NIT New Test Series NT-01 PDF

NIT NEW TEST SERIES NT - 01 Section-1 (Analytical Ability & Logical Reasoning) I. C@B Direction(1 to 4) : Read the following information to answer II. B ©A...

NIT NEW TEST SERIES NT - 01 Section-1 (Analytical Ability & Logical Reasoning) I. C@B Direction(1 to 4) : Read the following information to answer II. B ©A (a) (b) (c) (d) the given question: 7. Statements On a shelf are placed six volumes side by side labelled A, B, C, D, E and F.Three volumes B,C and E have green A  D, C @ B, D @ B covers while the other volumes have yellow covers.A,D Conclusions and B are new volumes while the rest are old volumes. A, C and B are law reports, while the rest are Gazet- I. D$C teers. II. B ©A 1. Which volume is new,yellow-covered and a Gazetteers? (a) (b) (c) (d) (a) B (b) D (c) C (d) F 8. Statements 2. Which is green-covered,old and a law report volume? A @ B, B © C, D @ C (a) A (b) B (c) C (d) D Conclusions 3. Which is the yellow-covered new law report volume? I. A$C (a) A (b) C (c) E (d) D II. B © D 4. Which of the following is the old volume of a Gazetteer? (a) (b) (c) (d) (a) C (b) D (c) E (d) B 9. Statements Directions (5-9) : In the following questions, the symbols A  C, B $ A, D ¥ C $, © , @ , ¥ and  are used as illustrated below : Conclusions ‘P $ Q’ means ‘P is neither greater than nor smaller I. B © D than Q’ II. B$D (a) (b) (c) (d) ‘P © Q’ means ‘P is neither smaller than nor equal to Q’ 10. A is 40m South-west of B,C is 40m South-East of B ‘P @ Q’ means ‘P is neither greater than nor equal to then, C is in which direction of A Q’ (a) South (b) West ‘T ¥ Q’ means ‘P is not greater than Q’. (c) East (d) North-East ‘P  Q’ means ‘P is not smaller than Q’. Directions (11-12) : Following questions have 2 statements Now in each of the following questions assuming the followed by 2 conclusions. Disregarding any commonly given statements to be true, find which of the two conclusions I and II given below them is/are definitely known fact, taking only statements as complete true, true ? mark your answer as : Give answer (a) if only Conclusion I is true. (a) If conclusion I follows Give answer (b) if only Colclusion II is true. (b) If conclusion II follows Give answer (c) if either Conclusion I or II is true. (c) If neither I nor II follows/either I or II follows Give answer (d) if neither Conclusion I nor II is true. (d) If both follow 5. Statements 11. Statements : A © B, B  C, Q $ A I. All humans are bad. Conclusions II. All the terrorists are humans. Conclusions : I. Q C I. All terroirsts are bad. II. A$C II. No human can be terrorist. (a) (b) (c) (d) 12. Statements : 6. Statements I. Some oranges are papayas. A ¥ B, P ¥ B, C ¥ P II. All appels are oranges. Conclusions www.impetusgurukul.com 18, Zone-II, M.P. Nagar, Bhopal  : 0755-4295319 NIT NEW TEST SERIES NT-01|1  Conclusions : (i) P, Q, R, S, T and U are six students procuring their I. Some apples are papayas. Master’s degree in six different subjects — English, II. Some papayas are apples. History, Philosophy. Physics, Statistics and Math- ematics. 13. If ENGLAND is written as 1234526 and FRANCE is writ- (ii) Two of them stay in hostel, two stay as paying guest ten as 785291, how is GREECE coded ? (PG) and the remaining two stay at their home. (a) 381171 (b) 381191 (c) 832252 (d) 835545 (iii) R does not stay as PG and studies Philosophy. Directions (14-16) : A is R’s daughter S is R’s sister. S’s (iv) The students studying Statistics and History do not daughter is called C and son is called D. L is C’s ma stay as PG. ter nal Aunt. (v) T studies Mathematics and S studies Physics. (vi) U and S stay in hostel. T stays as PG and Q stays at 14. A is L’s home. (a) Aunt (b) Nephew (c) Uncle (d) None 25. Who studies English ? 