INFOMATHS

THAPAR MOCK TEST-1

ARITHMETICS1. Two candidates contested an election. At the election

10% of the people on the voting list did not vote, and 60 votes recorded were rejected as illegal. The majority of the successful candidate was 38 and it was found that he had been supported by 47% of the whole number of the voter’s list. Legal votes recorded by successful candidates were (a) 2900 (b) 2814 (c) 2800 (d) 2914

2. The population of a city increases at the rate of 10%. If the present population is 40,000, population after 3 years will be (a) 53240 (b) 52000 (c) 53000 (d) 54150

3. A man sold his watch at a loss of 5%. Had he sold it for Rs. 56.25 more, he would have gained 10%. The C.P. of watch was (a) Rs. 475 (b) Rs. 375 (c) Rs. 575 (d) Rs. 275

4. A trademan purchases two types of sugar at the rate of Rs. 5 and Rs. 4 per kg. In what ratio should he mix them to earn a profit of 10%, if he sells the mixed sugar at Rs. 5 per kg? (a) 100 : 93 (b) 27:25 (c) 100 : 83 1/3 (d) 5:7 ½

5. After spending 8 ½ % of his income, a man saves Rs. 366, find his income (a) Rs. 410 (b) Rs. 415(c) Rs. 400 (d) Rs. 390

6. In 50 kg of sugar a man gets profit equal to S.P. of 15 kg of sugar, find % profit. (a) 20% (b) 25% (c) 24% (d) 30%

7. The original price of a T.V. set is Rs. 4000. If the price is discounted at 20% and then raised by 10%; then the new price of the television set is : (a) Rs. 3520 (b) Rs. 3590(c) Rs. 3600 (d) Rs. 3720

8. In a class 40% of the students have civics and 25% of the students have history and 10% have both civics and history as the optional subjects. Then the percentage of students who have neither civics nor history as optional is: (a) 40% (b) 45% (c) 50% (d) 55%

9. A factory employs skilled workers, unskilled workers and clerks in the ratios of 8:5:1 and wages of skilled person, unskilled person and clerks are in the ratios of 5:2:3. When 20 unskilled worker are employed then the total wages of all amount to Rs. 318. The daily wages of each category are: (a) Rs. 240, Rs. 60, Rs. 18 (b) Rs. 200, Rs. 80, Rs. 20(c) Rs. 150, Rs. 100, Rs. 50 (d) None of these

10. In an examination a candidate got 30% marks and failed by 10 marks and another candidate got 42% marks, which were 2 more than the pass marks. Maximum number of marks in the examination is: (a) 50 (b) 75 (c) 100 (d) 150

11. Atul comes to my house at equal interval of 6 days. Anil at interval of 8 days and Sunil at intervals of 10 days. They are all at my house today. How many

days must elapse before they all will be at my house on the same day again? (a) 60 Days (b) 90 Days (c) 120 Days (d) 130 Days

12. A beam 9 m long, 40 cm wide and 20 cm high is made up of iron. Which weigh’s 50 kg per cubic metre. The weight of the beam is : (a) 56 kg (b) 48 kg (c) 36 kg (d) 27 kg

13. The length of the longest rod that can be placed in a room 30 m long, 24 m broad and 18 m high, is: (a) 30 m (b) m (c) m (d) 6 m

14. The maximum length of a rod, that can be kept in a rectangular box of dimension 8 cm 6 cm 2 cm is: (a) cm (b) cm (c) cm (d) cm

15. A rectangular block 6 cm by 12 cm b6 15 cm is cut up into exact number of equal cubes. The least possible number of cubes will be: (a) 6 (b) 11 (c) 33 (d) 40

16. Three spherical metal balls of radii 6 cm, 8 cm and R cm are melted into a solid sphere of radius 12 cm, the value of R is: (a) 8 cm (b) 10 cm (c) 14 cm (d) 18 cm

17. A hollow garden roller 63 cm wide with a girth of 440 cm is made of iron 4 cm thick. The volume of the iron used is:(a) 57636 cm3 (b) 54982 cm3

(c) 56372 cm3 (d) 58752 cm3

18. The radius of a sphere is R and the radius of the based as well as the height of a cylinder is R. The ratio of the volume of the sphere to that of the cylinder is: (a) 4:3 (b) 3:4 (c) 2:3 (d) 3:3

19. Today Tuesday. After 62 days it will be: (a) Wednesday (b) Monday(c) Thursday (d) Sunday

20. What will be the day of the week on 1 January 2001? (a) Friday (b) Tuesday(c) Monday (d) Wednesday

REASONING Directions (Q. 1-2): Answer the following questions based on the letter – number sequence given below:E K M 3 P 5 7 R T V Z 9 D 1 F 1 X 4 6 G H J 2 8 W21. Which of the following letters/numbers will be

seventh to the left of the sixteenth letter/number from the left? (a) W (b) T (c) J(d) There is no such letter/number in the above sequence (e)

22. If the first twelve letters/numbers in the above, sequence are written in the reverse order, which of the following will be at eight position on left of the thirteenth letter/number from the right end?(a) 3 (b) T (c) R (d) P (e) N.O.T

23. Which of the following would come in place of the question mark (?) in the following letter – number series? PEC, R5F, T8I, VI2L, ?

