QUINTESSENCE:infomathsonline.com/Que_papers/NIMCET 13-Sol. CHK.doc · Web view5. A six faced die is a biased one. It is thrice more likely to show an odd number than to show an

INFOMATHSNIMCET-2013NIMCET-2013

SET-A SET-A

1. If and 6A–1 = A2 + cA + dl, where A-1

is A – inverse, I is the identity matrix, then (c, d) is NIMCET-2013

(a) (-6, 11) (b) (6, -11) (c) (11, - 6) (d) (6, 11)

2. Let and . Then the vector

satisfying and is

NIMCET-2013

(a) (b)

(c) (d)

3. Find the number of elements in the union of 4 sets A, B, C and D having 150, 180, 210 and 240 elements respectively, given that each pair of sets has 15 elements in common. Each triple of sets has 3 elements in common and A B C D = NIMCET-2013 (a) 616 (b) 512 (c) 111 (d) 702

4. If the straight line ax + by + c = 0 always passes through (1, - 2), then a, b, c are in NIMCET-2013 (a) A.P. (b) H.P. (c) G.P. (d) None of these

5. A six faced die is a biased one. It is thrice more likely to show an odd number than to show an even number. It is thrown twice. The probability that the sum of the numbers in the two throws is even is NIMCET-2013 (a) 4/8 (b) 5/8 (c) 6/8 (d) 7/8

6. If , then I8 + I6 equals NIMCET-2013

(a) 1/4 (b) 1/5 (c) 1/6 (d) 1/77. Let ABC be a triangle whose area is units with

side lengths |AB| = 8 units and |AC| = 5 units. Find possible values of the angle A. NIMCET-2013 (a) 60 or 120 (b) 45 or 135(c) 30 only (d) 90 only

8. Person A can hit a target 4 times in 5 attempts. Person B – 3 times in four attempts. Person C – 2 times in 3 attempts. They fire a volley. The probability that the target is hit atleast two times is NIMCET-2013 (a) 3/4 (b) 1/2 (c) 5/6 (d) 1

9. The value of the integral is

NIMCET-2013

(a) 0 (b) (c) (d)

10. If is a cube root of unity, then find the value of

determinant NIMCET-2013

(a) 3 (b) -3 (c) 32 (d) -32

11. If the vector and form three

coterminous edges of a parallelepiped, then the volume of parallelepiped is NIMCET-2013 (a) 8 (b) 10 (c) 4 (d) 14

12. In a G.P. consisting of positive terms, each term equals the sum of the next two terms. Then the common ratio of the G.P. is NIMCET-2013

(a) (b)

(c) (d)

13. If then what is the first

derivative of f(x)? NIMCET-2013 (a) 1/2 (b) -1/2 (c) 2 (d) -2

14. The solution of sin x + 1 = cos x such that 0 x 2 is NIMCET-2013

(a) 0, (b) (c) (d)

15. Let Tn denote the number of triangles which can be formed by using the vertices of a regular polygon of n sides. If Tn+1

– Tn = 21 then n equals NIMCET-2013 (a) 5 (b) 7 (c) 6 (d) 4

16. If and are the means of two distributions such

that and is the mean of the combined distribution, then NIMCET-2013 (a) (b)

(c) (d)

17. The area enclosed within the curve |x| + |y| = 1 (in square units) is NIMCET-2013 (a) (b) 1 (c) (d) 2

18. Let f(x) be a polynomial function of second degree and f(1) = f(-1). If a, b, c are in A.P., then f '(a), f '(b), f '(c) are in NIMCET-2013 (a) GP (b) HP (c) AGP (d) AP

19. Find the point at which, the tangent to the curve

has its slope . NIMCET-2013

(a) (3, 3) (b) (3, 2) (c) (2, 3) (d) (2, 2)20. Atal speaks truth in 70% and George speaks the truth in

60% cases. In what percentage of cases they are likely to contradict each other in stating the same fact?

NIMCET-2013

(a) (b) (c) (d)

21. A man observes the angle of elevation of the top of a mountain to be 30. He walks 1000 feet nearer and finds the angle of elevation to be 45. What is the distance of the first point of observation from the foot of the mountain?

NIMCET-2013

(a) ft. (b) ft.

(c) ft. (d) ft.

22. The sum of n terms of an arithmetic series is 216. The value of the first term is n and the value of the nth term is 2n. The common difference, d is NIMCET-2013 (a) 1 (b) 2/3 (c) 3/2 (d) 12/11

1 INFOMATHS/MCA/NIMCET-2013

INFOMATHS23. Force and are acting on a

particle and displace it from the point to the

point , then the work done by the force is

NIMCET-2013 (a) 18 units (b) 30 units(c) 24 units (d) 36 units

24. The value of ……. is NIMCET-2013

(a) 3 (b) 6 (c) 9 (d) None of these25. The minimum value of the function y = 2x3 – 21x2 + 36x –

20 is NIMCET-2013 (a) -120 (b) -126 (c) -128 (d) None of these

26. In how many different ways can the letters of the word “CORPORATION” be arranged so that all the vowels always come together? NIMCET-2013 (a) 810 (b) 1440 (c) 2880 (d) 50400

27. If logxy = 100 and log2 x = 10, then the value of y is NIMCET-2013

(a) 210 (b) 2100 (c) 21000 (d) 210000

28. The equations of the line parallel to the line 2x – 3y = 7 and passing through the middle point of the line segment joining the points (1, 3) and (1, -7) is NIMCET-2013 (a) 2x – 3y – 4 = 0 (b) 2x – 3y + 4 = 0 (c) 2x – 3y – 8 = 0 (d) 2x – 3y + 8 = 0

