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MaaRula MCA Entrance Classes AMIT KATIYAR (MCA-JNU) 117/0/687 In front of Anurag hospital, Crossing no. 9 Kanpur E-mail ID- [email protected] Cont. No. 9554548576, 8299331570 Visit us: www.maarulaclasses.in for online test series: www.maarulatest.com UPTU-2015 Duration- (2 Hour)

Add:-IN FRONT OF ANURAG HOSPITAL, 9 NO. CROSSING KANPUR Mo.No. 9554548576, 8299231570

AMIT KATIYAR

1. If 퐻 and 퐻 are two subgroups of a group G, then (푎)퐻 퐻 is a subgroup of G (푏)퐻 ∩ 퐻 is a subgroup of G (푐)퐻 ∪ 퐻 is a subgroup of G (푑)푁표푛푒 of the above

2. The generators of a cyclic group G = {푎,푎 ,푎 ,푎 , 푎 ,푎 ,푎 ,푎 = 푒} are (푎)푎 and 푎 Only (푏)a, 푎 ,푎 ,푎 (푐)푎 ,푎 , 푎 (푑) a, 푎 ,푎 ,푎

3. Suppose G is a group of order 29, then which of the following is true? (푎)G is not abelian (푏)G has no subgroup other than ϕ and (푐)There is a group H of order 29 which is not isomorphic to G (푑)G is a subgroup of a group of order 30

4. Which of the following statements is true? (푎)3 ⊆ {1, 3, 5} (푏)3∈{1, 3, 5} (푐){3}∈{1, 3, 5} (푑){3, 5}∈{1, 3, 5}

5. The number of all possible subsets of [1, {2, 3}} is: (푎)2 (푏)4 (푐)6 (푑)8

6. A class has 175 students. The following data shows the number of students obtaining one or more subjects. Mathematics 100, Physics 70, Chemistry 40, Mathematics and Physics 30, Mathematics and Chemistry 28, Physics and Chemistry 23, Mathematics, Physics and Chemistry 18. How many students have offered mathematics alone (푎)35 (푏)48 (푐)60 (푑)22

7. Let X be a family of sets and R be a relation on X defined by ‘A is disjoint from B’. Then R is: (푎)Reflexive (푏)symmetric (푐)Anti-symmetric (푑)Transitive

8. If A is the set of even natural number less than 8 and B is the set of prime numbers less than 7, then the number of relations from A to B is; (푎)2 (푏)9 (푐)3 (푑)2 − 1

9. Let the sets A and B are having m and n elements respectively (푚 ≤ 푛), then number of injective mappings from A to B is: (푎)M! (푏)n! (푐) !

( )!(푑)None of these

10. If f(x) is a polynomial, satisfies. The condition

푓(푥)푓 = 푓(푥) + 푓( ) and f(3)=28, then 푓(4) =

(푎)36 (푏)56 (푐)65 (푑)63 11. If 푓:푅 → 푅 and 푔:푅 → 푅 defined by 푓(푥) = 2푥 + 3 and

푔(푥) = 푥 + 7 then the value of x for which 푓 푔(푥) = 25 (푎) ± 1 (푏) ± 2 (푐) ± 3 (푑) ± 4

12. If 푓(푥) = |푥 − 2| and 푔(푥) = 푓[푓(푥)], then for 푥 >20, 푔 (푥) = (푎)-1 (푏)1 (푐)2 (푑)None of the above

13. If 푓: [1,∞) → [2,∞) is given by 푓(푥) = 푥 + , then 푓 (푥) equals:

(푎) 푥 +√푥 − 4 (푏)1 + √푥 − 4

(푐) 푥 − √푥 − 4 (푑)푁표푛푒 표푓 푡ℎ푒푠푒

14. Period of the function 푠푖푛 + 푐표푠 − 푐표푡 is: (푎)5 (푏)7 (푐)12 (푑)30

15. Domain of 푓(푥) = ( )( )( )( )

is:

(푎) [-2, -1]∪ [3, 4) (푏) (-2, -)∪ (3,−4)− {0, 1} (푐)Does not contain the interval (0, 1) (푑)Does not contain the set (−∞,−5)∪ (5, 6)