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INFOMATHS

(a) Y17O (b) X17M (c) X17O (d) X16O24. How many such pairs of letters are there in the word

CONTEMPORARY which have as many letter between them in the word as in the alphabetic sequence (i.e. A to Z)? (a) 1 (b) 2 (c) 3(d) 4 (e) More then 4

25. A cube is painted green on all sides. It is then cut into 64 cubes of equal size. How many of these smaller cubes are painted on one side only? (a) 8 (b) 4 (c) 14 (d) 24

26. a-b a c c a b a – a a b –c c a – aa—a –aa (a) aabbab (b) ababab(c) aaabab (d) abbaba

27. Among five boys, Vasant is taller than Manohar, but not as tall as Raju, Jayant is taller Than Datta, but shorter than Manohar. Who is the tallest is their group? (a) Raju (b) Manohar (c) Vasant (d) Cannot be determined (e) None of these

28. In a certain code, BOY is written as $* and Hour” is written as @*£0. How is “RUBY” written in that code? (a) 0£$ (b) 0$£ (c) $£0(d) £$0 (e) None of these

29. In a certain language QUEUE is written as Q 22 and CHURCH is written as 1UR1. Which of the following could be the most appropriate code of BANANA in that language? (a) B5A5 (b) 5N5A (c) B55A(d) BA5A5A (e) B5A5A

Directions: (26-35) Each of the questions below consists of a question and two statements marked P and Q given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and Give answer (a) If the data in statement P alone are sufficient to answer the question, while the data in statement Q alone are not sufficient to answer the question.Give answer (b) if the data in statement Q alone are sufficient to answer the question, while the data in statement P alone are not sufficient to answer the question. Given answer (c) If the data either in statement or in statement Q alone are sufficient to answer the question.Give answer (d) if the data even in both the statement P and Q together are not sufficient to answer the question.Give answer (e) if the data in both statement P and Q together are needed to answer the question 30. Who is the heaviest among Amol, Prabhu, Narayan

and Navin? P. Amol and Prabhu are of the same weight. Q. Prabhu weights more the Narayan, but les than Navin.

31. How many daughter does “L have? P. R’s father has three daughter Q. ‘T’ is R’s sister and daughter of L.

32. Who is the brother of C? P. D is the daughter of M.Q. M is the father of C.

33. Rajiv’s rank is 17th in his class. What is his rank from the last? P. There are 70 students in his class

Q. Abhijit who ranks 20th in Rajiv’s class is 51st from the last

34. A library contains only English, Hindi and Telugu novels. How many Telugu novels are there in the library? P. Of the one thousand novels in the library, fifty per cent novels are in English and Hindi. Q. The number of Hindi novels is double the number of English novels.

35. “You must renew your driving licence within tel days from the data of expiry.” What is the exact date before which the licence must be renewed? P. The statement was uttered on 17th FebruaryQ. It was a leap year.

36. The area of a playground is 484 sq metres. What is the perimeter? P. It costs Rs. 912 to put a fence around the playgroundQ. The playground is a perfect square.

37. How many students in a class play hockey? P. Two-thirds of the students play hockey while all the remaining 21 students play chess. Q. All the 42 students in the class who are above 16, play hockey.

38. What is Shubha’s date of birth? P. On 21st September, 1994, Shubha completes 15 years, 3 months and 5 days.Q. Shubha’s brother who is exactly two years younger to her, was born on June 16, 1981.

39. In a certain code language, “pe nop can means We like roses”. Which word means “roses”?P. “nop te cap” means We are honest”. Q. “pe me say” means “they like flowers”

40. If “sky” is called “sea”, “sea” is called “water”, “water” is called “air”, “air” is called “cloud” and “cloud” is called “river”, then what do we drink when thirsty? (a) Sky (b) Air (c) Water (d) Sea

Directions (Q. 11-15): Given below is a passage followed by several possible inferences which can be drawn from the facts stated in the passage. You have to examine each inference separately in the context of the passage and decide upon its degree of truth or falsity. Mark answer (a) if the inference is ‘definitely true’, i.e. it properly follows from the statement of facts given. Mark answer (b) if the inference is ‘probably true’ though not ‘definitely true’ in the light of the facts given. Mark answer (C) if the ‘data are inadequate’, i.e. from the facts given you cannot say whether the inference is likely to be true or false. Mark answer (d) if the inference is ‘probably false’ though not definitely false’ in the light of the facts given. Mark answer (e) if the inference is ‘definitely false’, i.e. it cannot possibly be drawn from the facts given or it contradicts the given facts.