29. In a ABC, (c + a + b) (a + b – c) = ab. The measure of the angle C is NIMCET-2013

(a) (b) (c) (d) None of these

30. The number of non-negative integers less than 1000 that contain the digit 1 are NIMCET-2013 (a) 92 (b) 93

(c) 102 - 92 (d) 103 - 93

31. The lines 3x – 4y + 4 = 0 and 6x – 8y – 7 = 0 are tangent to the same circle. The radius of this circle is

NIMCET-2013 (a) 3/2 (b) 3/4 (c) 4/5 (d) 7/10

32. The area of the parallelogram whose diagonals are

and is

NIMCET-2013 (a) (b) (c) (d)

33. If sin x + a cos x = b, then what is the expression for |a sin x – cos x| in terms of a and b? NIMCET-2013 (a) (b)

(c) (d)

34. If A and B are two events such that P(A B) P(A

B) and , then the events A and B are

NIMCET-2013 (a) Dependent (b) Independent (c) Mutually exclusive (d) None of these

35. If three vectors and

are coplanar, then is NIMCET-2013

(a) – 1 (b) – 2 (c) – 3 (d) – 4 36. The equation of the base of an equilateral triangle is x + y

= 2 and the vertex is (2, -1). The length of the side of the triangle is NIMCET-2013

(a) (b) (c) (d)

37. The total number of numbers that can be formed using the digits 3, 5 and 7 only if no repetitions are allowed, is

NIMCET-2013 (a) 39 (b) 105 (c) 15 (d) 27

38. If x = a cos t, y = b sin t, then is NIMCET-2013

(a) (b)

(c) (d)

39. A random variable X has the distribution law as given below:

x 1 2 3P(X = x) 0.3 0.4 0.3The variance of the distribution is NIMCET-2013 (a) 0.4 (b) 0.6 (c) 2 (d) None of these

40. The value of tan + 2 tan2 + 4 tan 4 + 8 cot 8 is NIMCET-2013

(a) cot (b) tan (c) sin (d) cos 41. The sum of integers between 200 and 400, that are

multiples of 7 is NIMCET-2013 (a) 8729 (b) 8700 (c) 8972 (d) 8279

42. is equal to NIMCET-2013

(a) 0 (b) 1 (c) 1/2 (d) 1/343. Two fair dice are tossed. What is the probability that the

total score is a prime number? NIMCET-2013 (a) 1/6 (b) 5/12 (c) 1/2 (d) 7/9

44. Find the equation of the circle which passes through (-1, 1) and (2, 1), and having centre on the line x + 2y + 3 = 0.

NIMCET-2013 (a) 2x2 + 2y2 – 2x + 7y – 13 = 0(b) x2 + y2 – 2x + 7y – 13 = 0(c) 2x2 + 2y2 + 2x + 7y – 13 = 0(d) x2 + y2 + 2x + 7y – 13 = 0

45. Let be the position vectors of three vertices A, B,

C of a triangle respectively. Then the area of this triangle is given by NIMCET-2013

(a) (b)

(c) (d) None of these

46. The sum of the focal distances of any point on the ellipse

with eccentricity e is given by

NIMCET-2013 (a) 2ae (b) 2b (c) 2a (d) 2be

47. If sinx + sin2x = 1, then cos2x + cos4x is equal to NIMCET-2013

(a) 0 (b) 1 (c) – 1 (d) 248. An experiment succeeds twice often as it fails. The

probability that in the next six trials there will be at least four successes is NIMCET-2013 (a) 240/729 (b) 496/729(c) 220/729 (d) 233/729

49. Sum of 20 terms of the series – 12 + 22 – 32 + 42 - …. is NIMCET-2013

(a) 180 (b) 200 (c) 210 (d) 220

50. If and then is

equal to NIMCET-2013

(a) (b) (c) (d)

ANALYTICAL ABILITY AND LOGICAL REASONING


INFOMATHS51. A train takes 18 seconds to pass completely through a

station 162 m long and 15 seconds through another station 120 m long, at the same speed. What is the length of the train, in meters?

NIMCET-2013 (a) 70 (b) 80 (c) 90 (d) 100

52. In a row of children facing North, Shamika is third to the right of Nikhil, who is 17th from the right end of the row. Ravi is 5th to the left of Shamika and is 20th from the left end. Totally how many children are there in the row?

NIMCET-2013 (a) 37 (b) 38 (c) 39 (d) None of these

53. Given that i) Some apples are blackberries. ii) Some doughnuts are apples. iii) No coconut is a doughnut. iv) All blackberries are coconuts. Which of the following statements is false?

NIMCET-2013 (a) Some blackberries are doughnuts(b) Some coconuts are apples (c) All coconuts are not apples (d) All doughnuts are not coconuts

Questions 54-56 are based on the following : In a family of 6 persons, there are two couples. The lawyer is the head of the family and has two sons-

Mukesh and Rakesh-both teachers. Mrs. Reena and her mother-in-law are layers.

Mukesh’s wife is a doctor and they have a son, Ajay. 54. Which of the following is definitely a couple?

NIMCET-2013 (a) Lawyer-Teacher (b) Doctor-Lawyer (c) Teacher - Teacher (d) None of these

55. What is the profession of Rakesh’s wife? NIMCET-2013 (a) Teacher (b) Doctor (c) Lawyer (d) cannot be determined

56. What is / was Ajay’s grandfather’s occupation?NIMCET-2013

(a) Teacher (b) Lawyer (c) Doctor (d) Cannot be determined

57. Find the missing element in the series A, CD, GHI, …, UVWXY NIMCET-2013 (a) LMNO (b) MNOP (c) NOPQ (d) OPQR

58. In a code language, FRIEND is coded as GTLISJ. Which of the following is coded as HWDVI in that language?

NIMCET-2013 (a) HAPPY (b) GUARD (c) BEADS (d) SPEED

59. There are four brothers Alan, Bob, Carl and Dave. Dave is two years older than Bob. Bob is one year younger than Carl. Alan, who is 34, is two years younger than Carl. Who is the oldest? NIMCET-2013 (a) Alan (b) Bob (c) Carl (d) Dave

Questions 60-62 are based on the following: An employee has been assigned the task of allotting offices

to six of the staff members. The offices are numbered 1 – 6. The offices are arranged in a row and they are separated from each other by six foot high dividers. Hence voices, sounds and cigarette smoke flow easily from one office to another.