16. The range of 푓(푥) = 푐표푠푥 + 푠푖푛푥+ √2 is: (푎) [0, 2] (푏) [0, 2√2] (푐) [-√2,√2] (푑)None of these

17. If 퐴 =1−23

,퐵 = [4 5 2],퐶 =2−35

then ABC=

(푎)3−69

(푏)369

(푐) 36−9

(푑)−369

18. If A=3 5 7−2 −3 11 1 2

then 퐴 =

(푎)7 3 263 1 −11−5 −2 0

(푏)7 3 −263 1 11−5 −2 1

(푐)3 1 117 3 −26−5 2 1

(푑)None of these

19. The matrix 휆 −1 4−3 0 1−1 1 2

is invertible if:

(푎)휆 ≠ −15 (푏)휆 ≠ −17 (푐)휆 ≠ −16 (푑)휆 ≠ −18 20. The system of linear equations:

2x – 3y + 6z = 4, 5x + 7y – 14z = 1, 3x + 2y – 4z = 0, have (푎)Unique solution (푏)No solution (푐)Infinitely many solutions (푑)None of these

21. If A is a 3 × 3 non-singular matrix and B is a 3 × 3 non-zero matrix in which every two rowed minor vanishes, then rank of AB is: (푎)1 (푏)2 (푐)3 (푑)0

22. The rank of the matrix

3 4 5 6 74 5 6 7 85

156

167 8 9

17 18 19

is

(푎)0 (푏)1 (푐)2 (푑)4

23. The eigen values of the matrix A = 2 2 11 3 11 1 2

are

(푎)1, 2, 4 (푏)1, 1, 5 (푐)1, 3, 3 (푑)2, 2, 3 24. Total number of words formed by the letters of the word

MISSISSIPPI in which any two S are separated, is equal to: (푎)7350 (푏)6300 (푐)12600 (푑)None of these

25. How many numbers can be made with the digits 3, 4, 5, 6, 7, 8 lying between 3000 and 4000 which are divisible

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AMIT KATIYAR

by 5 while repetition of any digit is not allowed in any number: (푎)60 (푏)12 (푐)120 (푑)24

26. A team of four students is to be selected from a total of 12 students. Total number of ways in which team can be selected such that two particular students refuse to be together and other two particular students wish to be together only, is equal to: (푎)220 (푏)182 (푐)226 (푑)None of these

27. There are 15 points in a plane of which 4 points lie in one straight line and another 5 points lie in another straight line. No two lines area parallel and no three of the remaining 6 points are collinear. The number of triangles that can be formed by joining these points is given by: (푎)443 (푏)442 (푐)441 (푑)None of these

28. The maximum number of points into which 4 circles and 4 straight lines intersect is: (푎)26 (푏)50 (푐)56 (푑)72

29. A number is chosen among the 100 natural numbers. Probability that the number chosen is a multiple of 4 or 6, is : (푎)17/100 (푏)3/100(푐)6/25(푑)11/20

30. A bag contains 3 red, 4 white and 5 blue balls. All balls are different. Two balls are drawn at random. The probability that they are of different colours is (푎)47/66 (푏)10/33(푐)5/22(푑)None of these

31. A anti-aircraft fun can take a maximum of 4 shots at an enemy plane moving away from it. The probabilities of hitting the plane at first, second, third and fourth shot are 0.4, 0.3, 0.2 and 0.1 respectively. The probability that the gun hits the plane is: (푎)0.7600 (푏)0.4096 (푐)0.6976(푑)None of these

32. The probability that a certain beginner at golf gets good shot. If he uses the correct club is 1/3, and the probability of a good shot with an incorrect club is ¼. In his big there are 5 different clubs only one of which is correct for the shot in question. If he choose a club at random and takes a stroke, the probability that he gets a good shot is: (푎)1/3 (푏)1/12 (푐)4/15 (푑)7/12

33. A person goes to office by car, scooter, bus or train, probability of which being 1/7, 3/7, 2/7 and 1/7 respectively. Probability that he reaches office late, if he takes car, scooter, bus or train are 2/9, 1/9, 4/9 and 1/9 respectively. Given that he reached office in time, then the probability that he travelled by a car is given by: (푎)1/7 (푏)2/7 (푐)3/7 (푑)None of these

