(Time: [Marks: 75] muquestionpapers...with the help of relevant timing diagram. b. Explain how 8 DIP...
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Transcript of (Time: [Marks: 75] muquestionpapers...with the help of relevant timing diagram. b. Explain how 8 DIP...
![Page 1: (Time: [Marks: 75] muquestionpapers...with the help of relevant timing diagram. b. Explain how 8 DIP switches can be interfaced with 8 bit 8085 microprocessor. Draw a neat diagram](https://reader033.fdocuments.us/reader033/viewer/2022060813/6091bc8575cd9d62211404a3/html5/thumbnails/1.jpg)
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Q. P. Code: 08237
1
(Time: 𝟐𝟏
𝟐 hours)
[Marks: 75] Please check whether you have got the right question paper.
N. B.: (1) All questions are compulsory. (2) Makesuitable assumptions wherever necessary and state the assumptions made. (3) Answers to the same question must be written together. (4) Numbers to the right indicate marks. (5) Draw neat labeled diagrams wherever necessary. (6) Use of Non-programmable calculator is allowed. 1. Attempt any three of the following: 15
a. Describe a Microprocessor based system.
b. Explain the terms:- i) Word ii) Byte iii) Nibble iv) Machine language v) Assembly language
c. Explain Tristate device logic and Buffer.
d. Write a short note on classification of memory.
e. Draw a neat label functional block diagram of 8085 microprocessor and explain the flags of the flag register.
f. Explain the timing diagram of the Memory Read Cycle.
2. Attempt any three of the following: 15
a. Explain the working of the OUT instruction in 8085 microprocessor.
b. Explain the memory mapped I/O with STA 8000H stored at memory address 2050H.
c. List and explain the various data transfer instruction.
d. What is a instruction, instruction word size? Write types of instruction based on size?
e. Explain the following instruction i) ADI ii) JC iii) XRA iv) ORI v) JNZ
f. Write an assembly program for 8085 microprocessor to add the content of C030H and C031H . Store the sum in C040H and carry at C041H.
[TURN OVER]
A7EDBFDB8F77D416BB550F33A03727C0
muques
tionpap
ers.c
om
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Q. P. Code: 08237
2
3. Attempt any three of the following: 15
a. Write an assembly program for 8085 microprocessor to transfer the contents of 10 memory location from C030H- C039H to C040H - C041H.
b. Explain the various Rotate Instruction for 8085 microprocessor
c. Calculate the time delay for the 8085-based Microcomputer with 2 MHz clock frequency. Label Mnemonics Operand T cycle MVI C,FFH 7 LOOP: DCR C 4 JNZ LOOP 10/7
d. Draw and explain a flowchart for a zero to nine counter.
e. What is a stack? What are the two operations on the stack? Explain with example.
f. Explain the execution of a CALL instruction for 8085 microprocessor and its effect on the stack pointer and program counter.
4. Attempt any three of the following: 15
a. Write an assembly program for 8085 microprocessor to convert 72BCD to its binary equivalent.
b. Explain the following instruction :- i) LHLD and SHLD ii) XCHG and XTHL iii) SBB
c. Explain the following :- i) Cross Assembler ii) Loader
d. What is the function performed by a debugger?
e. Explain the steps of 8085 microprocessor interrupt process.
f. Write a short note on 8085 microprocessor vectored interrupts.
5. Attempt any three of the following: 15
a. Explain the internal structure of the Pentium Pro Processor.
b. List any five Pentium instructions and explain the function of any two.
c. Explain the CPUID instruction in Pentium II.
d. Compare Core i3, i5 and i7 processors.
e. What are the features of the SPARC Architecture?
f. What are the various data format in the SPARC Architecture?
___________________________
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![Page 4: (Time: [Marks: 75] muquestionpapers...with the help of relevant timing diagram. b. Explain how 8 DIP switches can be interfaced with 8 bit 8085 microprocessor. Draw a neat diagram](https://reader033.fdocuments.us/reader033/viewer/2022060813/6091bc8575cd9d62211404a3/html5/thumbnails/4.jpg)
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Q. P. Code: 08235
1
(Time: 𝟐𝟏
𝟐 hours)
[Marks: 75] Please check whether you have got the right question paper.
N. B.: (1) All questions are compulsory. (2) Make suitable assumptions wherever necessary and state the assumptions made. (3) Answers to the same question must be written together. (4) Numbers to the right indicate marks. (5) Draw neat labeled diagrams wherever necessary. (6) Use of Non-programmable calculator is allowed. 1. Attempt any three of the following: 15
a. Differentiate between higher level and lower level programming language. Also differentiate between machine language and assembly language.
b. Draw and explain the block diagram of a computer with microprocessor as CPU.
c. Which are the basic four operations performed by the microprocessor? Explain the bus structure of 8085 microprocessor with necessary diagram.
d. Illustrate the memory address range of a memory chip with 1K bytes of memory. Explain how range can be changed by modifying the hardware.
e. With a neat diagram explain the functional pin configuration of the 40 pin IC8085.
f. What is the use of memory segment 8155 in a SDK-85 system? Draw the block diagram of 8155. How is interfacing of 8155 memory section done?
2. Attempt any three of the following: 15
a. Explain the use of OUT instruction. Also explain how the instruction is executed with the help of relevant timing diagram.
b. Explain how 8 DIP switches can be interfaced with 8 bit 8085 microprocessor. Draw a neat diagram to show how data and address bus of the microprocessor can be used for interfacing.
c. With a neat diagram discuss the programming model of 8085 microprocessor
d. Explain one byte, two byte and three byte instructions. Give at least one example for each.
e. List different addressing modes used by 8085 microprocessor. Write any one 1 byte and any one 2 byte instruction to perform arithmetic operation using 8085 microprocessor.
f. Differentiate between conditional and unconditional jump used in 8085 microprocessor. Explain different conditional jump instructions.