Coastal ecosystems are threatened by development-related activities along roughly half of the world’s coasts, according to a study conducted recently. The study indicates that about 34 per cent of the world’s coasts are at high potential risk of degradation and another 17 per cent are at moderate risk. Most of the coastal ecosystems potentially threatened by development are located within the northern temperate and northern equatorial zones. Europe with 86 per cent of its coasts at either high or

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INFOMATHS

moderate risk, and Asia with 69 per cent of its coasts in these categories are the regions whose coastal ecosystems are most threatened by degradations. 41. No further development work be carried out towards

the northern part of the world. 42. Coastal ecosystems of areas not affected by

development activities are more likely to be safe and protected.

43. The thrust development activities seems to be concentrated less across European coastal lines than the Asian costal lines.

44. Throughout the world seafood will become dearer in the near future.

45. Deep-sea marine life is in great danger now. GENERAL KNOWLEDGE 46. Match the following :

Sports person Sport A. Harsh Mankad 1. Chess B. Nitin Mongia 2. Sailing C. Suma Shirur 3 Shooting D. Surya Sekhar Ganguly 4. Tennis

A B C D A B C D (a) 1 2 3 4 (b) 1 3 2 4 (c) 4 2 3 1 (d) 4 3 2 1

47. Match the following : A. Basket ball 1. Lob B. Bridge 2. Revoke C. Golf 3. Pivot D. Tennis 4. Bunker

A B C D A B C D (a) 2 3 1 4 (b) 2 3 4 1 (c) 3 2 1 4 (d) 3 2 4 1

48. Match the following : Organization Location

A. National Cancer 1. Mumbai Research CentreB. Industrial Poison 2. Lucknow Science Research Centre C. NEERI 3. Nagpur D. Forest Research 4. Dehradun Institute

A B C D A B C D (a) 1 2 4 3 (b) 1 2 3 4 (c) 2 1 4 3 (d) 2 1 3 4

49. Match the following : Person Area in which

DistinguishedA. Rajendra Shah 1. Film industry B. Naresh Trehan 2. Computer Industry C. Azim Premji 3. Automobile industry D. Jagdish Khattar 4. Medical science

5. Literature A B C D A B C D

(a) 2 3 1 4 (b) 5 4 2 3 (c) 2 4 1 3 (d) 5 3 2 4

50. The song “Candle in the Wind” was sung by Elton John in honour of: (a) Elizabeth Taylor (b) Princess Diana (c) Ava Gardner (d) Audrey Hepbum

51. The title of ‘Sparrow’ is given to(a) Naponeo (b) Maj. Gen. Rajinde rsingh(c) Sardar Patel(d) T.T. krishnamachari

52. Consider the following countries of South Asia: 1. Bangladesh 2. India 3. Pakistan 4. Sri Lanka The descending order of literacy status of these countries is: (a) 4, 2, 1, 3 (b) 2, 4, 3, 1(c) 4, 2, 3, 1 (d) 2, 4, 1, 3

53. The Parliament of Japan is known as: (a) Assembly (b) Key(c) Senate (d) Diet

54. The government has decided to celebrate the Pravasi Bhartiya Divas every year on a day on which Mahatma Gandhi returned from South Africa. When is Pravasi Bhartiya Divas celebrated?(a) October 30 (b) June 17(c) January 9 (d) April 27

55. Who is called are ‘Father of Indian Renaissance’?(a) Rabindra Nath Tagore (b) Dayanand Saraswati (c) Raja Ram Mohan Rai (d) Vivekanand

ENGLISH Antonym 56. IGNORANCE

(a) erudition (b) experience (c) education (d) information

Fill in the blanks 57. They were talking ______ the UNO>

(a) on (b) about (c) with (d) in

58. _______ two weeks, he did not venture ______ the safety of his house. (a) with in for (b) for, beyond (c) for, over (d) over, for

Test of Errors 59. He considers me his sister. No error

A B C D E 60. We think him as a silly boy. No error

A B C D ECOMPUTERS 61. Generally, the speed of operation of a logic gate is

quoted in (a) seconds (b) milli seconds (c) nano seconds (d) micro seconds

62. Resistor-Ratio is used in linear ICs because (a) ratios increase input resistance (b) ratios increase amplifier gain(c) precise resister values are not possible with IC

processes(d) all of these

63. Which of the following is not functionally a complete set? (a) AND, OR (b) NOR(c) NAND (d) AND, OR, NOT

64. Which of the following logic expression is incorrect? (a) 1 0 = 1 (b) 1 1 0 = 1(c) 1 1 1 = 1 (d) 1 1 = 0

65. Which of the following Boolean algebra expression is incorrect? (a) A + = A + B(b) A + AB = b (c) (A + B) (A + B) = A + BC(d) (A + ) (A + B) = 1