Miss Robert needs to use the telephone quite often throughout the day. Mr. Mike and Mr. Brown need adjacent offices as they need to consult each other often while working. Miss. Hardy, is a senior employee and has to be allotted the office number 5, having the biggest window.

Mr. Donald requires silence in the offices next to his and Mr. Tim prefers to be as away as possible from Miss Robert. Mr. Mike and Mr. Donald are all smokers. Miss Hardy finds tobacco smoke allergic and consecutively the offices next to hers to be occupied by non-smokers. Unless specifically stated all the employees maintain an atmosphere of silence during office hours.

60. The ideal candidate to occupy the office farthest from Mr. Brown would be NIMCET-2013 (a) Miss Hardy (b) Mr. Mike (c) Mr. Tim (d) Mr. Donald

61. The three employees who are smokers should be seated in the offices. NIMCET-2013 (a) 1, 2 and 4 (b) 2, 3 and 6 (c) 1, 2 and 6 (d) 1, 2 and 3

62. The ideal office for Mr. Mike would be NIMCET-2013 (a) 2 (b) 6 (c) 1 (d) 3

63. A doctor said to his compound “I go to see the patients at their residence after every 3 hours 30 minutes. I have already gone to the patient 1 hour 20 minutes ago and next time I shall go at 1.40 P.M”. At what time this information was given to the compounder by the doctor?

NIMCET-2013 (a) 11.30 a.m. (b) 11.20 a.m. (c) 10.10 a.m. (d) None of these

64. Which pair of numbers comes next in the following series? 42 40 38 35 33 31 28 NIMCET-2013 (a) 25 22 (b) 26 23 (c) 26 24 (d) 25 23

Questions 65 and 66 are based on the following: i) All G’s are H’s ii) All G’s are J’s or K’s iii) All J’s and K’s are G’s iv) All L’s are K’s v) All N’s are M’s vi) No M’s are G’s

65. If no P’s are K’s, which of the following must be true?NIMCET-2013

(a) All P’s are J’s (b) If any P is a G, it is a J (c) No P is an H (d) If any P is an H, it is a G

66. Which of the following is inconsistent with one or more of the conditions? NIMCET-2013 (a) All H’s are G’s (b) All H’s that are not G’s are M’s (c) Some H’s are both M’s and G’s (d) No M’s are H’s

67. Shyam is taller than Pradeep and Pradeep is as tall as Anurag. But Anand is shorter than Suresh, who is as tall as Anurag. If Pradeep is taller than Praveen, who is the tallest of all? NIMCET-2013 (a) Pradeep (b) Praveen (c) Suresh (d) Shyam

68. When Rajeev was born his father was 32 years older than his brother and his mother was 25 years older than his sister. If Rajeev’s brother is 6 years older than Rajeev and his mother in 3 years younger than his father, how old was Rajeev’s sister when he was born? NIMCET-2013 (a) 15 yrs (b) 14 yrs (c) 7 yrs (d) 10 yrs

69. Dhoni starts from his office at 8 A.M. on a Sunday morning, travels 10 km towards West and then turns to his left and walks 8 km. Then he again turns to his left and walks 4 km and then stops. What is the shortest distance to his office from the point where he stopped?

NIMCET-2013 (a) 18 km (b) 8 km (c) 10 km (d) None of these

70. A treasure chest has less than 100 gold coins. The number of coins is (i) One more than a multiple of 3 (ii) Two more than a multiple of 4 (iii) Three more than a multiple of 5 and (iv) Four more than a multiple of 6 How many coins are there in the chest? NIMCET-2013 (a) 58 (b) 88 (c) 98(d) 38

71. Read the statements and then decide which of the conclusions logically follow. Statements : 1) All mangoes are golden in colour. 2) No golden coloured things are cheap.


INFOMATHSConclusions: (i) All mangoes are cheap. (ii) Golden coloured mangoes are not cheap.

NIMCET-2013 (a) Only conclusion i follows(b) Only conclusion ii follows (c) Either i or ii follows (d) Neither i nor ii follow

72. Pointing to a woman, Nirmal said "She is the daughter of my wife’s grandfather’s only child”. How is the woman related to Nirmal? NIMCET-2013 (a) Wife (b) Sister-in-law(c) Sister (d) None of these

73. Karan and Arjun run a 100 metres race, where Karan beats Arjun by 10 metres. To do a favour to Arjun, Karan starts 10 metres behind the starting line in a second 100 metre race. They both run at their earlier speeds. Which of the following is true in connection with the second race?

NIMCET-2013 (a) Karan and Arjun reach the finishing line simultaneously(b) Arjun beats Karan by 1 metre (c) Arjun beats Karan by 11 metres (d) Karan beats Arjun by 1 metre

Questions 74-76 are based on the following: There are three switches A, B and C which can be in on/OFF position. Their settings change as per the following rules:

(i) If A is the only switch as ON, change B to ON. (ii) If A and B are only switches as on change C to ON(iii) If all three switches ON, change C to OFF> (iv) For all other situations, all switches in ON are

changed to OFF and all switches in OFF are changed to ON.