3. Attempt any three of the following: 15
a. A data FF H is stored at a memory location C050 H. Write three different ways of moving this data segment to Accumulator.
b. Explain how 8085 microprocessor performs logical operation of comparing two data.
[TURN OVER]
S0232 / S1962 MICROPROCESSOR ARCHITECTURE
2C7370767C7B450E28DCC849F60DBBB9
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Q. P. Code: 08235
2
c. What is time delay? Why is it needed? Explain how time delay can be generated
using a register pair.
d. Write an 8085 assembly language program to count continuously in hexadecimal from FF H to 00 H (in descending order) in a system with 0.5µs clock period. Use register C to set up 1 ms delay between each count and display the number at one of the output ports.
e. What is Stack? Explain the use of SP register in 8085. Discuss the instructions PUSH and POP. Write a code to demonstrate use of any one instruction.
f. Explain the following concepts for subroutine program – i) Nesting ii) Multiple Ending Subroutine
4. Attempt any three of the following: 15
a. Write steps to convert a binary number to BCD. Write a program to convert given 8 bit binary number to BCD
b. Explain the use of DAA instruction. Also, perform the following operations with given packed BCD numbers – i) 77 + 48 ii) 84 - 48
c. What are utility programs? What is their use in software development systems? Discuss various tools used for developing software assembly language programs.
d. Write a note on two pass assemblers. Support your explanation with a program, if necessary.
e. What do you mean by vectored interrupts? Discuss each of 8085 vectored interrupt in brief.
f. Write a note on DMA.
5. Attempt any three of the following: 15
a. What are the different types of special Pentium registers? Describe them in brief.
b. With a neat internal block diagram, explain the internal structure of Pentium Pro microprocessor.
c. Discuss the SYSENTER and SYSEXIT instructions of Pentium II Processor.
d. Explain Hyper Threading Technology. Draw a neat diagram to indicate how dual core processor is constructed.
e. Discuss the features of SPARC microprocessor.
f. What are the basic categories of SPARC instructions? Discuss any two categories.
___________________________
S0232 / S1962 MICROPROCESSOR ARCHITECTURE
2C7370767C7B450E28DCC849F60DBBB9
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Q. P. Code: 08239
1
(Time: 𝟐𝟏
𝟐 hours)
[Marks: 75] Please check whether you have got the right question paper.
N. B.: (1) All questions are compulsory. (2) Make suitable assumptions wherever necessary and state the assumptions made. (3) Answers to the same question must be written together. (4) Numbers to the right indicate marks. (5) Draw neat labeled diagrams wherever necessary. (6) Use of Non-programmable calculator is allowed.
1. Attempt any three of the following: 15
a. What is a mathematical model? With the help of a flowchart, explain the of solving an engineering problem.
b. Create a hypothetical floating-point number set for a machine that stores information using 7-bit words. Employ the first bit for the sign of the number, the next three for the sign and the magnitude of the exponent, and the last three for the magnitude of the mantissa.
c. Suppose that you have the task of measuring the lengths of a bridge and a rivet and come up with 9999 and 9 cm, respectively. If the true values are 10,000 and 10 cm, respectively, compute (i) the true error and (ii) the true percent relative error for each case.
d. Use zero- through fourth-order Taylor series expansions to approximate the function 𝑓(𝑥) = −0.1𝑥4 − 0.15𝑥3 − 0.5𝑥2 − 0.25𝑥 + 1.2
from xi = 0 with h = 1. That is, predict the function’s value at xi+1 = 1.
e. Compute the condition number for
𝑓(𝑥) = 𝑡𝑎𝑛𝑥 𝑓𝑜𝑟 �̃� =𝜋
2+ 0.1 (
𝜋
2)
𝑓(𝑥) = 𝑡𝑎𝑛𝑥 𝑓𝑜𝑟 �̃� =𝜋
2+ 0.01 (
𝜋
2)
f. Explain blunders, formulation errors and data uncertainty.
2. Attempt any three of the following: 15
a. Find the roots of the equation 𝑥3 − 12.2𝑥2 + 7.45𝑥 + 42 = 0
between 11 and 12 using Regula-Falsi method correct up to 4 decimal places.
b. Find the roots of the equation 𝑥𝑡𝑎𝑛𝑥 = 1
near 4 using Newton Raphson method correct up to 4 decimal places.
c. Use the Secant method to find a solution to 𝑥 = 𝑐𝑜𝑠𝑥 correct up to 4 decimal places.
d. Given log 2 = 0.3010, log 3 = 0.4771, log 5 = 0.6990 and log 7 = 0.8451. Find the value of log 47.
[TURN OVER]
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Q. P. Code: 08239
2
e. The table below gives the value of 𝑡𝑎𝑛𝜃. Evaluate 𝑡𝑎𝑛67°20′
𝜃 65° 66° 67° 68° 69° 𝑡𝑎𝑛𝜃 2.1445 2.2460 2.3559 2.4751 2.6051
f. From the table of Bessel function 𝐽𝑛(1), estimate the value of 𝐽3
2
(1)
n −1 −
3
4 −
1
2 −
1
4
0 1
4
1
2
3
4
1
𝐽𝑛(1) -0.4401 0.0447 0.4311 0.6694 0.7652 0.7522 0.6714 0.5587 0.4401
3. Attempt any three of the following: 15
a. Solve the following simultaneous equations by Gauss – Jordan elimination method:
443
2925
1462
213
321
321
xxx
xxx
xxx
b. Solve the following simultaneous equations by Gauss – Seidel method:
4.71102.03.0
3.193.071.0
85.72.01.03
321
321
321
xxx
xxx
xxx
c. For the set of points (0, 2), (2, -2), (3, -1), evaluate (𝑑𝑦
𝑑𝑥)
2
d. Evaluate dxx
e x
1
0
1 using trapezoidal rule and Simpson’s 3/8 rule.
e. Solve yxdx
dy ; y(1) = 1 for the interval 1 (0.1) 1.2, using method of Taylor series.
f. Solve xy
xy
dx
dy
, where y(0) = 1, to find y(0.1) using Runge-Kutta method.