34. If sum of mean and variance of a binomial distribution is 4.8 for five trials, then distribution is:

(푎) + (푏) + (푐) + (푑)푁표푛푒 표푓 푡ℎ푒푠푒

35. A die is thrown 100 times. Getting an even number is considered a success. The variance of the number of successes, is: (푎)10 (푏)20 (푐)25 (푑)50

36. Line of best fit through X: -1 0 1 Y: 2 1 3 Is which of following (푎)Y = 3 + 0.8x (푏)Y = 2 + 0.5 x (푐)Y = 4 + 0.3x (푑)None of these

37. Suppose straight line of form y = 1 + bx is fitted to four points (0, 2), (1, 2), (2, 0) and (3, -1) by method of least squares, then value of b is (푎)− (푏)− (푐)− (푑)− 1

38. Which of following is correct missing term given X: 0 1 2 3 4 Y: 1 3 9 푦 81 (푎)28 (푏)31 (푐)46 (푑)21

39. The following table gives population of a city. Estimate the population is 1956. Year: 1941 1951 1961 1971 1981 1991 Pop: 12 15 20 27 39 52 in lacs (푎)15.44 lacs (푏)16.48 lacs (푐)17.44 lacs (푑)None of these

40. Using the successive bisection method the approximate value of a root of the equation 푥 − 푥 − 4 = 0 lying between 1 and 2 at the end of third iteration is; (푎)1.875 (푏)1.796 (푐)1.8125 (푑)None of these

41. The main components of second generation computers were: (푎)Levers (푏) vacuum tubes (푐)Transistors and diodes (푑)chip

42. The digital computer which simulates human intelligence belongs to: (푎)2nd generation (푏)3rd generation (푐)4th generation (푑)5th generation

43. Personal computers use a number of chips mounted on a main circuit board. What is the common name for such boards? (푎)Brother-board (푏)bather-board (푐)Mother-board (푑)main-board

44. The most common binary code in use today is (푎)BCD (푏)ASCII (푐)EBCDIC (푑)None of these

45. The CPU and memory are located on the: (푎)Expansion board (푏)motherboard (푐)Storage device (푑)output device

46. The term bit is short for: (푎)Megabyte (푏)binary language (푐)Binary digit (푑)binary number

47. One megabyte is equal to: (푎)102756 bytes (푏)1024000 bytes (푐)1048576 bytes (푑)none of these






AMIT KATIYAR

48. Which of the following is considered a direct- entry input device? (푎)Mouse (푏)Light Pen (푐)Optical Scanner (푑)All of the above

49. The memory which is ultraviolet light erasable and electrically programmable is: (푎)ROM (푏)PROM (푐)RAM (푑)EPROM

50. An integrated Circuit (IC) is: (푎)A complicated circuit (푏)Fabricated on a tiny silicon chip (푐)Much costlier than a single transistor (푑)An integrating device

51. DSL is and example of a …….. connection. (푎)Network (푏)wireless (푐)slow (푑)broadband

52. The metal of plastic case that holds all the physical parts of the computer is the: (푎)System unit (푏)CPU (푐) mainframe (푑) platform

53. Apple Macintoshes (Macs) and PCs use different ….. to process data and different operating systems. (푎)Languages (푏)mathods (푐)CPUs (푑)storage device

54. In the binary language each letter of the alphabet, each number and each special character is made up of a unique combination of; (푎)Eight bytes (푏)eight kilobytes (푐)Eight characters (푑)eight bits

55. Which of the following bus types are used by the Apple Macintosh computer? (푎)ISA (푏)Nu Bus (푐)EISA(푑)MCA

56. In BASIC, the command used to list a program; (푎)DIR (푏)LIST (푐)L (푑)CONTAINS

57. A while loop is more appropriate than a for loop when (푎)The body of the loop will be executed at last once (푏)The terminating condition occurs unexpectedly (푐)The program will be executed at least once (푑)The number of times the loop will be executed is known before the loop is executed

58. Heap: (푎)Is a region from where memory is allocated (푏)Lies between you program and the stack (푐)Is a finite area (푑)All of the above

59. The ASCII stands for (푎)American Standard code for information Interchange (푏)All purpose Scientific Code for Information Interchange (푐)American Security Code for Information Index (푑)None of these