74. If switches A and B are ON and C is OFF, their changed settings will be NIMCET-2013 (a) A ON, B OFF, C OFF (b) A ON, B ON, C ON(c) A ON, B OFF, C ON (d) A OFF, B ON, C OFF

75. If only B is ON, the changed setting will be NIMCET-2013

(a) A ON, B ON, C ON(b) A ON, B ON, C OFF(c) A ON, B OFF, C ON (d) A OFF, B OFF, C ON

76. If only B is ON in the changed setting, which of the following could have been the original setting?

NIMCET-2013 (a) A ON, B OFF, C OFF (b) A ON, B OFF, C OFF(c) A OFF, B ON, C OFF (d) A OFF, B OFF, C ON

77. If the third day of a month falls on Friday, what day will be on the fourth day after twenty first of the month?

NIMCET-2013 (a) Monday (b) Tuesday (c) Saturday (d) Thursday

78. Ana is a girl and has the same number of brothers as sisters. Andrew is a boy and has twice as many sisters as brothers. Ana and Andrew are the children of Emma. How many children does Emma have? NIMCET-2013 (a) 2 (b) 3 (c) 5 (d) 7

Questions 79-81 are based on the following: 1. Anu is taller than Cini 2. Eenu is shorter than Binu 3. Anu is shorter than Dany 4. Eenu is taller than Anu

79. The best answer to “Who is the tallest?” is NIMCET-2013 (a) Dany (b) Binu (c) Dany or Binu (d) Both Dany and Binu

80. Who is the shortest? NIMCET-2013 (a) Cini (b) Anu or Cini (c) Eenu (d) Insufficient data to conclude

81. Which of the following statements would help to logically order the persons according to their heights?

NIMCET-2013

(a) Binu is 7 feet tall (b) Danuy and Binu do not have equal height (c) Eenu is the tallest in the group (d) Dany is the tallest in the group

Questions 82 and 83 are based on the following:A blacksmith has five iron articles A, B, C, D and E, each having a different weight.

A weighs twice as much as B B weighs four and half times as much as C C weighs half as much as D D weighs half as much as E E weighs less than A but more than C

82. Which of the following article is heaviest in weight?NIMCET-2013

(a) A (b) B (c) C (d) D83. Which of the following represents the descending order of

weights of the articles? NIMCET-2013 (a) A, B, E, D, C (b) B, D, E, A, C (c) A, B, C, D, E (d) C, D, E, B, A

84. In a cricket season, India defeated Australia twice. West Indies defeated India twice. Australia defeated West Indies twice. India defeated New Zealand twice and West Indies defeated New Zealand twice. Which country has lost most number of times? NIMCET-2013 (a) India (b) Australia (c) New Zealand (d) West Indies

Questions 85 to 87 are based on the following: There are five persons A, B, C, D, E standing on six steps numbered 1, 2, 3, 4, 5, 6 from the bottom. At most one person is standing on each step. The step number on which A is standing, is two less than that of C. Step number on which B is standing is one more than that of D. 85. If A is standing on step 1, which of the following is true?

NIMCET-2013 (a) B is standing on step 2 (b) C is standing on step 4 (c) E is standing on step 3 (d) D is standing one step higher than C

86. If D is standing on step 1, on which step A could be standing? NIMCET-2013 (a) 2 or 4 only (b) 3 or 5 only (c) 3 or 4 only (d) 4 or 5 only

87. If there are two steps in between the steps on which A and D are standing, A must be standing on which of the following steps? NIMCET-2013 (a) 3 (b) 4 (c) 5 (d) 6

88. From the information given below: A + B means A and B are of the same age A – B means B is younger than A A + B means A is younger than B What does Sachin * Mohan – Ravi mean? NIMCET-2013 (a) Sachin is youngest (b) Ravi is youngest (c) Sachin is oldest (d) Mohan is oldest

89. Jimmy saw the time while going to the tennis court. He saw the hour hand is 20 away from 4. After he returned from tennis court, he noticed that the hour hand is 20 away from 4. If he took ten minutes to go to tennis court and he walked at the same speed while going to the tennis court and while returning, how much time did he spent at the tennis court? NIMCET-2013 (a) 60 minutes (b) 80 minutes (c) 70 minutes (d) 50 minutes

90. There are 8 balls looking alike, seven of which have equal weight and one is slightly heavier. The weighing balance is of unlimited capacity. Using this balance, the minimum number of weighings required to identify the heavier ball is NIMCET-2013 (a) 1 (b) 2 (c) 3 (d) 4

GENERAL ENGLISH91. Out of the alternatives, choose the appropriate phrase to

make the sentence meaningful. If you had joint accounts 4 INFOMATHS/MCA/NIMCET-2013

INFOMATHSwith _______ who died, then you will be responsible for the bills. NIMCET-2013 (a) everybody (b) anyone (c) everyone (d) someone

92. Choose the analogy that is closest in meaning to the pair: Diamond : Necklace NIMCET-2013 (a) Cars : roads (b) Flowers : Bouquet (c) Gold : Bangle (d) Books : Shop

93. Choose the suitable proposition for the blank to make a meaningful sentence. Suresh is angry _______ his servant.

NIMCET-2013 (a) about (b) on (c) by (d) with

94. Choose the correct alternative for the sentence below: The earth is always revolving round the sun

NIMCET-2013 (a) The earth revolves round the sun (b) The earth is revolving round the sun (c) The earth revolving round the sun (d) None of these

95. Choose the word that best expresses the meaning of the given idiom: “A close shave” NIMCET-2013 (a) A clean shave (b) a narrow escape (c) A guarded secret (d) A sudden fall

96. Pick the part of the sentence that has an error:My elder brother is a MA whereas I am only a BA

NIMCET-2013 (a) My elder brother (b) is a MA (c) whereas I am (d) only a BA

97. Choose the suitable phrasal verb for the blank in the sentence below. ……. My hopes when untimely rain threatened my crops. NIMCET-2013 (a) gave in (b) gave out (c) gave up (d) gave off

98. Out of the given alternatives, choose the word that is opposite in meaning to the word: AFFLUENT NIMCET-2013 (a) Reluctant (b) Poor (c) Clear (d) Enthusiastic

99. Fill in the blank with appropriate form of noun: Don’t blame yourself, it’s not your _______!

NIMCET-2013 (a) misunderstanding (b) error (c) slip (d) fault

100. Fill in the blank: The instructor, along with the class, _______ angry about the room change. NIMCET-2013 (a) are (b) have (c) has (d) is