4. Attempt any three of the following: 15
a Fit a straight line to the x and y values in the two rows:
x 1 2 3 4 5 6 7
y 0.5 2.5 2.0 4.0 3.5 6.0 5.2
b Fit a second degree parabola for the following:
x 2.5 3 3.5 4 4.5 5 5.5
y 4.32 4.83 5.27 5.47 6.26 6.79 7.23
c Fit the function 𝑓(𝑥; 𝑎0, 𝑎1) = 𝑎0(1 − 𝑒−𝑎1𝑥) to the data:
x 0.25 0.75 1.25 1.75 2.25
y 0.28 0.57 0.68 0.74 0.79
using initial guesses 𝑎0 = 1 𝑎𝑛𝑑 𝑎1 = 1. (Use Gauss Newton Method)
[TURN OVER]
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Q. P. Code: 08239
3
d Maximize yx 10050 subject to ;2500510 yx ;2000104 yx 4505.1 yx and
0;0 yx .
e A firm makes two types of furniture – chairs and tables. The contribution for each product as calculated by the accounting department is Rs. 20 per chair and Rs. 30 per table. Both products are processed on three machines M1 , M2 and M3 .The time required in hours by each product and total time available in hours per week on each machine are as follows:
MACHINE CHAIR TABLE AVAILABLE TIME
M1 3 3 36
M2 5 2 50
M3 2 6 60
How should the manufacturer schedule his production in order maximize contribution?
f An aged person must receive 4000 units of vitamin, 50 units of minerals and 1400 calories a day. A dietician advises to thrive on two foods F1 and F2 that cost Rs 4 and Rs 2 respectively per unit of food. It one unit of F1 contains 200 units of vitamins, 1 unit of mineral and 40 calories and one unit of F2 Contains 100 units of vitamins 2 units of minerals and 40 calories, formulate a linear programming model to minimize the cost of diet.
5. Attempt any three of the following: 15
a. The diameter of an electric cable; say X, is assumed to be a continuous random variable with p.d. f. 𝑓 ( 𝑥 ) = 6𝑥 ( 1 − 𝑥), 0 ≤ 𝑥 ≤ 1. (i) Check that above is p.d.f, (ii) Determine a number b such that P (X < b) = P (X> b)
b. Define and explain the concept of probability density function.
c. The probability mass function of a random variable X is zero except at the points 𝑖 = 0, 1,2. At these points it has the values 𝑝 (0) = 3𝑐3, 𝑝(1) = 4𝑐 − 10𝑐2, 𝑝(2) = 5𝑐 − 1 for some 𝑐 > 0. (i) Determine the value of c. (ii) Compute the following probabilities, 𝑃 (𝑋 < 2) 𝑎𝑛𝑑 𝑃 (1 < 𝑋 ≤ 2). (iii) Describe the distribution function and draw its graph.
(iv) Find the largest x such that 𝐹 (𝑥) < 1
2.
(v) Find the smallest x such that 𝐹 (𝑥) ≥1
3.
d. What is exponential distribution? Suppose the time till death after infection with Cancer, is exponentially distributed with mean equal to 8 years. If X represents the time till death after infection with Cancer, then find the percentage of people who die within five years after infection with Cancer.
e. The price for a litre of whole milk is uniformly distributed between Rs. 45 and Rs. 55 during July in Mumbai. Give the equation and graph the pdf for X, the price per litre of whole milk during July. Also determine the percent of stores that charge more than Rs. 54 per litre.
f. The monthly worldwide average number of airplane crashes of commercial airlines is 2.2. What is the probability that there will be (i) more than 2 such accidents in the next month? (ii) more than 4 such accidents in the next 2 months?
_____________________________
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Q. P. Code: 08240
1
(Time: 𝟐𝟏
𝟐 hours)
[Marks: 75] Please check whether you have got the right question paper.
N. B.: (1) All questions are compulsory. (2) Make suitable assumptions wherever necessary and state the assumptions made. (3) Answers to the same question must be written together. (4) Numbers to the right indicate marks. (5) Draw neat labeled diagrams wherever necessary. (6) Use of Non-programmable calculator is allowed.
1. Attempt any three of the following: 15 a. Explain the concept behind the conservation laws in science and engineering with
examples.
b. Explain the terms: i) Significant figures, ii) Accuracy, iii) Precision, iv) Truncation error, v) Round-off error.
c. Evaluate 𝑒−5 using the two formulae:
𝑒−𝑥 = 1 − 𝑥 +𝑥2
2−
𝑥3
3!+
𝑥4
4!− ⋯
And
𝑒−𝑥 =1
𝑒𝑥=
1
1 + 𝑥 +𝑥2
2+
𝑥3
3!+
𝑥4
4!+ ⋯
And compare with the true value 6.737947 X 10 – 3. Use five terms to evaluate each series and compute true and approximate relative errors as terms are added.
d. Use Taylor series expansions with n = 0 to 6 to approximate 𝑓(𝑥) = 𝑐𝑜𝑠𝑥 at xi+1 = π/3 on the basis of the value of f (x) and its derivatives at xi =π/4.
e. Evaluate and interpret the condition number for
𝑓(𝑥) =𝑠𝑖𝑛𝑥
1 + 𝑐𝑜𝑠𝑥 𝑓𝑜𝑟 𝑥 = 1.0001𝜋
f. What are total numerical errors? Discuss stability and condition of a mathematical problem.