60. EPROM stands for (푎)Enterprise Program Read Only Memory (푏)Electrically Program read only Memory (푐)Erasable Programmable Read Only Memory (푑)None of the above

61. A logic programming language specially suitable for artificial intelligence programmes is: (푎)ALGOL (푏)COBOL (푐)LISP (푑)PROLOG

62. The result of binary multiplication 10101×110 is (푎)111110 (푏)1111101 (푐)1111110 (푑)1111011

63. The result of binary division 110100/101 is: (푎)10110 (푏)101 R 10 (푐)101 (푑)110

64. Binary equivalent of hex (퐵퐶 9) is: (푎)1011 1100 1001 (푏)1001 1100 1011 (푐)1010 1100 1010 (푑)1101 1101 1010

65. The 9’s complement of 4637.82 is: (푎)53761.16(푏)46237.17 (푐)53762.17 (푑)52861.17

66. The equation, (5퐵퐶) = (푥) = (푦) , value of x and y are (푎)x = 011010111100 y = 3274 (푏)x = 011101101011 y = 3268 (푐)x = 011011100110 y = 3274 (푑)x = 010110111100 y = 3274

67. The expression for exclusion OR gate is: (푎)퐴̅ .퐵 + 퐴.퐵 (푏) 퐴̅.퐵 + 퐴퐵 (푐)(퐴.퐵)(퐴̅.퐵) (푑)(퐴̅.퐵) + 퐴. 퐵

68. Which of these are known as universal gates? (푎)AND, OR (푏)NAND, OR (푐)AND, NAND (푑)NAND, NOR

69. Find the value of z if z = (x + 푦).(x + y) and x = 1, y = 1? (푎)2 (푏)1 (푐)0 (푑)None of these

70. What is the value of 푧̅ if z = (푥̅.푦)+ (푥.푦) + (푥̅.푦) and 푥 = 1,푦 = 1? (푎)0 (푏)1 (푐)0 and 1 (푑)None of above

71. In a certain code, PRODUCTS is written as NPMBSARQ. How is COMPREHENSION written in that code? (푎)AMKNPCFCLOMLQ (푏)AMKNPCFCLQGML (푐)AMKNPCFCLQGNL (푑)AMKNPCFKOML

72. If a certain code ‘CORPORATIONS’ is written as ‘PROCTAROSNOI’, then how is JUDICIAL, written in that code? (푎)UJIDICLA (푏)IDUJICLA (푐)UJICLAIC (푑)IDUJLAIC

73. If HINDU is coded as 61257, and MAN is coded as 924, then INDIRA will be coded as (푎)454626 (푏)594921(푐)452787 (푑)884572

74. If ‘Men are very busy’ means ‘1234’, ‘Busy persons need encouragement’ means ‘4567’, ‘encouragement’ is very important’ means ‘3589’ and ‘Important persons are rare’ means ‘2680’, what is the code for ‘encouragement’ in that language? (푎)5 (푏)6 (푐)8 (푑)9

75. Pointing to a person in a photograph, Raman said, “She is the only daughter of the mother of my brother’s sister.” How is that person related to Raman? (푎)Uncle (푏)Father (푐)Mother (푑)None of the above

76. Pointing to a woman in photograph, Vijay said, “She is the daughter of the father of the sister of my brother”. How is that lady in photograph related to Vijay? (푎)Daughter (푏)wife (푐)Mother(푑)none of these

77. ‘P + Q’ means that P is the son of Q, ‘P – Q’ means that P is the wife of Q, ‘ P × Q’ means that P is the brother of Q, ‘P ÷ Q’ means that P is the mother of Q and ‘P = Q’






AMIT KATIYAR

means that P is the sister of Q. Then, what does X + Y – Z mean? (a)Z is the father of X (푏)Z is the son of X (푐)Z is the uncle of X (푑)Z is brother of X Direction (78-80): These questions are based on the information given below: Six girls are sitting in a circle. Sonia is sitting opposite of Radhika. Poonam is sitting right of Radhika but left of Deepti. Monika is sitting left of radhika. Kamini is sitting right of Sonia and left of Monika. Now Deepti and Kamini, Monika and Radhika mutually exchange their positions.