101. Choose the suitable word for the blank to make it a meaningful statement. What you say is _______ my comprehension. NIMCET-2013 (a) before (b) beside (c) behind (d) beyond

102. Fill in the blank with a suitable preposition : If you want to avoid traffic, you need to leave _______ 7.30 A.M. NIMCET-2013 (a) until (b) by (c) during (d) at

103. Choose the word that best expresses the meaning of the given idiom: “to smell a rat” NIMCET-2013 (a) To suspect something bad (b) To misunderstand (c) To detect bad smell (d) To forsake

104. Out of the given alternatives, choose the word that best expresses the meaning of the word ABRIDGE.

NIMCET-2013 (a) Judge (b) Release (c) Shorten (d) Dissolve

105. ‘a dog’s breakfast’ means NIMCET-2013 (a) Breakfast cooked for a dog (b) Breakfast cooked by a dog (c) Something that has been done very badly

(d) None of these106. Change the speech: She says, “I like going to the seaside”.

NIMCET-2013 (a) She says she likes going to the seaside (b) She says I like going to the seaside (c) She says that she liked going to the seaside(d) She says she like going to the seaside

107. Arrange the following to form a correct sentence P : will normally be granted Q : candidates should note R : that no request for S : change of centre NIMCET-2013 (a) SRQP (b) PRQS (c) QSPR (d) QRSP

108. Rewrite the sentence after correcting the error: She was one of the average student of the class.

NIMCET-2013 (a) She was one of the average students of the class (b) She is one of the average student of the class (c) She was one among the average student of the class (d) She is an average students of the class

109. Choose appropriate words to form a grammatically correct sentence: The decoration of the new house, including the furniture and curtains _______ NIMCET-2013 (a) is more pleasing (b) are more pleasing (c) is most pleasing (d) are pleasing

110. Fill in the blank: The President of the United States, accompanied by his advisors, _______ enroute to Europe. NIMCET-2013 (a) were (b) are (c) was (d) both (a) and (c)

COMPUTER AWARENESS111. All digital circuits can be realized by using only

NIMCET-2013 (a) Exclusive OR gates (b) Half adders (c) Multiplexers (d) OR gate

112. The Boolean function is equivalent to

NIMCET-2013 (a) a.b (b) a + b (c) (d)

113. Which of the following circuit is used as a memory device in computers? NIMCET-2013 (a) Flip-Flop (b) Rectifier (c) Comparator (d) All of these

114. Convert the Hexadecimal number 4DF to its octal equivalent NIMCET-2013 (a) 2333 (b) 2337 (c) 2773 (d) 2373

115. A tautology is a Boolean formula that is always true. Which of the following is a tautology? NIMCET-2013

(a) x (b)

(c) (d) 116. Acronym of EEPROM is NIMCET-2013

(a) Extended Erasable Programmable Memory(b) Electrically Erasable Read Only Memory(c) Electrically Erasable Programmable Read Only Memory (d) Extended Erasable Page-Oriented Memory

117. For reproducing sound, a CD audio player uses a NIMCET-2013

(a) Quartz crystal (b) Titanium needle (c) Barium ceramic (d) Laser beam

118. When we open an internet site, we see www. What does www stand for? NIMCET-2013 (a) World Wide Word (b) World Wide Web (c) Word Wide Webinar (d) Word Widing Works

119. The answer of the operation (10111)2 (1110)2 in hex equivalent is NIMCET-2013 (a) 150 (b) 14C (c) 142 (d) 13E


INFOMATHS120. The minimum number of bits to represent a character from

ASCII code set is NIMCET-2013 (a) 2 (b) 8 (c) 5 (d) 7

NIMCET – 2013SET-A

1 2 3 4 5 6 7 8 9 10A A D A B D A C D D11 12 13 14 15 16 17 18 19 20C D A D B D D D B C21 22 23 24 25 26 27 28 29 30A D C A C D C C C D31 32 33 34 35 36 37 38 39 40B A D B D C C A B A41 42 43 44 45 46 47 48 49 50A D B A B C B B C B51 52 53 54 55 56 57 58 59 60C B A A C D B B D C61 62 63 64 65 66 67 68 69 70D D A C B C D D C A71 72 73 74 75 76 77 78 79 80B A D B C B C D C A81 82 83 84 85 86 87 88 89 90D A A C D C B B A B91 92 93 94 95 96 97 98 99 100D B D A B B C B D D

101 102 103 104 105 106 107 108 109 110D B A C C A D A C C

111 112 113 114 115 116 117 118 119 120A B A B C C B B C D


INFOMATHS

NIMCET-2013SET-A SOLUTIONS

SOLUTIONS 1. Ans. (a) We have 6A–1 = A2 + cA + dI

Multiplying both side by A, we have6I = A3 + cA2 + dAA3 + cA2 + dA – 6I = 0 …(i)According to Cayley Hamilton Theorem

(1 - )[(1 - )(4 - ) + 2] = 0 3 - 62 + 11 - 6 = 0 …(ii)On comparing (i) and (ii) c = –6 and d = 11.

2. Ans. (a) Multiplying by b in the given relationWe have b.(a b) + b.c = 0 b.c = 0Also given that a.b = 3, suppose b = xi + yj + zkThus y - z = 3 and x - y - z = 0From these equations x = 2z + 3, y = z + 3.So the vector b = (2z + 3)i + (z + 3) j + zkNow again from the relation (a b) + c = 0.We get z = – 2, thus vector b = -i + j - 2k.

OR by choices (a) gives b = -i + j - 2k a = j-k then a.b=3 and a

3. Ans. (d) n(A B C D) = n (A) + n(B) + n(C) + n(D) – n (A B) – n(B C) ……….

= 150 + 180 + 210 + 240– 4C2 . 15 + 4C3 . 3 – 0 = 780 – 90 + 12 = 702

4. Ans. (a) ax + by + c = 0 passes through (1, –2)So point will satisfy the equationWe have, a – 2b + c = 0 a + c = 2bSo a, b, c are in A.P.