2. Attempt any three of the following: 15 a. Find the roots of the equation
2𝑥 − 3𝑠𝑖𝑛𝑥 − 5 = 0 using Regula-Falsi method correct up to 3 decimal places.
b. Find the roots of the equation 𝑥4 − 2.03𝑥3 + 2.03𝑥2 − 2.03𝑥 + 1.03 = 0
in the neighbourhood of x = 1 using Newton Raphson method correct upto 5 decimal places.
c. Determine the real root of 𝑓(𝑥) = 4𝑥3 − 6𝑥2 + 7𝑥 − 2.3 using bisection method correct upto 3 decimal places.
[TURN OVER]
FD36E319242C3AC6C8390B2D525D564B
![Page 16: (Time: [Marks: 75] muquestionpapers...with the help of relevant timing diagram. b. Explain how 8 DIP switches can be interfaced with 8 bit 8085 microprocessor. Draw a neat diagram](https://reader033.fdocuments.us/reader033/viewer/2022060813/6091bc8575cd9d62211404a3/html5/thumbnails/16.jpg)
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Q. P. Code: 08240
2
d. Given log 2 = 0.3010, log 3 = 0.4771, log 5 = 0.6990 and log 7 = 0.8451. Using Lagrange’s
formula, find log 47.
e. The following table shows the number of students and range of marks. Find the number of students who have secured less than 45 marks.
Marks 30-40 40-50 50-60 60-70 70-80
No. of Students
31 45 32 27 15
f. Given:
X: 1 2 3 4 5 6 7 8
f(x) 0.01 0.004 0.02 0.12 0.15 0.257 0.325 0.231
Find f(7.5)using Newton’s backward interpolation formula
3. Attempt any three of the following: 15 a. Solve the following simultaneous equations by Gauss – Seidel method:
141022
13102
1210
321
321
321
xxx
xxx
xxx
b. Solve the following system of equations by Gauss-Jordan method
15527
8652
4328
zyx
zyx
zyx
c. The table for f(x) is given below. Evaluate )(xfdx
dand )(
2
2
xfdy
dat x = 0.1
x 0.0 0.1 0.2 0.3 0.4
f(x) 1.000 0.9975 0.9900 0.9776 0.9604
d. Evaluate dxx
x
0
2
cos45
sinusing Simpson’s 3/8th rule.
e. Solve )log( yxdx
dy ; y(1) = 2 for x = 1.2 and x = 1.4 using Euler’s modified method,
taking h = 0.2.
f. By using Runge-Kutta method of order 4 to evaluate )4.2(y from the following
differential equation ),()(' yxfxy where yxyxf )1(),(
Initial condition 1)2( y , 2.0h correct upto 4 decimals.
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Q. P. Code: 08240
3
4. Attempt any three of the following: 15 a Use least square technique to fit a line xaay 10 10 ,aa constants for the
following data
x 5 15 18 20 30 35 y 12 14 20 18 28 22
b Fit a second degree parabola for the following
x -2.5 -2 -1.5 -0.5 0 0.5 1.5
y 14.32 14.83 15.27 15.47 16.26 16.79 17.23
c Use multiple regression to fit the following data:
x1 x2 y
0 0 5
2 1 10
2.5 2 9
1 3 0
4 6 3
7 2 27
d Solve the following LPP graphically Minimize 212 xxz subject to 402 21 xx ;
303 21 xx ; 6034 21 xx ; 021 xx
e In a college, scholarship is to be given to the students of XI and XII classes. It is decided that at least 5 students from class XI and at least 4 students from class XII should get scholarship. Each scholarship holder of class XI will get Rs. 30 per month and each scholarship holder of class XII will get Rs. 40 per month. The total number of scholarship holders should not be less than 10 but should not be greater than 15. How many students of each class should be selected so as to (i) minimise (ii) maximise the amount spent on scholarship?
f Solve LPP graphically. A company produces two products x and y each of which requires three types of processing. The length of time for processing each unit and profit per unit are given below
Product x Product y Capacity
Process I 12 12 840
Process II 3 6 300
Process III 8 4 480
Profit 5 7
How many units of each product the company produce per day to maximize profit?
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Q. P. Code: 08240
4
5. Attempt any three of the following: 15 a. State and explain the properties of distribution functions. b. A random variable X has the following probability distribution:
𝑥 0 1 2 3 4 5 6 7 𝑝(𝑥) 0 𝑘 2𝑘 2𝑘 3k 𝑘2 2𝑘2 7𝑘2 + 𝑘
(i) Find 𝑘, (ii) Evaluate 𝑃 (𝑋 < 6), 𝑃 (𝑋 ≥ 6), and 𝑃 ( 0 < 𝑋 < 5),
(iii) If 𝑃 (𝑋 ≤ 𝑐) > 1
2, find the minimum value of 𝑐, and (iv) Determine the
distribution function of X.
c. Prove that the geometric mean G of the distribution 𝑑𝐹 = 6(2 − 𝑥) (𝑥 − 1) 𝑑𝑥, 1 ≤𝑥 ≤ 2 is given by 6 log (16G) = 19.
d. The time between release from prison and the commission of another crime is uniformly distributed between 0 and 5 years for a high-risk group. Give the equation and graph the pdf for X, the time between release and the commission of another crime for this group. What percent of this group will commit another crime within two years of their release from prison?
e. A manufacturer claims that at most 10 per cent of his product is defective. To test this claim, 18 units are inspected and his claim is accepted if among these 18 units, at most 2 are defective. Find the probability that the manufacturer's claim will be accepted if the actual probability that a unit is defective is (i) 0.05 (ii) 0.10 (iii) 0.15 (iv) 0.20.
f. The lifetimes in years for a particular brand of cathode ray tube are exponentially distributed with a mean of 5 years. What percent of the tubes have lifetimes between 5 and 8 years? Draw a graph of the pdf and shade the area which represents the probability of the event 5 < X < 8, where X represents the lifetimes.
