The ISRO Computer Science (CS) Scientist Engineer test held on July 3, 2016
(Sunday). Total questions were 80 and test
duration were 90 Minutes. Here is the solution of paper according to me of set B.
- The Answer Key 2016 for All Sets by ISRO: Click here
- For complete preparation for ISRO Computer Science visit my this article: Click Here
- For ISRO Answer Key and Solutions Computer Science Scientist Engineer 2015: Click here
- For ISRO Answer Key and Solutions Computer Science Scientist Engineer 2014: Click here
- For ISRO Answer Key and Solutions Computer Science Scientist Engineer 2013: Click here
- For ISRO Answer Key and Solutions Computer Science Scientist Engineer 2011: Click here
- For ISRO Answer Key and Solutions Computer Science Scientist Engineer 2009: Click here
- For ISRO Answer Key and Solutions Computer Science Scientist Engineer 2008: Click here
- For ISRO Answer Key and Solutions Computer Science Scientist Engineer 2007: Click here
41. Given the relations
employee (name, salary, deptno) and
department (deptno, deptname, address)
Which of the following queries cannot be expressed using the basic relational algebra operations (U, -, x, π, σ, p)?
(a) Department address of every employee
(b) Employees whose name is the same as their department name
(c) The sum of all employees’ salaries
(d) All employees of a given department
Correct Answer: (c)
Explanation: We can't generate relational algebra of aggregate function using basic operations.
Note: Same question had asked in GATE CS 2000 exam.
Reference: http://www.geeksforgeeks.org/database-management-system-set-1/
42. Trigger is
(a) Statement that enables to start any DBMS
(b) Statement that is executed by the user when debugging an application program
(c) The condition that the system tests for the validity of the database user
(d) Statement that is executed automatically by the system as a side effect of a modification to the database
Correct Answer: (d)
Explanation: A database trigger is procedural code that is automatically executed in response to certain events on a particular table or view in a database.
Note: Same question asked in many exams.
Reference: https://en.wikipedia.org/wiki/Database_trigger
43. The order of a leaf node in a B+ tree is the maximum number of (value, data record pointer) pairs it can hold. Given that the block size is 1K bytes, data record pointer is 7 bytes long, the value field is 9 bytes long and a block pointer is 6 bytes long, what is the order of the leaf node?
(a) 63
(b) 64
(c) 67
(d) 68
Correct Answer: (a)
Explanation: Lets suppose order is n. A B+ tree leaf node contains following items:
- n Value fields; here 9 bytes long it is
- n data record pointers; here 7 bytes long
- 1 block pointer to point next block; here it is 6 bytes long
A B+ tree node size should <= block size
Here, n9 + n7 + 6 <= 1K
=> 9n + 7n + 6 <= 1024
=> 16n <= 1018
=> n <= 1018/16
=> n <= 63.625
=> n = 63
Note: Same question had asked in GATE 2007 CS exam.
Reference: http://gateoverflow.in/1261/gate2007_63
44. A clustering index is defined on the fields which are of type _________.
(a) Non-key and ordering
(b) Non-key and non-ordering
(c) Key and ordering
(d) Key and non-ordering
Correct Answer: (a)
Explanation: Clustering index is defined on an ordered data file. The data file is ordered on a non-key field.
- Ordered data file means data have a specific order/sequence.
- Data is ordered on basis of some non-key field instead a key field.
- All the data that have same non-key value taken as a single cluster.
Note: Same question had asked in GATE CS 2008.
Reference: http://gateoverflow.in/414/gate2008_16
45. The extent to which the software can continue to operate correctly despite the introduction of invalid inputs is called as
(a) Reliablity
(b) Robustness
(c) Fault tolerance
(d) Portability
Correct Answer: (b)
Explanation: robustness is the ability of a computer system to cope with errors during execution and cope with erroneous input. All other given options have different purposes and meaning.
Reference: https://en.wikipedia.org/wiki/Robustness_(computer_science)
46. Which one of the following is a functional requirement?
(a) Maintainability
(b) Portability
(c) Robustness
(d) None of the mentioned
Correct Answer: (d)
Explanation: Maintainability, Portability and Robustness all are non-functional requirements. Functional requirements are related to a functionality. A functionality is described as a set of inputs, the behavior, and outputs.
Reference: http://gateoverflow.in/55559/isro2016-62
47. Configuration management is not concerned with
(a) Controlling changes to the source code
(b) Choice of hardware configuration for an application
(c) Controlling documentation changes
(d) Maintaining versions of software
Correct Answer: (b)
Explanation: Configuration management is the task of tracking and controlling changes in the software. Option (b) is not relevant to software.