5. Ans. (b) Let the probability to show an even number = PAccording to question probability to show an oddnumber = 3P3P + P = 1as P(E)+P(Ec)=1

and

Now the sum of the numbers in two throws is evenwhen either both are odd or even.

So required probability

6. Ans. (d)

7. Ans. (a) We know that area of triangle

= 60 or 120

8. Ans. (c) The Probability that the target is hit atleast two times is

9. Ans. (d) …(i)

…(ii)

Adding (i) and (ii)

10. Ans. (d)

by C1C1+C2

11. Ans. (c) The volume of parallelopiped

= 4

12. Ans. (d) Let the terms be a, ar, ar2, ar3….According to the condition we havea = ar + ar2 1 – r – r2 = 0


INFOMATHS

Since r is positive as GP consists of positive terms,

hence

13. Ans. (a)

14. Ans. (d) sin x + 1 = cos xcos x – sin x = 1

Putting n = 0 and 1, x = 0 and

15. Ans. (b) According to the question we haven+1C3 – nC3 = 21 We know 8C3 – 7C3 = 21 n = 7

16. Ans. (d) (result)

17. Ans. (d) The graph of the given function is given below :

|x| + |y| = 1 x y = 1

This is a square of side , so area =

square unit.

18. Ans. (d) Suppose the 2 degree polynomial is f(x) = px2 + qx + r Given that f (1) = f (-1) p + q + r = p - q + r q = 0Hence f ' (x) = 2px and f '(a), f '(b), f '(c) will be 2pa,2pb and 2pc, will be in AP.

19. Ans. (b) Slope

and y = 2

Required point is (3, 2).

20. Ans. (c) They are likely to contradict each other in stating the same fact only when one will speak truth and other will speak lie so the required probability is

TL+LT=

21. Ans. (a)

[ as ]

The distance of the first point of observation from

the foot of the mountain

22. Ans. (d) According to the question Tn = 2n, a = n

2n = n + (n – 1)d n = (n – 1)d

We have

by putting

n2 = 2 72 n = 12

23. Ans. (c) Resultant force | = 5i + 3j + 2k and the displacement is 2i - 2j +10k

Work done is (5i + 3j + 2k).(2i - 2j +10k)= 10 – 6 + 20 = 24.

24. Ans. (a) The number

= 91/2 = 3.

25. Ans. (c) y = 2x3 – 21x2 + 36x – 20 8 INFOMATHS/MCA/NIMCET-2013

x=h

INFOMATHS

at is point of minima

is min. value

26. Ans. (d) Required ways

= 50400 as 5 vowels( 3 O’s,1 A, 1 I) and 6 consonants( 2 R’s and others different)

27. Ans. (c) log2x =10 x = 210 y = (210)100 y = 21000.

28. Ans. (c) Slope of line 2x – 3y = 7 is .

Required line is parallel to this line so slope of the

line will be .

Mid point of line segment joining the points (1, 3) and (1, –7) is (1, –2)

Required line is

3y + 6 = 2x – 2 2x - 3y - 8 = 0

29. Ans. (c) (a + b)2 - c2 = aba2 + b2 + 2ab - c2 = aba2 + b2 + ab - c2 = 0a2 + b2 - c2 = -ab

We know

30. Ans. (d) The three digit numbers containing 1 is total nos. – nos not containing 1=103 - 93

31. Ans. (b) Since the lines are parallel, thus distance between them is the diameter of the circle.

The lines are 3x - 4y + 4 = 0 and

Distance between them is

Thus the radius is

32. Ans. (a) Area of the parallelogram whose sides are p

and q is |p q| = magnitude of

= magnitude of -2i -14 j -10k

33. Ans. (d) Given that sin x + a cos x = b ,suppose asin x - cos x = pSquaring and adding, we havesin2x + a2cos2x + a2sin2x + cos2x = b2 + p2

p2 = 1 + a2 – b2 Hence |p| = |a sin x - cos x | .

34. Ans. (b)

Now P(A B) = P(A) + P(B) – P(A B)

Since P(A).P(B) = P(A B)

, thus the events are independent.

35. Ans. (d) Since the vectors are coplanar, hence

36. Ans. (c) Suppose the triangle is ABC

Length of perpendicular

Thus side of the triangle is

as B = 60

37. Ans. (c) Single digit numbers are 3.Two digit numbers are 3×2 = 6Three digit numbers are 3×2×1 = 6Total numbers are 15.

38. Ans. (a)


INFOMATHSSuppose

Now

as .

39. Ans. (b) We know that variance is

Where mean Thus variance is= (1 – 2)2 0.3 + (2 – 2)2 0.4+ (3– 2)2 0.3 = 0.6

40. Ans. (a) We know that

Adding and subtracting cot from the given expression, we have

= -8 cot8 + 8cot 8 + cot = cot [Alternate method: The question can be easily solved by putting value of in the questions and in the four choices. Only choice (A) is correct.]

41. Ans. (a) The integers will be 203 + 210 + ……+ 399

There are terms in the series.

Sum

42. Ans. (d) The given expression is

(Applying L Hospital rule)

43. Ans. (b) The sum of the dices can be 2, 3, 5, 7, 11. Thus the number of ways of getting these sums are 1, 2, 4, 6 and 2 respectively. Required probability is

44. Ans. (a) Since the centre lies on the line x + 2y + 3 = 0, suppose the centre is (– 2 – 3, ), then its distance from the given two points (– 1, 1) and (2, 1)(– 2 – 3 + 1)2 + ( – 1)2 =(– 2 – 3 – 2)2 +(–1)2

(– 2 – 2)2 = (– 2 – 5)2

, thus the centre is

Radius is thus the equation of the circle is

2x2 + 2y2 – 2x + 7y – 13 = 0. [Alternate method: Question can also be solved by checking the choices which satisfies the given points (– 1, 1) and (2, 1)]

45. Ans. (b) The two adjacent sides of the triangle are

represented by and , thus it’s area

will be

46. Ans. (c) This is a standard result, PS + PS' = 2a. where S and S’ are foci of ellipse.

47. Ans. (b) From the given relations sin x + sin2x = 1, sin x = 1 – sin2x = cos2x or cos2 x = sin x The given expression is cos2x + cos4x can be written as sinx + sin2x that is 1.

