placement qns

7/25/2019 Placement Qns

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Department of ECE, KLS’ VDRIT, Haliyal

Vacation Assignment for 3rd Semester students. Submission date: 25th Jan 2015

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Q1. What is the frequency, amplitude and the phase angle of the sinusoidally varying voltage

signal v(t) = 25 sin(300 t + /6). Also determine the RMS value of the voltage.π π

Q2. Evaluate the following

a. Sum of odd values from 1 to 50

b. f(t) = 2t3 + 5t2 + 3.4t + 2, for t= -2, -1.5, -1.0,......2.0 and plot t Vs f(t)

c. f(t) = x(t) = eat for t= -1 to +1 with an interval of 0.1and a=-2. Plot t Vs f(t)

d. Repeat c) for a = 2

e. plot x(n) = a|n| for n= -10, -9, ……..9,10 with a = 0.5

f. Repeat e) for a = -0.5

g. Repeat e) for a = 2, Compare the results of e) f) and g)

Q3. Find partial fraction expansion of f(z) = (z-5) / (z-1)(z-2)(z-3)

Q4. To cover a distance of 105 KMs in 1 hour 45 minutes, what should be the average speed of

the car?Q5. Find real values of the number a for which a.i (‘a’ is real and ‘ai’ is the imaginary value) is a

solution of the polynomial equation z4 - 2z3 + 7z2 - 4z + 10 = 0. Then find all roots of this

equation.

Q6. Find the real value of m such that the equation 2 z2 - ( 3+ 8i )z - ( m + 4i) = 0 has a real root.

Then find the roots.

Q7. Find the sum S = 1 + ½ + ¼ + ⅛ + 1/16 + --------------------

Q8. Evaluate the following. (i)(1+2i)2 (ii) (i)5 (iii) (i)-6 (iv) (i)3/(i)-15 (v) 3(i)2 -4(i)5

Q9. Determine the complex number z which satisfies z(3+3i) = 2 - i

10. Solve for real x and y in the equation x + yi = (1-i)(2+8i)

11. Draw a right angle triangle and define sin(θ), cos(θ) and tan(θ)12. Prove the following trigonometric identities

i) sin(θ + φ) = sin(θ) cos(φ) + cos(θ) sin(φ)

ii) cos(θ + φ) = cos(θ) cos(φ) - sin(θ) sin(φ)

iii) sin(θ) sin(φ) = 0.5[cos(θ - φ) - cos(θ + φ)]

iv) cos(θ) cos(φ) = 0.5[cos(θ - φ) + cos(θ + φ)]

v) sin(θ) cos(φ) = 0.5[sin(θ - φ) + sin(θ + φ)]

13. State Euler’s formula. Express sin(θ) and cos(θ) in terms of e jθ

14. e jωt is a unit rotating vector (anticlockwise) with an angular speed of ω radians per second.

If ω = 100 radians / second, show the position of the vector in a complex plane, at t= 0.2sec.

15. Evaluate the following definite integralsi) ii) iii) iv)∫

1

0

x3 dx ∫0.1

0

e3 x in( x)dx ∫0.5

0

s cos( x)dx ∫0.5

0

e−2 x

16. Find AB where A = [1 2 3; 4 5 6; 7 8 9] and B=[4 3 2 1; 8 7 6 5; 1 0 5 2]

17. Find A-1 and det(A) of the square matrix A = [1 2 3; 4 5 6; 7 8 9]

18. Define integration by parts. Demonstrate the use of this concept to find sin( x)dx∫0.2

0

e−2 x



19. B is twice as fast as A and C is twice as fast as B. If A alone can complete the job in 28

days, how many days will A, B and C take to complete the job working together?

20. A passenger train running at 60 km/hr leaves the railway station 5 hours after a goods train

had left and overtakes it in 4 hours. What is the speed of the goods train?

21. A train 300 m. long passes a pole in 15 sec. Find the speed.

22. A train running between two stations A and B arrives at its destination 15 minutes late, whenits speed is 45 km/hr. and 36 minutes late when its speed is 36 km/hr. find the distance between

the stations A and B.

23. If you travels at a speed of 20 km/hr, then you will reach college late by 15 minutes and if

travels at a speed of 50 km/hr, then you will reach 15 minutes earlier. How far is the college?

24. A and B run a km and A wins by 1 min. A and C run a km and A wins by 375 mtrs. B and C

run a km and B wins by 30 sec. Find the time taken by B to run a km.

25. If you deposit Rs. 10,000 in a bank with interest rate 9% per annum. Assuming the period to

be 5 years and interest is compounding on monthly basis, what will be the maturity amount you

will receive at the end of 5 years ?

26. Two clocks begin to strike 12 together. One strikes in 33 seconds and the other in 22 secs.What is the interval between the 6th stroke of the first and the 8th stroke of the second?

27. Prove that one radian is less than 60o

28. A man takes 7.5 minutes to walk along the diagonal of a square field at the rate of 2km/hr.

find the area of the square field in m2.

29. Out of thousand people, 450 subscribe for India Today and 600 for Outlook magazine. 200

subscribe for both. How many do not subscribe to any magazine?

30. If log10x = 98 – x log 107 find x

31. If a, b, c are any three consecutive integers, find the value of log (1 + ac)

32. Find the logarithm of 1728 to the base of 2 √3

33. Find two numbers which are such that one-fifth of the greater exceeds one-sixth of thesmaller by ‘4’; and such that one-half of the greater plus one-quarter of the smaller equals ‘38’.

34. A man left Rs.1750 to be divided among his two daughters and four sons. Each daughter

was to receive three times as much as a son. How much did each son and daughter receive?

35. The sum of a certain number and its square root is 90. Find the number.

36. In a family, eleven times the number of children is greater by 12 than twice the square of the

number of children. How many children are there in the family?

38. Find three consecutive positive integers such that the square of their sum exceeds the sum

of their squares by 214.

39. Two friends A and B start on a holiday together, A with Rs.380 and B with Rs.260. During

the holiday, B spends 4 rupees more than A and when holidays end, A has 5 times as much asB. How much has each spent?

40. A carpet whose length is times its width is laid on the floor of a rectangular room, with a61

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margin of 1 foot all around. The area of the floor is 4 times that of the margin. Find the width of

the room.

============== End of 40 Questions ============ Happy New Year===============

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placement qns

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