_____________________________
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Q.P. Code: 33412
1
(2½ Hours)
[Total Marks: 75]
N. B.: (1) All questions are compulsory.
(2) Make suitable assumptions wherever necessary and state the assumptions made.
(3) Answers to the same question must be written together.
(4) Numbers to the right indicate marks.
(5) Draw neat labelled diagrams wherever necessary.
(6) Use of Non-programmable calculators is allowed.
1. Attempt any three of the following: 15
a. Water accounts for roughly 60% of total body weight. Assuming it can be categorized
into six regions, the percentages go as follows. Plasma claims 4.5% of the body weight
and is 7.5% of the total body water. Dense connective tissue and cartilage occupies 4.5%
of the total body weight and 7.5% of the total body water. Interstitial lymph is 12% of
the body weight, which is 20% of the total body water. Inaccessible bone water is
roughly 7.5% of the total body water and 4.5% total body weight. If intracellular water
is 33% of the total body weight and transcellular water is 2.5% of the total body water,
what percent of total body weight must the transcellular water be and what percent of
total body water must the intracellular water be?
b. What is a mathematical model? With the help of a flowchart, explain the of solving an
engineering problem.
c. Discuss the aspects of round-off errors while storing floating point numbers in computer.
d. Use zero- through fourth-order Taylor series expansions to approximate the function:
𝑓(𝑥) = −0.1𝑥4 − 0.15𝑥3 − 0.5𝑥2 − 0.25𝑥 + 1.2 from xi = 0 with h = 1. That is, predict the function’s value at xi+1 = 1.
e. Explain Total numerical error, formulation error and data uncertainty.
f. Define accuracy and precision. What are round-off errors? Explain.
2. Attempt any three of the following: 15
a. Determine the real root of 𝑓(𝑥) = −26 + 85𝑥 − 91𝑥2 + 44𝑥3 − 91𝑥2 + 𝑥5 between
0.5 and 1.0 correct up to 3 decimal places using bisection method.
b. Determine the positive real root of ln(𝑥4) = 0.7 between 0.5 and 2 using method of
false position.
c. Solve: 𝑥 − 0.8 − 0.2𝑠𝑖𝑛𝑥 = 0 using Newton Raphson method correct upto 4 decimal
places starting with initial value 0.
d. From the table of Bessel function 𝐽𝑛(1), estimate the value of 𝐽3
2
(1)
n –1 −3
4 −
1
2 −
1
4 0
1
4
1
2
3
4 1
Jn(1) –0.4401 0.0447 0.4311 0.6694 0.7652 0.7522 0.6714 0.5587 0.4401
e. Find f (8.4) if f (8.1) = 16.94410, f (8.3) = 17.56492, f (8.6) = 18.50515,
f (8.7) = 18.82091 using Lagrange’s Interpolation formula.
f. Using the necessary interpolation formula find f(1) and f(1.5) from the table:
x –1 0 2 3
f(x) –8 3 1 12
[TURN OVER]
Paper / Subject Code: 77504 / Numerical & Statistical Methods.
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Q.P. Code: 33412
2
3. Attempt any three of the following: 15
a. Solve the following system by using the Gauss-Jordan elimination method.
𝑥 + 𝑦 + 𝑧 = 5
2𝑥 + 3𝑦 + 5𝑧 = 8
4𝑥 + 5𝑧 = 2
b. Use the Gauss-Seidel iterative technique to find approximate solutions to
𝑎 + 𝑏 + 2𝑐 = 1
2𝑎 − 𝑏 + 𝑑 = −2
𝑎 − 𝑏 − 𝑐 − 2𝑑 = 4
2𝑎 − 𝑏 + 2𝑐 − 𝑑 = 0
c. Given log 280 = 2.4472, log 281 = 2.4487, log 283 = 2.4518, log 286 = 2.4564. Find
[𝑑
𝑑𝑥(𝑙𝑜𝑔𝑥)]
𝑥=280
d. Evaluate the following using Simpson’s 3/8th rule.
∫𝑠𝑖𝑛2𝜃
5 + 4𝑐𝑜𝑠𝜃𝑑𝜃
𝜋
0
e. Use Euler’s method to approximate the solution for
𝑦′ = 𝑡−2(𝑠𝑖𝑛2𝑡 − 2𝑡𝑦), 1 ≤ 𝑡 ≤ 2, 𝑦(1) = 2 𝑤𝑖𝑡ℎ ℎ = 0.5
f. Solve 𝑦′ = 𝑦 − 𝑡2 + 1, 𝑦(0) = 0.5, 0 ≤ 𝑡 ≤ 2 using Runge Kutta 4th order method
with h = 0.5
4. Attempt any three of the following: 15
a. Fit a second order polynomial to the data given below:
x 0 1 2 3 4 5
y 2.1 7.7 13.6 27.2 40.9 61.1
b. Fit a straight line to the given data regarding x as the independent variable.
x 1 2 3 4 5 6
y 1200 900 600 200 110 50
c. Consider the data below:
x 1 2 3 4
y 1 7 11 21
Use linear least-squares regression to determine a function of the form y = bemx for the
given data by specifying b and m.
d. A farmer can plant up to 8 acres of land with wheat and barley. He can earn ₹ 5,000 for
every acre he plants with wheat and ₹ 3,000 for every acre he plants with barley. His
use of a necessary pesticide is limited by federal regulations to 10 gallons for his entire
8 acres. Wheat requires 2 gallons of pesticide for every acre planted and barley requires
just 1 gallon per acre. What is the maximum profit he can make? Solve graphically.
e. The Bead Store sells material for customers to make their own jewelry. Customer can
select beads from various bins. Grace wants to design her own Halloween necklace from
orange and black beads. She wants to make a necklace that is at least 12 inches long, but
no more than 24 inches long. Grace also wants her necklace to contain black beads that
are at least twice the length of orange beads. Finally, she wants her necklace to have at
least 5 inches of black beads.