48. Ans. (b) Suppose probability of success is 2p and

that of failure is p, then 2p + p = 1 hence

probability of success is and that of the failure is

. Now of 6 trials, there must be at least 4

successes, required probability is

49. Ans. (c) The series can be written as(-12 + 22) + (-32 + 42) + …. (-192 + 202)= 3 + 7 + 11 +…….+ 39There will be 10 terms in the A.P. series given above.Hence the required sum

50. Ans. (b)


INFOMATHS

51. Ans. (c) Let the speed of the trains is S m/sec and length of the train be l mts. Then

…(i)

…(ii)

By solving (i) and (ii), we getS = 14 m/sec and l = 90 mts.

52. Ans. (b)

So total number of students is= 19 + 1 + 2 + 13 + Ravi + Nikhil + Shamika = 38

53. Ans. (a) Using the given statements, Venn Diagram can be like this

So except choice (A) all are true.

Solutions for 54 to 56: There are total 6 person in that family and from which two are couples.

And it is given that Mrs. Reena and his mother in law so head of the family will be her mother in law.

54. Ans. (a) Lawyer teacher is definitely a couple.

55. Ans. (c) Rakesh wife is Mrs. Reena who is a lawyer.

56. Ans. (d)

57. Ans. (b)The pattern is

Hence the missing term is MNOP.

58. Ans. (b) Given that FRIEND is coded as GTLISJ, which means we are adding 1, 2, 3, .. to the corresponding alphabets.

So GUARD will be coded as HWDVI

59. Ans. (d) Dave = 2 + BobBob = Carl – 1Alan = Carl – 2Given that Alan is 34 years old, hence 34 = Carl – 2 Carl = 36, Bob = 35 and Dave = 37 Solutions for 60 to 62: The arrangements of all the candidates will be as follows:1 2 3 4 5 6Tim Donald Mike Brown Hardy Robert

60. Ans. (c) Farthest from Mr. Brown is office 1. Answer is Mr. Tim.

61. Ans. (d) 62. Ans. (d)

63. Ans. (a) When doctor was saying to compounder it was 1 hour 20 mins take then he earlier visited the patient and he visits in every 3 hour 30 minutes. Next time he will visit at 1 : 40. So his earlier visit was at 10 : 10 so the information was given to compounder is 1 hr. 20 min late i.e. 11:30 A.M.

64. Ans. (c)

So the next terms will be 26 and 24. Solutions for 65 to 66: The combined Venn Diagram of these all statements can be like then

65. Ans. (b) If P is not K and it is in G than it has to be J because G is only either J or K.

66. Ans. (c) If some H are both M and G then it means there is some part common between M and G which is contradictory with No M are G.

67. Ans. (d) Shyam > Pradeep = AnuragSuresh > AnandSuresh = AnuragPradeep > PraveenCombining the informationShyam > Pradeep = Anurag = Suresh > Anand > Pradeep > PraveenSo the tallest person is Shyam.


INFOMATHS68. Ans. (d) As per given information when Rajeev was

born his father was 32 years older than his brother, and his mother was 25 years older than his sister, and three years younger than his father. So when Rajeev’s brother is 6 years old. Rajeev’s brother Father Mother6 38 35So his sister is 10 years older when he born.

69. Ans. (c) The diagram is given below:

So the shortest distance is 10 km.

70. Ans. (a) Gold coins are less than 100. In terms of 3k+1, 4k+2, 5k + 3, 6k + 4 so the total number of coins will be LCM (3, 4, 5, 6)k – Constant difference= 60k – 2. So number of coins will be 58.

71. Ans. (b)

So, only conclusion II follows Solutions for 72 to 73: Here we can write all given conditions in terms of equations likeA = 2B, B = 4.5C, 2C = D, 2D = E. Now from these equations we can write the following ratios:A : B : C : D : E2 : 1

9 : 21 : 2

1 : 2So A : B : C : D : E = 18 : 9 : 2 : 4 : 8

72. Ans. (a)

73. Ans. (a)

Solutions for 74 to 76: Here we are taking ON means 1 and OFF means 0.Condition 1 can be written as this

A B CInitial 1 0 0Changed to 1 1 0

Condition 2 can be written as thisA B C

Initial 1 1 0Changed to 1 1 1

Condition 3 can be written as this

A B CInitial 1 1 1Changed to 1 1 0

Except these three conditions in any other case we will change 1 to 0 and 0 to 1.

74. Ans. (b) If A = 1, B = 1 and C = 0 than it will be changed according to condition 2 i.e. A = 1, B = 1 and C = 1.

75. Ans. (c) If A = 0, B = 1 and C = 0 than it will be changed according to condition 4 i.e. A = 1, B = 0 and C = 1.

76. Ans. (b) If A = 0, B = 1 and C = 0 after change than this change is not because of condition 1, 2 and 3, So initial position should be A = 1, B = 0 and C = 1.

77. Ans. (c) Third of a month is Friday then 25th of the same month will be Saturday.

78. Ans. (d) If Andrew has one brother than he must have two sisters of whom one is Ana will not have equal number of brother and sister, so andrew has two brothers and four sisters of whom one is Ana who has three brothers and three sisters. Hence the total number of children of Emma is seven.

Solutions for 79 to 81: By the given conditions we can say Binu > Eenu > Anu > Cini

Dany > AnuHere Binu is taller than Eenu is taller than Anu is taller than Cini. Dany is taller than Anu but the relation of Dany with Binu and Eenu is not clear.