Reference: https://gateoverflow.in/55717/isro2016-63
48. A company needs to develop a strategy for software product development for which it has a choice of two programming languages L1 and L2. The number lines of code (LOC) developed using L2 is estimated to be twice of the LOC developed with L1. The product will have to be maintained for five years. Various parameters for the company are given in the table below.
| Parameter | Language L1 |
Language L2 |
| Man years needed for development |
LOC/10000 |
LOC/10000 |
| Development Cost per man year |
र 10, 00, 000 |
र 7, 50, 000 |
| Maintenance Time |
5 years |
5 years |
| Cost of maintenance per year |
र 1,00,000 |
र 50, 000 |
Total cost of the project includes cost of development and maintenance. What is the LOC for L1 for which of the cost of the project using L1 is equal to the cost of the project using L2?
(a) 10,000
(b) 5,000
(c) 7,500
(d) 75,000
Correct Answer: (b)
Explanation:
Let L1 = x
Then L2 will be = 2x
Find LOC for L1 for which cost using L1 is same to cost using L2
=> Cost using L1 = Cost using L2
=> (x/10000) * 10,00,000 + (5 * 1,00,000) = (2x/10000) * 7,50,000 + (5 * 50,000)
=> 100x + 5,00,000 = 150x + 2,50,000
=> 50x = 2,50,000
=> x = 5000
Note: Same question had asked in GATE CS 2011
Reference: http://gateoverflow.in/2107/gate2011_5
49. A company needs to develop a digital signal processing software for one of its newest inventions. The software is expected to have 20000 lines of code. The company needs to determine the effort in person-months needed to develop this software using the basic COCOMO model. The multiplicative factor for this model is given as 2.2 for the software development on embedded systems, while the exponentiation factor is given as 1.5. What is the estimated effort in person-months?
(a) 196.77
(b) 206.56
(c) 199.56
(d) 210.68
Correct Answer: (a)
Explanation:
LOC given = 20,000 => KLOC = 20
Effort applied (E) = a
b X (KLOC)
bb man-months
Where a
b (multiplicative factor) given = 2.2
Where b
b (exponentiation factor) given = 1.5
So solve, E = 2.2 X (20)
1.5 man-months
=> E = 196.77
Reference: http://gateoverflow.in/55666/isro2016-65
50. In the spiral model of software development, the primary determinant in selecting activities in each iteration is
(a) Iteration size
(b) Cost
(c) Adopted process such as Rational Unified Process or Extreme Programming
(d) Risk
Correct Answer: (d)
Explanation: The spiral model is a risk-driven process model generator for software projects.
Based on the unique risk patterns of a given project, the spiral model guides a team to adopt elements of one or more process models, such as incremental, waterfall, or evolutionary prototyping.
Note: Same question had also asked in GATE IT 2007 exam.
Reference: https://en.wikipedia.org/wiki/Spiral_model
51. Bit stuffing refers to
(a) Inserting a '0' in user stream to differentiate it with a flag
(b) Inserting a '0' in flag stream to avoid ambiguity
(c) Appending a nibble to the flag sequence
(d) Appending a nibble to the user data stream
Correct Answer: (a)
Explanation: The term "bit stuffing" broadly refers to a technique whereby extra bits are added to a data stream, which do not themselves carry any information, but either assist in management of the communications or deal with other issues. In computer networks, Zero-bit insertion is a particular type of bit stuffing used in some data transmission protocols to aid clock recovery from the data stream.
Note: Same question had asked in ISRO 2007 exam.
Reference: http://gateoverflow.in/49497/isro2007-24-isro2016-67
52. Dynamic routing protocol enable routers to:
(a) Dynamically discover and maintain routes
(b) Distribute routing updates to other routers
(c) Reach agreement with other routers about the network topology
(d) All of the above
Correct Answer: (d)
Explanation: all the options (a), (b), and (c) are basic needs to handle by the dynamic routing protocols.
Reference: https://en.wikipedia.org/wiki/Dynamic_routing
53. In Ethernet CSMA/CD, the special bit sequence is transmitted by media access management to handle collision is called
(a) Preamble
(b) Postamble
(c) Jam
(d) None of these
Correct Answer: (c)
Explanation: CSMA/CD uses a carrier sensing scheme in which a transmitting data station detects other signals while transmitting a frame, and stops transmitting that frame, transmits a jam signal, and then waits for a random time interval before trying to resend the frame. The jam signal or jamming signal is a signal that carries a 32-bit binary pattern sent by a data station to inform the other stations of the collision and that they must not transmit.