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INFOMATHS

66. Given the following Karnaugh map, determine the corresponding switching function in its form

WX

YZ 00 01 11 10

00 1 1 1

0111 1 1

10 1 1(a) F(w, x, y, z) =x’z’ +(b) F(w, x, y, z) = (x’ +z’) (w +z’) (x + y + z)(c) F(w, x, y, z) = xy +w’ z +x’y’z’(d) F(w, x, y, z) = x’z’ + wz’ wz’ + xyz

67. The logic expression for the output of the circuit shown in the figure is (a) (b) (c) (d)

68. Flip-flop circuits can be used for (a) scaling (b) rectification (c) modulation (d) counting

69. printf (“%d”, prin f (“tim”));(a) results in a syntax error(b) outputs tim 3(c) outputs garbage (d) prints tim and terminate abruptly

70. Size of the array need not be specified, when (a) initialization is a part of definition (b) it is a declaration (c) it is a formal parameter(d) it is an actual argument (e) all of thee

71. The following program fragment int k = - 7 ;print f (“%d”, 0 < !k) ; (a) prints 0 (b) prints a non-zero value(c) is illegal(d) prints an unpredictable value

72. The following program fragment int i = 5;do {putchar (i + 100) ; print f (“%d”, i - - ) ; }while (i) ; results in the printing of (a) i5h4g3f2el (b) i4h3g2fle0(c) an error message (d) none of these

73. The following program main ( ) {printf (“tim”) ;main ( ) ; }(a) is illegal(b) keeps on printing tim (c) prints tim once(d) none of these

74. The following program main ( ) {static int a { } = {7, 8, 9} ;print f (“%d”, a {2} = 2 [a] + A [2]; (a) results in bus error (b) results I segmentation violation error (c) will not compile successfully (d) none of these

75. The register which holds the address of the location to or from which data are to be transferred is known as (a) index register (b) instruction register (c) memory address register (d)memory data register

76. Which of the following is used as storage locations both in the ALU and the control section of a computer ?(a) Accumulator (b) Register (c) Adder (d) Decoder

77. Which of the consists of an array of gates which can be used to patch an error in a ROM or alter the meaning of instruction? (a) RAM (b) EAPROM(c) PLA (d) PSW

78. Relative to the program translated by a compiler, the same program when interpreted runs (a) faster (b) slower (c) at the same speed (d) may be faster or slower

79. A system of letters, numbers symbols adopted by computer manufacturer as an abbreviated form of instruction sets is called (a) mesh (b) monitor (c) modern (d) mnemonic

80. Introducing parity bit error detection does not imply (a) odd number of error detection (b) automatic error detection (c) increase in the length of the code (d) increase in the hardware in the system

81. Assume that each character code consists of 8 bits. The number of characters that can be transmitted per second through an asynchronous serial line at 2400 baud ate, and with two stop bits is (a) 109 (b) 216(c) 218 (d) 219

82. In a microprogrammed control unit the micro instruction M1 and the control signals (a, b, c ……) they generate are: M1 : a, b, e, f M2 : b, c, d, e M3 : a, c, e, g Determine the total number of maximal compatibility classes (MCCs) for the control signals (a) 2 (b) 3(c) 4 (d) 5

73. In a parallel processing system with k micro-processors, each processor makes a request at most every 2 micro seconds and each request can ask for a maximum of 64 bits. These request are made over a high speed shared but with a maximum throughout of 100 megabits. Assume that with each request, 40 bits are required for transmission of the data-address and protocol. Approximately what is the maximum

4

x

y

z

ABC

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INFOMATHS

value of K for which the system can operate without any delays at peak load. (a) 1 (b) 2 (c) 3 (d) 4

84. Match the following: (1) An 8-bit wide 5 word sequential memory will have

(a) 8 Fixed ‘AND’ gates and 4 programmable

(2) A 256 4 EPROM has

(b) Eight 4 bit shift registers

(c) 4 words of 32-bits each (d) 8 address pins and 4 data pins output

85. If we use 3 bits in the instruction word to indicate if an index register is to be used and if necessary, which one is to be used, then the number of index registers to be used in the machine will be (a) 3 (b) 6 (c) 7 (d) 8

86. Formatting for a floppy disk refers to (a) arranging the data on the disk in contiguous

fashion (b) writing the directory (c) erasing the system area(d) writing identification information on al tracks

and sectors 87. Listed below are some operating system abstractions

(in the left column) and the hardware components (in the right column)? (A) Thread 1. Interrupt (B) Virtual address space 2. Memory(C) File system 3. CPU(D) Signal 4. Disk (a) (A) – 2, (B) – 4, (C) – 3, (D) – 1 (b) (A) – 1, (B) – 2, (C) – 3, (D) – 4(c) (A) – 3, (B) – 2, (C) – 4, (D) – 1(s) (A) – 4, (B) – 1, (C) – 2, (D) – 3

