maps. Karnaugh map is nothing but a rectangle made up of certain number of squares, each square representing a Maxterm or minterm.
Q.6 A group of two adjacent 1’s on a K-map is called
a) pair.
b) quad.
c) octet.
d) triplet.
Answer:
(a)
Explanation: To reduce Boolean expression, adjacent 1’s are encircled. If, 2 adjacent 1’s are encircled, then it makes a pair.
Q.7 A group of 1’s on k-map, whose all 1’s are overlapped by other groups, is known as
a) canonical group.
b) redundant group.
c) octet group.
d) quad group.
Answer:
(b)
Explanation: Redundant group is a group in which all 1’s are overlapped by pairs, quads, octets. The removal of redundant group leads to much simpler expression.
Q.8 A diagram that represents AND’s and OR’s by intersecting circles is known as
a) venn diagram.
b) truth table.
c) veitch diagram.
d) K-map.
Answer:
(a)
Explanation: Venn diagrams or set diagrams, developed by John Venn, show all hypothetically possible logical relation between a finite collection of sets.
Q.9 XOR gate followed by an inverter is known as
a) XOR GATE.
b) XNOR.
c) NXOR.
d) NOR.
Answer:
(b)
Explanation: Combination of XOR and NOT is XNOR. In this, inputs must have even number of 1’s to get a 1 (high) output.
Q.10 Simplification of Boolean expression AB+ABC+ABCD+ABCDE yields
a) ABCDE.
b) AB.
c) AB+CD+EF.
d) A+B+C+D+E.
Answer:
(b)
Explanation: Repeated application of absorption theorem x + xy=x, gives the desired result.
Q.11 An equivalent representation for the Boolean expression A’+1 is
a) A.
b) A’.
c) 1.
d) 0.
Answer:
(c)
Explanation: From the Boolean expression A+1=1, let A = A’. Then A’+1=1.
Q.12 If, F=A’B’+C’+D’+E’, then the correct expression for F’ will be
a) F’=(A+B)CDE.
b) F’=ABCDE.
c) F’=A’B’C’D’E’.
d) F’=AB(C+D+E).
Answer:
(a)
Explanation: By applying Demorgan’s theorem twice, the above result can be found.
Q.13 The simplification of Boolean expression (A+B)’(C+D+E)’+(A+B)’ will be
a) A+B.
b) AB.
c) A’+B.
d) A+B’.
Answer:
(a)
Explanation: By applying the property x + xy = x, with x = (A+B)’ = A’B’ AND y=(C+D+E)’, the above result is obtained.
Q.14 The Boolean expression that is algebraically complete is
a) F=xy.
b) F=x+y.
c) F=x’.
d) F=x+y’.
Answer:
(d)
Explanation: F(x,y)= x+y’ can generate AND, OR and NOT function. Therefore this F is algebraically complete.
Q.15 The simplification of F(X,Y,Z)= XZ+Z(X’+XY) is
a) Y.
b) Z.
c) X.
d) XYZ.
Answer:
(b)
Explanation: The best explanation for the expression F= XY+Z(X’+XY) is Z.
Q.16 The relationship, which represents the dual of Boolean property x+x’y=x+y, is
a) x(x’+y)=x+y.
b) x(x’+y)=xy.
c) y(x+y)=xy.
d) xyz=1.
Answer:
(b)
Explanation: By simplifying the above expression, the result will be obtained.
Q.17 The best definition of literal is
a) a Boolean variable.
b) complement of boolean variable.
c) 1 or 2.
d) actual understanding of Boolean expression.
Answer:
(c)
Explanation: Literal means an elementary proposition or its negation in logical expression. For example: 1 or 2.
Q.18 A logic gate, whose output is high only when one or more inputs are high, is
a) OR.
b) AND.
c) NAND.
d) NOR.
Answer:
(a)
Explanation: In OR gate, the output is 1 when one or more inputs are 1.
Q.19 A gate with just one input and one output is
a) AND.
b) OR.
c) NOT.
d) XOR.
Answer:
(c)
Explanation: NOT gate is also known as inverter gate as the output is just the complement of the input.
Q.20 The gates, which are known as universal gates, are
a) AND and OR.
b) NAND and XOR.
c) XNOR and OR.
d) NAND and NOR.
Answer:
(d)
Explanation: NAND and NOR are said to be universal gates as all the other gates can be realized by using these two gates.
Q.21 The binary code in which each successive number differs only in one place is
a) gray code.
b) black code.
c) red code.
d) green code.
Answer:
(a)
Explanation: The binary code 00,01,11,10 is called gray code. It is because of this reason box numbering scheme is in this order only.
Q.22 One of the property of Karnaugh maps is
a) map twisting.
b) map rolling.
c) map concatenation.
d) map paging.
Answer:
(b)
Explanation: Map rolling means roll the map i.e. consider the map as if its left edges are touching the right edges and top edges are touching bottom edges.
Q.23 The compound logical statements, which are always true are called
a) tautologies.
b) fallacies.
c) truth values.
d) closure values.