Reference: https://en.wikipedia.org/wiki/Carrier_sense_multiple_access_with_collision_detection
54. Which network protocol allows hosts to dynamically get a unique IP number on each bootup?
(a) DHCP
(b) BOOTP
(c) RARP
(d) ARP
Correct Answer: (a)
Explanation:
- Dynamic Host Configuration Protocol (DHCP) and Bootstrap Protocol (BOOTP), both does allows hosts to dynamically get a unique IP Number. But differ in few things. BOOTP was designed to provide an IP address during the host is booting up while DHCP provide an IP address at any time when a host tries to connecting a server.
- Reverse ARP (RARP) is used to get IP address corresponding to a MAC address.
- Address Resolution Protocol (ARP) is used to get MAC address corresponding to an IP address.
Reference:
http://gateoverflow.in/55521/isro2016-06
55. In a token ring network, the transmission speed is 107 bps and the propagation speed is 200 m/μs. Then 1 bit delay in this network is equivalent to
(a) 500 m of cable
(b) 200 m of cable
(c) 20 m of cable
(d) 50 m of cable
Correct Answer: (c)
Explanation:
in 1 second, bits transmit = 10
7 bps
1 bit takes time to transmit = .10 μs
Propagation speed is = 200 m in 1 μs
So, 1 bit delay in network is = 200 m * .10 μs = 20 m of cable
Note: Same question had asked in GATE CS 2007 exam.
Reference: http://gateoverflow.in/1264/gate2007_66
56. The address of a class B host is to be split into subnets with a 6-bit subnet number. What is the maximum number of subnets and the maximum number of hosts in each subnet?
(a) 62 subnets and 262142 hosts
(b) 64 subnets and 262142 hosts
(c) 62 subnets and 1022 hosts
(d) 64 subnets and 1024 hosts
Correct Answer: (c)
Explanation:
- In class B, first 2 octet are reserved for Network ID and remaining 2 octet for Host ID
- So first 6 bits of 3rd octet are used for subnet and remaining 10 bits for hosts.
- Maximum number of subnets = 26 - 2 = 62
- Note that 2 is subtracted because subnet values consisting of all zeros and all ones (broadcast).
- And no of hosts = 210 - 2 = 1022
- 2 is subtracted for Number of hosts is also. The address with all bits as 1 is reserved as broadcast address and address with all host id bits as 0 is used as network address of subnet.
Note: Same question had asked in GATE CS 2007.
Reference: http://gateoverflow.in/1265/gate2007_67
57. The message 11001001 is to be transmitted using the CRC polynomial x3+1 to protect it from errors. The message that should be transmitted is
(a) 11001001000
(b) 11001001011
(c) 11001010
(d) 110010010011
Correct Answer: (a)
Explanation:
In CRC we send a dividend to receiver generated by CRC procedure at sender.
Dividend that require to send to receiver
= data unit padded by (number of divisor bits -1) remainder bits at sender
Data unit = 1100 1001
Divisor = 1001 because
CRC polynomial is x3+1
Remainder = 011
Dividend that require to send to receiver = 1100 1001 011
1100
1001 000 <--- data unit's right side padded by 3 zero bits
1001 <--- divisor
101
1 <--- result (note that XOR with
the divisor done)
1001 <--- divisor
10
00 <--- result
1001 <--- divisor
1
100 <--- result
1001 <--- divisor
101
0 <--- result
1001 <--- divisor-----------------
0
011 <--- remainder (3 bits). Division algorithm stops here as quotient is equal to zero.
Note: Same question had asked in GATE CS 2007 and similar question had asked in ISRO 2015.
Reference: http://gateoverflow.in/1266/gate2007_68
58. What is the maximum size of data that the application layer can pass on to the TCP layer below?
(a) Any size
(b) 216 bytes - the size of TCP header
(c) 216 bytes
(d) 1500 bytes
Correct Answer: (a)
Explanation: Application layer can send any size of data. There is no limit defined by standards. The lower layers divides the data if needed.
Note: Same question had asked in GATE CS 2008
Reference: http://gateoverflow.in/412/gate2008-14-isro2016-74
59. Frames of 1000 bits are sent over a 106 bps duplex link between two hosts. The propagation time is 25 ms. Frames are to be transmitted into this link to maximally pack them in transit (within the link).