79. Ans. (c)

80. Ans. (a)

81. Ans. (d)

82. Ans. (d) Karan beats by 10 meter in a race of 100 meter that means when Karan runs 100 meter Arjun runs 90 meters, so the ratio of their speeds is 10 : 9. Hence in the second race when Karan runs 110 meters Arjun will run 99 meters only, so Karan will beat Arjun by 1 meter.

83. Ans. (c) The given data can be tabulated in the following manner:

Win LossIndia 4 2Australia 2 2West Indies 4 2New Zealand 0 4

So New Zealand lost the maximum number of matches.

84. Ans. (a) Solutions for 85 – 87: With the given conditions there can be many cases like:

Case 1 Case 2 Case 3 Case 4 Case 5 Case 6Step 6 - B B - C CStep 5 B D D C - -


INFOMATHSStep 4 D - C - A AStep 3 C C - A - BStep 2 - - A B B DStep 1 A A - D D -

85. Ans. (d) If A is standing on step 1 then C must be on step 3, so only choice D is possible.

86. Ans. (c) If D is standing on step 1 than B is at step 2 and A can be at step 3 or 4.

87. Ans. (b) If there are two steps between A and D than A can be at step 1, 2 or 4.

88. Ans. (b) Sachin and Mohan are of same age and Ravi is younger to both of them. So Ravi is youngest.

89. Ans. (a) When Jimmy left and returned his house the Hour hand is 20o away from 4 in both the cases. That means he left his house at 3:20 and returned at 4:40. So he was out for 80 minutes but he took 20 minutes to go and return back. Hence he spends 60 minutes in all at tennis court.

90. Ans. (b) We will divide these 8 balls in three groups of 3, 3 and 2. First we will compare first two groups which are either equal or not equal. If they are equal than the heavier ball is out of last two balls which can be identified in one more weighing. But if they are not equal then the heavier ball is among the first two groups of three balls each. Now from the group which have heavier ball, we will put one and one ball on weighing balance which will be again equal or not equal. If it is equal than the third ball is heavier ball, otherwise out of these two.

91. Ans. (d) Someone – because you can have joint accounts with a particular person and not with ‘anyone’ and ‘everyone’.

92. Ans. (b) Stringing together of diamonds forms a necklace and many flowers tied together form a Bouquet.

93. Ans. (d) The verb angry is always followed by prepositions ‘at’ or ‘with’.

94. Ans. (a) Because universal truths are expressed in simple present tense.

95. Ans. (b) Close shave is a narrow escape.

96. Ans. (b) It should be “an M.A.” because the sound of vowel ‘e’ is clear in pronunciation of letter ‘em’.

97. Ans. (c) ‘Gave up’ means abandon, surrender. Hence abandon all Hope.

98. Ans. (b) Affluent means rich so its opposite is poor.

99. Ans. (d) The popular usage is blame for one’s fault.

100. Ans. (d) The principle subject here is ‘The Instructor’, which is singular. Hence ‘is’.

101. Ans. (d) Comprehension means understanding and when you are not able to understand, it is ‘beyond your comprehension’. Here beyond means outside.

102. Ans. (b) Here the sentence is giving a general advice that you should leave by 7.30. At 7.30 would mean a specific time and instruction.

103. Ans. (a) To have suspicion or doubt about something is to smell a rat.

104. Ans. (c) Abridge means to abbreviate or reduce. Hence ‘shorten’.

105. Ans. (c) A bad piece of work is denoted as a dog’s breakfast.

106. Ans. (a) The sentence in direct speech tells you a habitual action; hence the tense will not change in indirect speech.

107. Ans. (d) Q is the only opening sentence in the question, which is logically followed by R as in “note that”.

108. Ans. (a) We always use one among the many. Hence ‘one of the average students’

109. Ans. (c) Here the principle subject is ‘The decoration’ which is singular, hence ‘is’ should be used. We cannot use more pleasing because there is no comparison in the story.

110. Ans. (c) Here again the principle is ‘The President’ which is singular. Hence ‘was’ should be used as a singular helping verb.

111. Ans. (a) XOR and XNOR are the universal gates. All the other gates can be realized by these gates and so as all the other circuits too. So the answer is (A) exclusive OR gates

112. Ans. (b) This is the property, which says .

113. Ans. (a) Flip-flop is the most basic memory device used in computer organizations which is used to store 1 bit of data (either 0 (off state if flip flop) or 1(on state if flip flop)). All the other memory units are constructed using these flip-flops only.

114. Ans. (b) First covert the given no. into its equivalent binary form using 4 bits for each decimal digit. Then convert that binary no. into octal reorientation using the group of 3 bits from right to left.So the binary representation for the given number is4(0100), D(1101),F(1111) = 010011011111Octal representation is 2337.

115. Ans. (c) We know that , thus which is always 1.

116. Ans. (c)


INFOMATHS

117. Ans. (b) LASER stands for Light Amplification by Stimulated Emission of Radiation. Compact Disc (CD) works on the principle of LASER only.

118. Ans. (b)

119. Ans. (c) If you know binary multiplication then this question will be solved very easily and rapidly too. The answer of binary multiplication is 101000010 The hexadecimal equivalent of this is 142. Second

approach is to covert both the binary into decimal, multiply, convert the answer into hexadecimal.

120. Ans. (d) As we know 7 bits can be used to represent numbers from 0 to 127(total 128). From these 7 bits we can represent any character printable or non printable Later UTF-8 was introduced where each character was represented using 8 bits, the 8th bit was used to represent sign but still with 7 bits we can represent any character so the answer is 7.

MY PERFORMANCE ANALYSISNo. of QuestionsAttempted (=A)

No. of RightResponses (=R)

No. of WrongResponses (=W)

Net Score(NS = R – 0.25W)

Percentage Accuracy(= PA= 100R/A)


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