88. CPU has two modes-privileged and non-privileged. In order to change the mode from privileged to non-privileged (a) a hardware interrupt is needed (b) a software interrupt is needed (c) a privileged instruction (which does not genrate

an interrupt) is needed(d) a non-privileged instruction (which does not

generate an interrupt) is needed 89. The binary equivalent of the octal Numbers 13.54 is

(a) 1011.1011 (b) 1101.1110(c) 1001.1110 (d) all of these

90. The octal equivalent of 111 010 is (a) 81 (b) 72 (c) 71 (d) all of these

91. The decimal equivalent of binary number 0.0111 is (a) 4.375 (b) 0.4375(c) 0.5375 (d) –0.4375

92. De Morgan’s first theorem says that a NOR gate is equivalent to a bubbled (a) AND (b) XAND(c) XOR (d) NOR

93. The two’s complement is binary system is useful for expressing (a) positive’s numbers (b) negative numbers (c) both positive and negative numbers (d) none of these

94. ASCII code is an (a) alpha (b) numeric code(c) alphanumeric code (d) cyclic code

95. Icons are (a) types command (b) verbal commands (c) picture commands (d) imaginary commands

96. Adders (a) adds 2 bits(b) is called so because a full involves two half-

adders (c) needs two input and generates two output (d) all of these

97. Let A be a set having ‘n’ elements. The number of binary operations that can be defined on A is (a) (b)

(c) (d) 98. The values of x and y, if (x567)8 + (2yx5)8 = (71yx)8

is (a) 4, 3 (b) 3, 3 (c) 4, 4 (d) 4, 5

99. The SCII code’56, represents the character (a) V (b) V(c) a (d) carriage return

100. Programming in a language that actually controls the path of signals or data within (a) micro programming(b) systems programming(c) assembly language programming(d) machine language programming

A1 1

1 B CA

MATHS101. A person wishes to make up as many different

parties as he can out of his 20 friends such that each party consists of the same number of persons. The number of friends he should invite at a time is(a) 5 (b) 10 (c) 8 (d) none

102. The number of divisors of the form(4n + 2) where n 0 of the number 240 is (a) 3 (b) 4 (c) 8 (d) 10

103. The number of ordered triplets of positive integers which are solutions of the equation x + y + z = 100 is(a) 6005 (b) 4851 (c) 5081 (d) none

104. nCr + 2nCr + 1 + nCr + 2 is equal to (2 r n)(a) 2nCr + 2 (b) n + 1Cr + 1

(c) n + 2Cr + 2 (d) none of these105. For any two events A and B in a sample space

(a) P (B) 0, is

always true(b) does not hold(c) if A & B are independent ( d ) i f A a n d B a r e d i s j o i n t

106. The binomial distribution with mean 20 and S.D. 4 is

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INFOMATHS

(a) (b)

(c) (d) none of these

107. If A1, A2, …, An are nn independent events such that

i = 1, 2, ..., n.The probability that

none of the n events occurs is

(a) (b)

(c) (d) none of these

108. A man takes a step forward with probability 0.4 and backward with probability 0.6. The probability that at the end of eleven steps he is one step away from the starting point is(a) 11C6(0.24)5 (b) 11C6(0.4)6 (0.6)5

(c) 11C6(0.6)6 (0.4)5 (d) none of these109. The set (A B C) (A BC CC)C CC is

equal to(a) B CC (b) A C( c ) B C ( d ) n o n e

110. If and are roots of the equation x2 + x + 1 = 0. The equation whose roots are 19, 7 is

(a) x2 – x – 1 = 0 (b) x2 – x + 1 = 0(c) x2 + x – 1 = 0 (d) x2 + x + 1 = 0

111. If 1, 1, 2, ……, n-1 are the n, nth roots of unity, then the value of (1 + 1) (1 + 2) …. (1 + n – 1) is(a) n (b) – n(c) –n/2 + 1 (d) none of these

112. If 1 and is a nth root of unity, then value of 1 + 4 + 92 + 163 + …. + n2 n–1 is(a) –n (b) n2/(1–)(c) [n2 (–1)–2n]/(–1)2 (d) none of these

113. If the roots of the equation

are equal in magnitude but opposite in sign, then the value of k is(a) 0 (b) 1 (c) 2 (d) none of these

114. If x = 2 + 22/3 + 21/3, then the value of x3 – 6x2 + 6x is(a) 3 (b) 2 (c) 1 (d) none of these

115. If x = c is a root of order 2 of a polynomial ƒ(x), then x = c is also root of the polynomial(a) ƒ’ (x) (b) ƒ(x) (c) ƒ (x) (d) none of these

116. If ( 1) is a cube root of unity, then

equals

(a) 0 (b) 1 (c) i (d) 117. If 1, and 2

are cube roots of unity, then

is equal to …………

118. If cos + 2 cos + 3 cos = sin + 2sin + 3 sin = 0 and + + = n, then cos 3 + 8cos 3 + 27 sin 2 =

(a) 0 (b) 3 (c) 18 (d) –18119. Two finite sets have m and n elements respectively.