What is the minimum number of bits (i) that will be required to represent the sequence numbers distinctly? Assume that no time gap needs to be given between transmission of two frames.
(a) i = 2
(b) i = 3
(c) i = 4
(d) i = 5
Correct Answer: (d)
Explanation:
per second bits = 10
6
Number of bits in a frame = 1000
per second frames = 1000000 / 1000 = 1000
per millisecond frames = 1000/1000 = 1
Propagation time = 25 ms
Number of frames to send in 25 ms = 25
Bits need to represent sequence of 25 frames = log
225 = 5
Note: Same question had asked in GATE CS 2009
Reference: http://gateoverflow.in/1340/gate2009-57
60. Which of the following is TRUE only for XML but NOT for HTML?
(a) It is derived from SGML
(b) It describes content and layout
(c) It allows user defined tags
(d) It is restricted only to be used with web browsers
Correct Answer: None of These
Explanation:
All given options true for both HTML and XML. Since latest versions of HTML and web browsers we can also use user defined tags in HTML well.
Note: Same question had asked in GATE IT 2008
Reference: http://gateoverflow.in/3279/gate2008-it_19
61. Consider a system with 2 level caches. Access times of Level 1 cache, Level 2 cache and main memory are 1ns, 10 ns, and 500 ns, respectively. The hit rates of Level 1 and Level 2 caches are 0.8 and 0.9, respectively. What is the average access time of the system ignoring the search time within the cache?
(a) 13.0 ns (b) 12.8 ns (c) 12.6 ns (d) 12.4 ns
Correct Answer: (c)
Explanation:
Formula to calculate avg access time: (h1 t1) + (1- h1) h2 t2 + (1 - h1) (1 - h2) tm
= (0.8 * 1 ns) + ((1 - 0.8) * 0.9 * 10 ns) + ((1 - 0.8) * (1 - 0.9) * 500 ns)
= 0.8 ns + 1.8 ns +10 ns = 12.6 ns
Note: Same question asked in GATE IT 2004 exam.
Reference: http://gateoverflow.in/3653/gate2004-it_12
62. If a class C is derived from class B, which is derived form class A, all through public inheritance, then a class C member function can access
(a) Only protected and public data of C and B
(b) Only protected and public data of C
(c) All data of C and private data of A and B
(d) Public and protected data of A and B and all data of C
Correct Answer: (d)
Explanation:
| Access | public |
protected |
private |
|---|
| Same class |
yes |
yes |
yes |
| Derived classes |
yes |
yes |
no |
| Outside classes |
yes |
no |
no |
Reference: http://gateoverflow.in/55530/isro2016-14
63. Which one of the following is correct about the statements given below?
I. All function calls are resolved at compile-time in C language.
II. All function calls are resolved at compile-time in C++.
(a) Only II is correct
(b) Both I and II are correct
(c) Only I is correct
(d) Both I and II are incorrect
Correct Answer: (c)
Explanation: The early binding (static binding) refers to compile time binding and late binding (dynamic binding) refers to runtime binding. C supports only Early Binding but C++ support both binding. Similar statements are:
I. All function calls are resolved at compile-time in Procedure Oriented Programming.
TRUE
II. All function calls are resolved at compile-time in OOPS.
FALSE
Note: This question asked in many exams.
Reference: http://gateoverflow.in/55534/isro2016-79
64. When a DNS server accepts and uses incorrect information from a host that has no authority giving that information, then it is called
(a) DNS lookup
(b) DNS hijacking
(c) DNS Spoofing
(d) None of the mentioned
Correct Answer: (c)
Explanation:
- DNS lookup is the process by which a DNS record is returned from a DNS server.
- DNS hijacking or DNS redirection is the practice of subverting the resolution of DNS.
- DNS spoofing occurs when a DNS server accepts and uses incorrect information.
Reference: http://gateoverflow.in/55536/isro2016-16
65. Which of the following is true?
(a) √3 + √7 = √10
(b) √3 + √7 <= √10
(c) √3 + √7 < √10
(d) √3 + √7 > √10
Correct Answer: (d)
Explanation:
Lets solve it fast, do square both side and then see.
Square of LHS (√3 + √7)
2 = 3 + 7 + 2√3√7 = 10 + something
Square of RHS (√10)
2 = 10
Square of LHS > Square of RHS => LHS > RHS => √3 + √7 > √10
66. What is the sum to infinity of the series,
3 + 6x2 + 9x4 + 12x6 + ..... given |x| < 1 ?