Find the constraints, sketch the problem and find the vertices (intersection points).
[TURN OVER]
Paper / Subject Code: 77504 / Numerical & Statistical Methods.
E6FFC4D3905F9A53C13D50E8C4554E81
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Q.P. Code: 33412
3
f. A garden shop wishes to prepare a supply of special fertilizer at a minimal cost by
mixing two fertilizers, A and B.
The mixture is to contain: at least 45 units of phosphate, at least 36 units of nitrate
at least 40 units of ammonium. Fertilizer A costs the shop $.97 per pound.
Fertilizer B costs the shop $1.89 per pound. Fertilizer A contains 5 units of phosphate
and 2 units of nitrate and 2 units of ammonium, fertilizer B contains 3 units of phosphate
and 3 units of nitrate and 5 units of ammonium. How many pounds of each fertilizer
should the shop use in order to minimize their cost?
5. Attempt any three of the following: 15
a. The amount of bread (in hundreds of pounds) X that a certain bakery is able to sell in a day is
found to be a numerical valued random phenomenon, with a probability function specified by
the probability density function f(x), given by
f(x) = A . x for 0 ≤ x ≤ 5
= A(10 – x) for 5 ≤ x ≤ 10
= 0, otherwise
i. Find the value of A such thatf(x) is a probability density function.
ii. What is the probability that the number of pounds of bread that will be sold
tomorrow is
• more than 500 pounds
• less than 500 pounds
• between 250 and 750 pounds?
b. Suppose the life in hours of a certain kind of radio tube has the probability density
function:
f(x) =100
x2, when x ≥ 100
= 0, when x < 100
What is the probability that none of three such tubes in a given radio set will have to be
replaced during the first 150 hours of operation? What is the probability that all three of
the original tubes will have been replaced during the first 150 hours?
c. The diameter of an electric cable; say X, is assumed to be a continuous random variable
with p.d.f.
𝑓 ( 𝑥 ) = 6𝑥(1 − 𝑥), 0 ≤ 𝑥 ≤ 1. i. Check that the function is p.d.f.
ii. Determine a number b such that P(X < b) = P(X > b)
d. If 20% of the bolts produced by a machine are defective, determine the probability that,
out of 4 bolts chosen at random, (i) 1, (ii) 0, and (iii) at most 2 bolts will be defective.
e. A department in a works has 10 machines which may need adjustment from time to time
during the day. Three of these machines are old, each having a probability of 1/11 of
needing adjustment during the day, and 7 are new having corresponding probabilities of
1/21. Assuming that no machine needs adjustment twice on the same day, determine the
probability that on a particular day
i. just 2 old and no new machines need adjustment.
ii. If just 2 machines need adjustment, they are of the same type.
f. In a book of 520 pages, 390 typo-graphical errors occur. Assuming Poisson law for the
number of errors per page, find the probability that a random sample of 5 pages will
contain no error.
_____________________________
Paper / Subject Code: 77504 / Numerical & Statistical Methods.
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Q. P. Code: 08242
1
(Time: hours)
[Marks: 75] Please check whether you have got the right question paper.
N. B.: (1) All questions are compulsory. (2) Makesuitable assumptions wherever necessary and state the assumptions made. (3) Answers to the same question must be written together. (4) Numbers to the right indicate marks. (5) Draw neat labeled diagrams wherever necessary. (6) Use of Non-programmable calculator is allowed. 1. Attempt any three of the following: 15
a. Write down advantages and disadvantages of procedure oriented language.
b. Explain object oriented development.
c. Write down benefits of using object oriented programming.
d. Write a short note on Data abstraction and data encapsulation.
e. Explain dynamic binding with example. Give proper example.
f. What is inheritance? Explain with example the concept of multiple inheritances.
2. Attempt any three of the following: 15
a. What is friend function? Write a friend function to display mark sheet of the F. Y. B. Sc. IT student.
b. What is class? Explain with example how objects are passed as argument to member function and objects are returned from member function.
c. Write a C++ program to design a class - cours.e For reading and displaying the course information, the getInfo() and displayInfo() methods will be used respectively. The getInfo() will be private method. Write down C++ program to implement the class.
d. What is inline function? Explain with example.
e. What is use of constructor? Explain with example parameterized constructor.
f. Write a C++ program to demonstrate the use of constructor and destructor.
3. Attempt any three of the following: 15
a. What is function overloading? Explain with example.
b. What is operator overloading? Write down the rules for operator overloading.
c. How binary operators are overloaded? Write a C++ program to overload binary operator +.
d. What is method overriding? Explain with example.
e. Explain with example abstract class.
f. Explain virtual destructor. Give suitable example.
[TURN OVER]
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Q. P. Code: 08242
2
4. Attempt any three of the following: 15
a. Can private members of a base class are inheritable? Justify.
b. Explain with example multilevel inheritance.
c. Explain how a base class is derived in public and private mode.
d. Write a C++ program to implement following hierarchy.
e. What is exception? Explain exceptions handling mechanism?
f. What happen when raised exception is not caught by catch block? Explain with suitable example.
5. Attempt any three of the following: 15
a. Explain with example how function templates are used.
b. Explain how compiler calls to a class and function template.
c. Write a C++ program which defines and uses student class template.
d. What is file? Write down the steps for manipulating files in C++.
e. Explain the hierarchy of file stream class.
f. What are different methods of opening a file? Write a program to open file and enter student details into the file using any method.
___________________________
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![Page 25: (Time: [Marks: 75] muquestionpapers...with the help of relevant timing diagram. b. Explain how 8 DIP switches can be interfaced with 8 bit 8085 microprocessor. Draw a neat diagram](https://reader033.fdocuments.us/reader033/viewer/2022060813/6091bc8575cd9d62211404a3/html5/thumbnails/25.jpg)
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Q. P. Code: 08243
(Time: hours)
[Marks: 75] Please check whether you have got the right question paper.