The total number of subsets of first set is 56 more than the total number of subsets of the second set. The values of m and n respectively are(a) 7, 6 (b) 6, 3 (c) 5, 1 (d) 8, 7

120 If (log3x) (logx2x) (log2xy) = logxx2, then y equals (a) 9 (b) 18 (c) 27 (d) 81

121. If ƒ(x) = , then ƒoƒoƒ(x)

(a) (b)

( c ) (d) none of these

122. If ƒ(a) = 2, ƒ(a) =1, g(a) = 1, g(a) = 2, then the

value of is

(a) 5 (b) (c) 5 (d) none of these

123. The value of is

(a) a1 + a2 + … + an (b)

(c) (d) a1 a2 …. an

124. If the function ƒ(x) =

= K, x = 0is continuous at x = 0, then the value of K is(a) 1 (b) 1 (c) 0 (d) e

125. The domain of definition of the function

ƒ(x) = is

(a) [0, 2] (b) [0, 2) (c) [1, 2] (d) N.O.T126. The value of n I for which the function

ƒ(x) = has 4 as its period

(a) 2 (b) 3 (c) 5 (d) 4

127. If a, b, c, d are positive, then

=(a) ed/b (b) ec/a

(c) e(c+d)/ a+b (d) e128. Let ƒ(2) = 4 and ƒ (2) = 4. Then

is given by

(a) 2 (b) 2 (c) 4 (d) 3129. If ƒn(x), gn (x), hn (x), n = 1, 2, 3 are polynomial in x

such that ƒn (a) = gn (a) = hn (a), n = 1, 2, 3 and

F(x) = . Then F(a) is

equal to(1) 0 (b) ƒ1(a) g2 (a) h3 (a)

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INFOMATHS

(c) 1 (d) none of these130. If a + b + c = 0, then the equation 3 ax2 + 2bx + c = 0

has(a) at least one real root in (0, 1)(b) one root in (1, 0) and the other in (1, 2)(c) both imaginary roots(d) two coincident roots

131. Let g(x) = ƒ(x) + ƒ(1 x) and ƒ(x) < 0, 0 x 1. Then

(a) g (x) increase on

(b) g (x) decrease on

(c) g (x) = constant on

(d) (d)g (x) increases on & decreases on

132. The curves ax2 + by2 = 1 and ax2 + by2 = 1 intersect orthogonally if

(a) (b)

(c) (d) none of these

133. If ƒ(a) = a2, (a) = b2 and ƒ(a) = 3 (a) then

is

(a) b2/a2 (b) b/a (c) 2b/a (d) none of these134. The greatest value of

ƒ(x) = cos (xe[x] + 7x2 3x), x [1, ) is (a) 1 (b) 1 (c) 0 (d) none of these

135. If + c,

then ƒ(x) equals(a) cos x (b) sin x (c) tan x (d) 1

136. is equal to

(a) loge + c (b) 2 loge + c(c) 2 log + c (d) 2 loge + c

137. dx is equal to

a. (x a) cos a + sin a log sin (x a) + cb. (x a) cos x + log sin (x a) + cc. sin (x a) + sin x + cd. cos (x a) + cos x + c

138. If = A cot4x + B cot2x + log | ƒ(x) | + C(a) a = 1/4 (b) A = 1/4(c) B = 1/2 (d) ƒ(x) = sin x

139. Solution of the equation

(x + 2y3) = 0 is (y > 0)

(a) x = y3 + Ay (b) y (1 xy) = Ax

( c) x (1 xy) = Ay (d) x (1 + xy) = Ay

140. where [ ] denotes the greatest integer

function is(a) (b) (c) (d)

141.