(a) 3 / (1 + x2)
(b) 3 / (1 + x2)2
(c) 3 / (1 - x2)2
(d) 3 / (1 - x2)
Correct Answer: (d)
Explanation: Given is Infinite Geometric Series. Need to find out sum. Lets do.
3 + 6x2 + 9x4 + 12x6 + .....
- We can find the sum of all finite geometric series. But in the case of an infinite geometric series when the common ratio is greater than one, the terms in the sequence will get larger and larger and if you add the larger numbers, you won't get a final answer. The only possible answer would be infinity.
- So, we don't deal with the common ratio greater than one for an infinite geometric series. If the common ratio lies between −1 to 1, we can have the sum of an infinite geometric series.
- In this question common ratio is x2, and |x| < 1. So common ratio is less than 1. Now can go to calculate sum by a available formula:
Sum = a1 / (1− r)
Sum = 3 / (1-x2)
Reference: http://hotmath.com/hotmath_help/topics/infinite-geometric-series.html
67. lim x → 0 (√(1+x) - √(1-x)) / x is given by
(a) 0
(b) -1
(c) 1
(d) 1/2
Correct Answer: (c)
Explanation: While solving given equation, indeterminate form 0/0 is occurring. Way to solve it, apply L'Hopital's Rule. Rule says, we need to do is differentiate the numerator and differentiate the denominator and then take the limit.
- Differentiate √(1+x) = 1 / 2√(x+1)
- Differentiate √(1-x) = - 1 / 2√(1-x)
- Differentiate x = 1
lim x → 0 ((1 / 2√(x+1)) + (1 / 2√(1-x))) / 1
= ((1/2) + (1/2)) =
1
Reference: http://www.derivative-calculator.net/
68. If (G, .) is a group such that (ab)-1 = a-1b-1, ∀ a, b ∈ G, then G is a/an
(a) Commutative semi group
(b) Abelian group
(c) Non-abelian group
(d) None of these
Correct Answer: (b)
Explanation: In abstract algebra, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written. See the proof of given statement in question on clicking link below of reference.
Reference: http://math.bu.edu/people/tkohl/teaching/fall2002/ch2-17.pdf
69. A given connected graph G is a Euler Graph if and only if all vertices of G are of
(a) Same degree
(b) Even degree
(c) Odd degree
(d) Different Degree
Correct Answer: (b)
Explanation: Euler proved that a necessary condition for the existence of Eulerian circuits is that all vertices in the graph have an even degree, and stated without proof that connected graphs with all vertices of even degree have an Eulerian circuit. The term Eulerian graph has two common meanings in graph theory. One meaning is a graph with an Eulerian circuit, and the other is a graph with every vertex of even degree.
Reference: https://en.wikipedia.org/wiki/Eulerian_path
70. Maximum number of edges in a n - node undirected graph without self-loops is
(a) n2
(b) n(n-1)/2
(c) n-1
(d) n(n+1)/2
Correct Answer: (b)
Explanation: There is no self loops and this is undirected graph. Then maximum number of edges will be:
(n * (n-1)) / 2
Reference: https://en.wikipedia.org/wiki/Graph_(discrete_mathematics)
71. The minimum number of NAND gates required to implement the Boolean function A + AB' + AB'C is equal to
(a) 0 (Zero)
(b) 1
(c) 4
(d) 7
Correct Answer: (a)
Explanation: For minimal number of gates required first minimize the given Boolean function:
A + AB' + AB'C
= A (1 + B' + B'C)
= A
=> We do not need any gate to implement this because output same as input. And we only need input A.
72. The minimum Boolean expression for the following circuit is
(a) AB + AC + BC
(b) A + BC
(c) A + B
(d) A + B + C
Correct Answer: (a)
Explanation: Trace the circuit and write boolean expression as below:
A(B+C) + AB + (A+B)C
= AB + AC + AB + AC + BC
= AB + AC + BC
73. For a binary half-subtractor having two inputs A and B, the correct set of logical expression for the outputs D (= A minus B) and X (= borrow) are
(a) D = AB + A'B, X = A'B
(b) D = A'B + AB', X = AB'
(c) D = A'B + AB', X = A'B
(d) D = AB + A'B, X = AB'
Correct Answer: (c)
Explanation: Half subtractor circuit is given below:
Difference D is always XOR of inputs and Borrow is always AND of complimented value of first input and value of second input.