Answer:
(a)
Explanation: Tautology is a statement of proposional logic, which holds for all truth-values of its atomic proposition.
Q.24 The device, which controls the flow of the current, is known as
a) trigger.
b) switch.
c) ammeter.
d) voltmeter.
Answer:
(b)
Explanation: A switch is an electrical component, which can break an electrical circuit, interrupting the current or diverting it from one conductor to another.
Q.25 The compound statements, which are always false are called
a) fallacies.
b) tautologies.
c) false statements.
d) unknown statements.
Answer:
(a)
Explanation: A fallacy is an argument, which may convince others but is not logically sound.
Q.26 The inverse property can be described as
a) X+X’=1.
b) X+X=X.
c) X(X+Y)=X.
d) X.X=1.1.
Answer:
(a)
Explanation: X+X’ =1 is an inverse property and others are idemponent and involution laws.
Q.27 The most powerful law of Boolean algebra is
a) idempotent law.
b) involution law.
c) absorption law.
d) demorgan’s law.
Answer:
(d)
Explanation: Demorgan’s law states (X+Y)’=X’.Y’ and (X.Y)’=X’+Y’, which is used to reduce the complexity of Boolean expression.
Q.28 Product of n literals is known as
a) minterm.
b) maxterm.
c) minmax.
d) maxmin.
Answer:
(a)
Explanation: A minterm in n variables x1,x2,x3,……………., xn is defined as a product (using AND operation) of n literals (variables).
Q.29 Sum of n literals is known as
a) maxmin.
b) minmax.
c) minterm.
d) maxterm.
Answer:
(d)
Explanation: A maxterm in n variables x1,x2,x3,………………, xn is defined as a sum (using OR operation) of n variables.
Q.30 The property in the given expression – (x+1=1 and x*0=0 can be explained with the help of principle of
a) absorption.
b) idempotent.
c) involution.
d) duality.
Answer:
(d)
Explanation: Any algebraic equality is derived from the axioms of Boolean algebra remains true when the operators OR and AND are interchanged and identity elements 0 and 1 are interchanged. This property is known as duality principle.
Q.31 The table, which gives the various values of output for the given value of input, is known as
a) logical table.
b) truth table.
c) combinational table.
d) binary table.
Answer:
(b)
Explanation: Truth table is a table, which represents all the possible values of logical variables along with all the possible results of the given combinations of values.
Q.32 The expression is said to be canonical, if and only if
a) it consists of minterms only.
b) it consists of maxterms only.
c) both minterms and maxterms.
d) either minterms or maxterms.
Answer:
(d)
Explanation: When a Boolean expression is represented purely as sum of minterms or product terms, it is said to be in canonical sum of products form. When a Boolean expression is represented purely as product of maxterms, it is said to be in canonical product of sum form of expressions.
Q.33 The one statement that can be defined under logical statement category is
a) try to run fast.
b) do not tell a lie.
c) go for the breakfast.
d) Australia is the world cricket champion, 2003.
Answer:
(d)
Explanation: Logical statement is one that can result into either true or false values.
Q.34 The double inversion law is also known as
a) idempotence law.
b) involution law.
c) commutative law.
d) associative law.
Answer:
(b)
Explanation: It is involution law as it is stated by first inverting the expression and then inverting it all over again.
Q.35 The law, which explains the given expression – X+XY=X, is
a) absorption law.
b) distributive law.
c) complemetary law.
d) commutative law.
Answer:
(a)
Explanation: The expression can be proved with the help of truth table. The values of X AND X+XY are the same and this law is known as absorption law.
Q.36 The complement of the Boolean expression F= AB’+C’D’ is given by
a) A’B’CD.
b) A+B+C’+D’.
c) (A’+B).(C+D).
d) (A+B’).(C+D).
Answer:
(c)
Explanation: This can be proved by using DeMorgan’s first law and then by using DeMorgan’s second law.
Q.37 The expression [(x+y)’+(x+y)’]’ can be simplified as
a) x+y.
b) xy.
c) x’y.
d) xy’.
Answer:
(a)
Explanation: The above expression can be simplified by using the DeMorgan’s first theorem.
Q.38 The expression X(Y+Z)=XY+XZ can be stated under
a) commutative law.
b) associative law.
c) distributive law.
d) DeMorgan’s law.
Answer:
(c)
Explanation: The above expression is a distributed law, which can be proved with the help of truth tables. Both columns X(Y+Z) and XY+YZ in the truth table will be identical.
Q.39The decision which results into either yes or no is called a
a) binary decision.
b) logical decision.
c) compound decision.
d) symbolic decision.
Answer:
(a)
Explanation: It is known as binary decision as there are two values either true or false.
Q.40 The dual for the expression X+`XY will be given by
a) X.(X+`Y).
b) X.(X+Y).
c) `X.(X+Y).
d) X.(`X+Y).
Answer:
(d)
Explanation: Using duality principle, changing (+) to (.) and vice versa and by replacing 0’s with 1’s and1’s with 0’s,the dual of the expression can be obtained.