N. B.: (1) All questions are compulsory. (2) Make suitable assumptions wherever necessary and state the assumptions made. (3) Answers to the same question must be written together. (4) Numbers to the right indicate marks. (5) Draw neat labeled diagrams wherever necessary. (6) Use of Non-programmable calculator is allowed. 1. Attempt any three of the following: 15
a. What is Object Oriented Programming? State any three advantages and applications.
b. Explain concept of encapsulation and abstraction.
c. Explain the relationship between object and class.
d. What is Polymorphism? Give example for the same.
e. What is inheritance? State its types.
f. Give comparison between Object oriented and Procedure oriented programming languages.
2. Attempt any three of the following: 15
a. What is constructor? State the rules for constructor.
b. Explain the concept of passing object as an argument.
c. Write a program to implement the concept of constructor and destructor.
d. Write a program to design a class MyCalculator with add(), mul() and sub() methods.
e. Explain the concept of friend function with suitable example.
f. Write a program to implement the concept of pointer to object.
3. Attempt any three of the following: 15
a. What is overloading? Write a program to demonstrate the concept of function overloading.
b. What is operator overloading? State the rules for operator overloading.
c. List the operators that cannot be overloaded. Write a program to add two complex numbers by overloading binary operator.
d. What is static member and function? State its characteristics.
e. What is method overriding? Explain the use of virtual function.
f. What is abstract class? State the properties of abstract class.
[TURN OVER]
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2
Q. P. Code: 08243
4. Attempt any three of the following: 15
a. What are access specifiers? Explain the use of each.
b. Write a program to implement the concept of single level inheritance.
c. Write a C++ program to handle various exceptions.
d. Explain the use of throw and catch keywords with proper syntax.
e. Explain the difference between deriving a class in public mode and private mode.
f. Write a program to implement the inheritance for the given hierarchy.
5. Attempt any three of the following: 15
a. What is generic programming? Explain the use of generic programming.
b. Explain with example the use of class templates.
c. Write a program to implement the concept of function template.
d. What are file operations? Explain different modes of files.
e. Write a program to read data from user and write to the file.
f. Write a program to copy the content from file1 to file2.
___________________________
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Q. P.Code : 33403
1
(2½ Hours) [Total Marks: 75]
N. B.: (1) All questions are compulsory.
(2) Make suitable assumptions wherever necessary and state the assumptions made.
(3) Answers to the same question must be written together.
(4) Numbers to the right indicate marks.
(5) Draw neat labeled diagrams wherever necessary.
(6) Use of Non-programmable calculators is allowed.
1. Attempt any three of the following: 15
a. Discuss procedure oriented programming paradigm. Also discuss its characteristics.
b. What is object oriented programming paradigm? Discuss its characteristics.
c. Define any two of the following
(i) Classes (ii) Objects (iii)Data abstraction
d. Discuss benefits and applications of oops.
e. Explain static and dynamic binding.
f. Write a short note on data abstraction and data encapsulation.
2. Attempt any three of the following: 15
a. What is a class? How a class can be defined? Discuss various ways of defining
member functions of a class.
b. What are objects? How they can be declared? Also discuss memory allocation for
objects in object oriented programming.
c. How data members and member functions of a class can be accessed. Write a program
to demonstrate the concept of accessing public members of a class.
d. What is a constructor? List various types of constructors. Explain copy constructor
with programming example.
e. Declare a class rectangle with data members as length and breadth, and member
functions as getdata() to read data and display() to find and display area and perimeter
of a rectangle. Also write main method to implement the class.
f. What is a friend function? How it can be declared? What are its characteristics?
3. Attempt any three of the following: 15
a. Define function overloading and operator overloading. Write down the rules for
overloading operators.
b. Write a C++ program to add two complex numbers by overloading binary + operator.
c. What do you understand from data conversion between objects and basic types? List
various type conversions.
d. Write a C++ program to demonstrate conversion from user defined to basic data type.
e. What is this pointer? Write a C++ program to demonstrate use of this pointer.
f. What are virtual functions? What are the rules for writing virtual functions?
4. Attempt any three of the following: 15
a. What is inheritance? Discuss different forms of inheritance.
b. Discuss public, private and protected data members and member functions. When to
declare which type of data members/member functions.
c. Write a C++ program to demonstrate use of hybrid inheritance.
d. What is an exception? Explain exception handling mechanism in detail.
[TURN OVER]
Paper Code: 77501 / Object Oriented.
BE5409A152DADF6AC3EE3D4028DBD4BA
![Page 29: (Time: [Marks: 75] muquestionpapers...with the help of relevant timing diagram. b. Explain how 8 DIP switches can be interfaced with 8 bit 8085 microprocessor. Draw a neat diagram](https://reader033.fdocuments.us/reader033/viewer/2022060813/6091bc8575cd9d62211404a3/html5/thumbnails/29.jpg)
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Q. P.Code : 33403
2
e. What happens when raised exception is not caught by catch block? Explain with
suitable example.
f. Write a C++ program to show use of multiple catch statements.
5. Attempt any three of the following: 15
a. Explain various methods to detect end of file.
b. Write a program to open two files country and capital simultaneously and print the
nameof the capital in front of the country.
c. Explain the use and purpose of following functions
(i) seekg() and seekp()
(ii) tellg() and tellp()
d. What are class templates? Explain their use. How they can be declared?
e. Define a class named vector. Illustrate the use of vector class template for performing
the scalar product of int type vectors as well as float type vectors.
f. What is a function template? Write a C++ program to demonstrate the use of function
templates?
_____________________________
Paper Code: 77501 / Object Oriented.