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

142. is equal to

(a) 0 (b) 1 (c) 5/2 (d)

143. The area of the figure bounded by the curves y = cos x

and y= sin x and the ordinates x = 0 and x = is

(a) (b)

(c) (d)

144. The sum of n terms of the series 12 – 22 + 32 – 42 + 52 – 62 + …. is

(a) (b)

(c) – n (n + 1) (d) none of these145. If A and G be the AM and GM respectively between

two numbers, then the numbers are(a) (b) A

(c) A (d) G 146. The least value of ‘a’ for which 51+x + 51–x a/2, 25x +

25–x are three consecutive terms of an AP is(a) 10 (b) 5 (c) 12 (d) none of these

147. f |x| < 1 and |y| < 1, the sum to infinity of the series x + y, (x2 + xy + y2), (x3 + x2y + xy2 + y3), …. is

(a) (b)

(c) (d)

148. If y = then the value of

y2 + 2y is(a) 2 (b) –2 (c) 0 (d) none of these

149. If [x] denotes the greatest integer less then or equal to x, then (a) is an even integer (b) is an odd integer(c) depends on n (d) none of these

150. If then the sum of the infinite series an

is

(a) e (b) e–1 (c) (d)

7

INFOMATHS

151. The sum of the series 2{7–1 + 3–1.7–3 + 5–1.7–5 + …] is

(a) loge (b) loge

(c) 2loge (d) 2 loge 152. If the pair of the straight lines x2 – 2pxy – y2

= 0 bisects the angles between the lines between the lines x2 – 2qxy – y2 = 0, then pq =

(a) 1 (b) –1 (c) 0 (d) none153. The orthocentre of the triangle formed by the line

bx + ay = ab and the co-ordinate axis is

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

154. Area of parallelogram formed by the lines y = mx, y = mx + 1, y = nx and y = nx + 1 equals

(a) (b)

(c) (d)

155. The length of the tangent from a point on the circle x2 + y2 + 2gx + 2ƒy + c1 = 0 to the circle x2 + y2 + 2gx + 2ƒy + c2 = 0 is(a) (b) c2 – c1

(c) 0 (d) N.O.T156. The value of for which the circles

x2 + y2 + x + 4y + 4 = 0 and x2 + y2 + x + 4y + 1 = 0 cut orthogonally is

(a) –6 (b) 6 (c) 3 (d) –3157. The circles x2 + y2 + 2ax + c = 0 and

x2 + y2 + 2by + c = 0 touch if

(a) (b)

(c) (d)

158. The equations of the tangent drawn from the origin to the circle x2 + y2 – 2rx – 2hy + h2 = 0, are

(a) x = 0 (b) y = 0(c) (h3 – r2) x – 2xhy = 0 (d) (h2 – r2) x + 2rhy = 0

159. The eccentricity of the conjugate hyperbola of the hyperbola x2 – 3y2 = 1 is

(a) 2 (b) (c) 4 (d)

160. If are unit vectors and is the angle

between them then is

(a) (b) sin (c) 2 sin (d) sin 2

161. If are non-coplanar unit vectors such that

, then the angle between &

is

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

162. is

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

163. are vectors reciprocal to the non-

coplanar vectors , then

(a) (b) 1 (c) 0 (d) 4

164. A constant force is applied at

the point (1, –1, 2). Then the vector moment of about the point (2, –1, 3) is

(a) (b)

(c) (d) 165. The unit vector perpendicular to vectors

forming a right handed system is

(a) (b)

(c) (d) 166. Let a, b, c be distinct non-negative numbers. If the

vectors lie in a plane, then c is(a) the A.M. of a and b (b) the G.M. of a and b(c) the H.M. of a and b (d) equal to zero

167. Volume of the parallelopiped whose coterminal edges are

is(a) 5 units (b) 6 units (c) 7 units (d) N.O.T>

168. If and and

are non-coplanar, then is equal to

(a) (b) (c) (d) none169. Given two vectors

and

then the value

of is

(a) (b) 7 (c) 3 (d)

170. f a1, a2, a3, ..., an is an AP with common difference d, then

is equal to

(a) (b)

(c) (d)

8

INFOMATHS

171. wo angles of a triangle are cot–12 and cot–13. Then the third angle is

(a) (b) (c) (d) 172. If sin x + cosec x = 2, then sinnx + cosecnx is equal to

(a) 2 (b) 2n (c) 2n – 1 (d) 2n – 2

173. If

then det A is independent of(a) a (b) x (c) n (d) none

174. If Pn = cosn + sinn then 2P6 – 3P4 + 1 = (a) 2 (b) 3 (c) 0 (d) 1

175. The set of values of x for which

is

(a) (b)

(c) (d)

176. The equation(cos p –1) x2 + (cos p) x + sin p = 0, where x is a variable, has real roots. Then the interval of p may be any of the following

(a) (0, 2) (b) (–, 0) (c) (d) (0, )177. The solution set of

(2cosx –1) (3 + 2cosx) = 0 in the interval 0 x 2is

(a) (b)

(c) (d) none of these

178. If 1 + sin + sin2 + .... to = 4 + 2 , 0 < < ,

, then =

(a) (b) (c) (d) 179. The locus of the point of intersection of lines x cos

+ y sin = a and x sin – y cos = b is ( is a variable)(a) 2(x2 + y2) = a2 + b2 (b) x2 – y2 = a2 – b2