D = A XOR B = A'B + AB'
X= A' AND B = A'B
74. Consider the following gate network
Which one of the following gates is redundant?
(a) Gate No. 1
(b) Gate No. 2
(c) Gate No. 3
(d) Gate No. 4
Correct Answer: (b)
Explanation: Boolean expression generated by given circuit is:
w' + w'z + xyz' where
w' + w'z will always be w'(1+z) = w'. So there is no importance of Gate no. 2 that is a AND gate and giving w'z because no significance of this.
75. The dynamic hazard problem occurs in
(a) Combinational circuit alone
(b) Sequential Circuit only
(c) Both (a) and (b)
(d) None of the above
Correct Answer: (c)
Explanation: A dynamic hazard is the possibility of an output changing more than once as a result of a single input change.
Note: Asked in many other exams.
76. The logic circuit given below converts a binary code y1, y2, y3 into
(a) Excess-3 code
(b) Gray code
(c) BCD code
(d) Hamming code
Correct Answer: None of these
Explanation: May figure in this question have mistake. None of the given option satisfies by this circuit.
If there x3 = y2 XOR y3 then this would be Gray code but here is x3 = y1 XOR y2 XOR y3 that doesn't looks relevant.
77. The circuit shown in the figure below is
(a) An oscillating circuit and its output is square wave(b) The one whose output remains stable in '1' state
(c) The one having output remains stable in '0' state
(d) Has a single pulse of three times propagation delay
Correct Answer: (a)
Explanation: Given circuit is having NOT gates. The NOT gate changes 0 state into '1' and '1' state into '0'. So its simple that given circuit is oscillating circuit.
78. If 12A7C16 = X8, then the value of X is
(a) 224174
(b) 425174
(c) 6173
(d) 225174
Correct Answer: (d)
Explanation: Lets to conversion from HEX (base-16) to OCT (base-8)
HEX to BINARY of given is: 0001 0010 1010 0111 1100
Start right to left to convert BINARY to OCT, take 3-3 bits for OCT digits
0001 0010 1010 0111 1100 => 225174
79. The Excess-3 Code is also called
(a) Cyclic Redundancy Code
(b) Weighted Code
(c) Self-Complementing Code
(d) Algebraic Code
Correct Answer: (c)
Explanation: The Excess‐3 is a self‐complementing, non-weighted code.
- Excess-3
is a digital code related to BCD that is derived by adding 3 to each
decimal digit and then converting the result of that addition to 4-bit
binary.
- Since no definite weights can be assigned to the four digit position, excess-3 is an unweighted code that has advantages in certain arithmetic operations.
- Example: Excess-3 code of 5 (0101) is 8 (1000).
- The key feature of the excess-3 code is that it is self-complementing.
This means that the 1's complement of an excess-3 number is the
excess-3 code for the 9's complement of the corresponding decimal
number.
- The
9's complement of a decimal number is found by subtracting each digit
in the number from 9. For example, the 9's complement of 4 is 5. The
excess-3 code for decimal 4 is 0111. The 1's complement of this is 1000,
which is the excess-3 code for the decimal 5 (and 5 is the 9's
complement of 4).
http://www.belc.bu.edu.eg/belc/downloadcenter/coursescontent/logic_design/step/Copy%20of%20022.htm
80. The simplified Sum of Product form of the following Boolean expression
(P + Q' + R') (P + Q + R) (P + Q + R')
(a) (P'Q + R)
(b) (P + QR')
(c) (PQ' + R)
(d) (PQ + R)
Correct Answer: (b)
Explanation: Lets solve the given Boolean expression:
(P + Q' + R') (P + Q + R) (P + Q + R')
=> (PP + PQ + PR + Q'P + Q'Q + Q'R + R'P + R'Q + R'R) (P + Q + R')
=> (
P +
PQ +
PR + Q'
P + Q'R + R'
P + R'Q) (P + Q + R')
=> (
P(1 + Q + R + Q' + R') + Q'R + R'Q)) (P + Q + R')
=> (
P + Q'R + R'Q) (P + Q + R')
=> (
PP +
PQ +
PR' + Q'R
P + Q'RQ + Q'RR' + R'Q
P + R'QQ + R'QR')
=> (
P(1 + Q + R' + Q'R + R'Q
) +
Q'R
Q + Q'
RR' + R'
QQ +
R'Q
R')
=> (P +
R'Q +
QR')
=> (P + QR')