BE5409A152DADF6AC3EE3D4028DBD4BA
![Page 30: (Time: [Marks: 75] muquestionpapers...with the help of relevant timing diagram. b. Explain how 8 DIP switches can be interfaced with 8 bit 8085 microprocessor. Draw a neat diagram](https://reader033.fdocuments.us/reader033/viewer/2022060813/6091bc8575cd9d62211404a3/html5/thumbnails/30.jpg)
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Q. P. Code: 08246
1
(Time: 𝟐𝟏
𝟐 hours)
[Marks: 75] Please check whether you have got the right question paper.
N. B.: (1) All questions are compulsory. (2) Make suitable assumptions wherever necessary and state the assumptions made. (3) Answers to the same question must be written together. (4) Numbers to the right indicate marks. (5) Draw neat labeled diagrams wherever necessary. (6) Use of Non-programmable calculator is allowed. 1. Attempt any three of the following: 15
a. List and explain important applications of internet in brief.
b. Explain different approaches to style sheets.
c. Write a short note on internet address.
d. How hyperlinks are created in HTML? Explain with the help of an example.
e. What is search engine? Explain its working.
f. Write HTML code to design following web page:
A. Scripting Languages
i. VB SCRIPT
ii. JAVA SCRIPT
B. DBMS
ORACLE
MY SQL
2. Attempt any three of the following: 15
a. What is image map? Write the difference between client-side and server-side image mapping.
b. Write the purpose of using: rowspan, colspan, cellspacing and cellpadding in Table tag. Give example.
c. Write HTML code for embedding an audio and video in a web page.
d. Explain the semantic tags of HTML5.
e. Write HTML code to design a form to enter name of the user, his/her password, and gender (radio button for male/female), hobbies (checkbox for reading/singing/sports), favorite color (list box red/green/blue) and submit and reset button.
f. Explain <DIV> tag with the help of suitable example.
3. Attempt any three of the following: 15
a. Differentiate between client side and server side JavaScript.
b. Write a JavaScript program to display all the prime numbers between 1 and 100.
c. List and explain the methods of string object of JavaScript.
[TURN OVER]
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Q. P. Code: 08246
2
d. Explain the following operators of JavaScript:
(i) new (ii) delete (iii) this (iv) void (v) ,(Comma)
e. Write the codes to design following web page and validate all the controls placed on the form using JavaScript as given: Name should not be blank, Check email-id is valid, Check Pin code is 6 digits long.
Name:
Email-id:
Pin code:
SUBMIT
f. Define events and event handlers. List various types of mouse event.
4. Attempt any three of the following: 15
a. Write the difference between GET and POST methods in PHP.
b. Explain different types of arrays available in PHP.
c. Write a PHP program to demonstrate the use of different string functions.
d. Explain error handling in PHP.
e. Write a short note on variables in PHP.
f. Write a PHP program to create one dimensional array.
5. Attempt any three of the following: 15
a. What is a cookie? How to store and retrieve the values in cookie in PHP?
b. Explain any five PHP/MYSQL functions with example.
c. Write a PHP program to send email with attachment.
d. How to start and destroy a session and how to store a session variable in PHP? Explain.
e. Write a short note on regular expressions in PHP.
f. Write a PHP code to create a database “Company” and to create a table “Employee” (emp_id, emp_name,emp_dept,emp_salary).
___________________________
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Q. P. Code: 08245
1
(Time: 𝟐𝟏
𝟐 hours)
[Marks: 75] Please check whether you have got the right question paper.
N. B.: (1) All questions are compulsory. (2) Make suitable assumptions wherever necessary and state the assumptions made. (3) Answers to the same question must be written together. (4) Numbers to the right indicate marks. (5) Draw neat labeled diagrams wherever necessary. (6) Use of Non-programmable calculator is allowed. 1. Attempt any three of the following: 15
a. What is internet? Explain any two applications of internet.
b. Write a short note on domain name server.
c. Write a short note on search engine.
d. Explain the structure of HTML5 file.
e. List different formatting tags. Explain with example any three of them.
f. List and explain different types of cascading style sheets.
2. Attempt any three of the following: 15
a. Explain with example how text based navigation bar is created.
b. What is image map? Explain with example server side image map.
c. List various HTML5 semantic tags. Explain with example any four of them.
d. Explain following attributes of td tag: i. rowspan ii. colspan iii. width iv. valign v. bgcolor
e. Write a HTML5 program to display college admission form.
f. List various tags used to embed audio in a page. Explain with example any two of them.
3. Attempt any three of the following: 15
a. Explain any five special operators of java script.
b. Write html code to display factorial of number entered by user.(use do while loop)
c. What is the purpose of break and continue statement. Give suitable example.
d. Explain regular expression in java script.
e. List different methods of document object. Explain with example any two of them.
f. Explain following event attributes: i. onblur ii. onchange iii. ondblclick iv. onkeydown v. onmousedown
4. Attempt any three of the following: 15
a. How PHP variables are used? Explain with example.
b. Write down the rules to determine the “truth” of any value not already of the Boolean type:
c. Explain doubly quoted strings in PHP. Give suitable example.
d. Explain the ternary operator with example.
[TURN OVER]
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Q. P. Code: 08245
2
e. Write the purpose of following string methods: i. strcasecmp ii. strrpos iii. strstr iv. chop v. strtolower
f. List and explain functions for inspecting arrays.
5. Attempt any three of the following: 15
a. Explain join with suitable example.
b. List various fetching functions. Explain with example any two of them.
c. List and explain function used to create database programmatically.
d. Write a PHP program to display boolean data from database on checks button.
e. Write down the use of following PHP-MySQL functions i. mysql_affected_rows ii. mysql_data_seek iii. mysql_fetch_array iv. mysql_field_type v. mysql_insert_id
f. Explain following session functions: i. session_register ii. session_is_registered iii. session_unset iv. session_decode v. session_id
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