(c) x2 + y2 = a2 + b2 (d) none of these180. The set of lines ax + by + c = 0, where 3a + 2b + 4 = 0

is concurrent at the point

(a) (b)

(c) (d) none of these

181. The image of the pair of lines represented by ax2 + 2hxy + by2 = 0 by the line mirror y = 0 is(a) ax2 – 2hxy – by2 = 0 (b) bx2 – 2hxy + ay2 = 0(c) bx2 + 2hxy + ay2 = 0 (d) ax2 – 2hxy + by2 = 0

182. The length of the tangent drawn from any point on the circle x2 + y2 + 2gx + 2ƒy + c = 0 to the circle x2 + y2 + 2gx + 2ƒy + c1 = 0 is(a) c1 – c (b) c – c1 (c) (d)

183. A and B two non zero square matrices such that AB = 0, then(a) both A and B are singular (b) either of them is singular (c) neither matrix is singular(d) none of these

184. If a, b, c are in A.P. then the value of

is

(a) 3 (b) –3 (c) 0 (d) none185. If y = sinmx, then the value of the determinant

where yn = is

(a) m9 (b) m2 (c) m3 (d) none

186. Set r = . Then

the value of is

(a) (b) . 2n + . 2n + . 4n

(c) 2 + 3 + 4 (d) none of these

187. If A = , then trace of matrix A

is(a) 17 (b) 25 (c) 3 (d) 12

188. is equal to(a) (b)

(c) (d) 0189. If a variable X takes values 0, 1, 2,....., n with

frequencies proportional to the binomial coefficients nC0, nC1, nC2, ...., nCn, then the var (X) is

(a) (b) (c) (d) none

190. The coefficient of correlation between X and Y is 0.6. Their covariance is 4.8, Var(X) = 9. Then y is(a) 8/3 (b) 3/8 (c) 8/9 (d) none

191. Karl Pearson's coefficient of correlation between two variables X and Y is defined by

(a)

(b)

9

INFOMATHS

(c)

(d) none of these192. The number 71993 when divided by 100 leaves

the remainder:(a) 01 (b) 07 (c) 43 (d) 49

193. The congruence 125. 133. 155 x 1 (mod 11) has the solutions.(a) x 5 (mod 11) (b) x 4 (mod 11) (c) x 3 (mod 11) (d) No solution

194.

(a) f (b) 2f (c) tan f (d) sin f 195.

i

s(a) x2 + y2 + z2 (b) (x2 + y2 + z2)–1

( C ) 0( C ) 0 ( D ) 1( D ) 1

196.

a. 4 x2y2 cos2 (x2y2)b. 4 x2y2 (x2 + y2)c. 4 x2y2 (x2 + y2) cos2 (x2 y2)d. None of these

197. If = 3n, find the value of n

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

198. Find the value of

(a) 4 (b) 6 (c) (d) (e) none

199. is

equal to(a) 1 (b) 2 (c) 3 (d) 4

200. The maximum value of the function z = 4x + 3y subject to the constraints 3x + 2y 160, 5x+2y200, x + 2y 80. x 0, y 0 is : (a) 320 (b) 300 (c) 250 (d) N.O.T

MOCK TEST – I 1 2 3 4 5 6 7 8 9 10D A B C C B A B A C11 12 13 14 15 16 17 18 19 20C C C C D B D A B C21 22 23 24 25 26 27 28 29 30B C C D D C A A C E31 32 33 34 35 36 37 38 39 40E D C A D B C C E B41 42 43 44 45 46 47 48 49 50E D B C C C D B B B51 52 53 54 55 56 57 58 59 60B C D C C A B B E B61 62 63 64 65 66 67 68 69 70C C A B B D A B B E71 72 73 74 75 76 77 78 79 80A A B D C B C B D B81 82 83 84 85 86 87 88 89 91C D B B C D C D B B91 92 93 94 95 96 97 98 99 100B A B C C D C D B C

MATHS THAPAR MOCK TEST- I 101 102 103 104 105 106 107 108 109 110B B B C A C B BC A D

111 112 113 114 115 116 117 118 119 120D C A B A A 3 C B A

121 122 123 124 125 126 127 128 129 130A C D A D A A C A A

131 132 133 134 135 136 137 138 139 140D A D B A C A BCD A B

141 142 143 144 145 146 147 148 149 150B D A D B C A A A C

151 152 153 154 155 156 157 158 159 160A B A D D A B C C A

161 162 163 164 165 166 167 168 169 170A C B D B B D C D B

171 172 173 174 175 176 177 178 179 180B A C C A D B D C A

181 182 183 184 185 186 187 188 189 190D D A C D D A C A

191 192 193 194 195 196 197 198 199 200B B C C D D D A B D

10