78. Who will be opposite to Sonia? (푎)Radhika (푏)Monika(푐)Kamini(푑)sonia

79. Who will be sitting left of Kamini? (푎)Poonam (푏)Deepti (푐)Radhika (푑)Sonia

80. Who will be sitting left of deepti? (푎)Sonia (푏)Monika (푐)Radhika (푑)Poonam

81. In a row of children facing North, shweta is fifteenth from the left and Jyoti is third to the left of Shweta. Ram who is seventh to the right of Jyoti is fifth from the right end of the row. What is shweta’s position from the fight end? (푎)12th (푏)10th (푐)8th (푑)9th

82. In a row of 40 boys facing the North, Amar is 6th to the right of Sandeep and Sandeep is 11th to the left of Vijay. If Amar is 28th from the right end of the row, what is the position of Vijay from the left end of the row? (푎)17th (푏)21st (푐)20th (푑)18th

83. Select from the given diagrams, the one that illustrates the relation ship among the given three classes: Judge, Thief, Criminal

84. Which is the most suitable Venn diagram among the following, which represents interrelationship among Antisocial elements, Pick pockets and Black mailers?

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

85. If Tall is equivalent to circle, Army men to triangle and strong to square, indicate which number will represent strong army men? (푎)3 (푏)4 (푐)5 (푑)6

1 2 4

7

3 6 5

86. Study the diagram below and identify the region representing youth who are employed but not educated. (푎)4 only (푏)1, 4, 7 (푐)4, 7 (푑)4, 5, 6 A B Youth 1 2 3 Educated 4 5 6 7 Employed C

87. Arrange the given words in alphabetical order and choose the one that comes first. (푎)Signature (푏)Sight (푐)shrine (푑)Shrill

88. Arrange the given words in alphabetical order and tick the one that comes in the middle. (푎)Transform (푏)Transport (푐)Transplant (푑)Transfer

89. If the first five words in the sentence, “Meeta’s mother meets me many times” are rearranged in the alphabetical order, which will be the middle word? (푎)Meeta (푏)mother (푐)meeta (푑)me

90. How many letters are there in the word ‘CREATIVE’ which have as many letters between them in the word as in the alphabet? (푎)1 (푏)2 (푐)3 (푑)4

91. The letters skipped in between the adjacent letters in the series are followed by equal space. Which of the following series observes this rule? (푎)HKNGSW(푏)RVZDFG (푐)RVZDHL (푑)SUXADF

92. Find missing character: 134, 245, 356, 467, …… (푎)579 (푏)578 (푐)568 (푑)478

93. Find wrong term: 89, 78, 86, 80, 85, 82, 83 (푎)83 (푏)82 (푐)86 (푑)78

94. Find missing character: AD, EH, IL, ?, QT (푎)LM (푏)MN (푐)MP (푑)OM

95. Find missing character: bc_b_c_b_ccb (푎)cbcd (푏)bbcd (푐)cbbc (푑)bcbc

96. Find missing character: abb_baa_a_bab_aba






AMIT KATIYAR

(푎)abba (푏)abab (푐)ccac (푑)aabb 97. Find missing character:

(푎)49 (푏)50 (푐)60 (푑)69 29 27 29 30 59 40 39 80 33 42 70 31 ? 80 10 45 43 43 44 39 20

Directions (98-99): In each question below are given two statements followed by two conclusions numbered I and II. You have to take the given two statements to be true even if they seem to be at variance from commonly known facts. Read the conclusions and then decide which of the given conclusions logically follows from the two given statements, disregarding commonly known facts.

Give answer (a) if only conclusion I follows: (b) if only conclusion II follows: (c) if either I or II follows: (d) if neither I nor II follows and (e) if both I and II follow.

98. Statements: All apples are oranges. Some oranges are papayas. Conclusion :I. Some apples are papayas. II. Some papayas are apples.

99. Statements: All lamps are hooks. No hook is coloured. Conclusions I. Some lamps are coloured. II. No lamp is coloured. Direction (100): The following questions consist of two words each that have a certain relationship to each other, followed by four lettered pairs of words. Select the lettered pair that has the same relationship as the original pair of words.

100. Crown: Royal (푎)Throne: Regal (푏)Wrap : Ermine (푐)Pen : Author (푑)Crucifix : Religion




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