15. C is R’s (a) R (b) S (c) T (d) None (a) Nephew (b) Niece (c) Uncle (d) None 26. Which of the following combinations of subject and place 16. D is L’s of stay is not correct ? (a) Niece (b) Aunt (c) Nephew (d) None (a) English — Hostel (b) Mathematics — PG (c) Philosophy — Home (d) Physics — Hostel 17. Vimal was born on 9th June 1975. The day on his birth- day was : 27. Which of the following pairs of students stay one each (a) Monday (b) Tuesday (c) Wednesday (d) Friday at hostel and at home ? (a) QR (b) SR 18. In the following number series, a wrong number is given (c) US (d) Data inadequate find out that number 3, 10, 19, 30, 42, 58, 75 28. Which subject does Q study ? (a) 10 (b) 42 (c) 58 (d) 19 (a) History (b) Statistics (c) History or Statistics (d) Data inadequate 19. The average of four consecutive even numbers is 7. Which of the following is the first number ? 29. Which of the following pairs of students stay at home ? (a) 2 (b) 6 (c) 4 (d) None (a) PQ (b) QR (c) RS (d) ST 20. The difference between the sum of two numbers and Directions (Q.30 and 31) : their product is 20. What is the difference between these A group of seven singers, facing the audience, are stand- two numbers ? ing in a line on the stage as follows : (a) 10 (b) 15 (c) 30 (d) data inadequate (i) D is to the right of C 21. A train running at the speed of 180 km/hr crosses a pole (ii) F is near in one minute. What is the length of the train ? (iii) B is to the left of F (a) 50 m (b) 500 m (c) 3 m (d) None (iv) E is to the left of A 22. Four years ago, the father’s age was three times the (v) C and B have one person between them age of his son. The total of the ages of the father and the son after four years will be 64 years. What is father’s (vi) A and D have one singer between them age at present ? 30. Who is on the extreme right ? (a) 44 years (b) 36 years (c) 32 years (d) None (a) D (b) F (c) G (d) E 23. At 2 : 15 o’clock, the hour and minute hands of a clock 31. If we start counting from the left, on which number is C? form an angle at : (a) Ist (b) 2nd (c) 3rd (d) 5th 1 1 (a) 30° (b) 5° (c) 22 ° (d) 7 ° 32. In a certain code language, ‘851’ means ‘good sweet 2 2 fruit’; ‘783’ means ‘good red rose’ and ‘341’ means 24. A total of 28 handshakes was exchanged at the conclu- ‘rose and fruit’. Which of the following digits stands for sion of a party. Assuming that each participant was ‘sweet’ in that language ? equally polite toward all the others the number of people (a) 8 (b) 5 (c) 1 (d) 3 present was : (a) 14 (b) 28 (c) 56 (d) 8 33. Pointing towards a person in a photograph, Anjali said, “He is the only son of the father of my sister’s brother”. Direction for Questions 25 to 29 How is that person related to Anjali ? Read the following information carefully and answer (a) Mother (b) Father the questions that follow : (c) Maternal uncle (d) None of these 2| NIT NEW TEST SERIES NT-01 18, Zone-II, M.P. Nagar, Bhopal  : 0755-4295319 www.impetusgurukul.com  Section-2 (Computer) Directions (Q.34 to 38) : Read the following information to 41. UPS stands for answer the given question : (a) Undefined phlying suspect (i) Five friends P, Q, R, S and T travelled to five different (b) Uniform Power Supply cities of Chennai, Calcutta, Delhi, Bangalore and (c) Uninterrupted Power System Hyderabad by the different modes of transport of Bus, (d) Universal Power Source Train, Aeroplane, Car and Boat from Mumbai. 42. The digital computer was developed primarily in (ii) The person who travelled to Delhi did not travel by (a) USSR (b) Japan boat. (c) USA (d) UK (iii) R went to Bangalore by car and Q went to calcutta 43. A hexadecimal number system has a base of by aeroplane. (a) 2 (b) 4 (c) 8 (d) 16 (iv) S travelled by boat where as T travelled by train. 44. If input values in ‘AND’ gate are 0 and 1 then output is : (v) Mumbai is not connected by bus to Delhi and (a) 0 (b) 1 (c) 0 or 1 (d) can’t say Chennai. 45. The fastest memory among the following is 34. Which of the following combination of person and mode (a) main memory (b) cache memory is not correct? (c) auxiliary memory (d) None of these (a) P-Bus (b) Q-Aeroplane (c) R-Car (d) T-Aeroplane 46. RAM is (a) Random access (b) Volatile 35. Which of the following combinations is true for S ? (c) Sequential access (d) a and b both (a) Delhi - Bus (b) Chennai - Bus (c) Chennai - Boat (d) Chennai - Train 47. Conversion of an octal number 74328 to its binary number equivalent is : 36. Which of the following combinations of place and mode is not correct ? (a) 1111000110 1112 (b) 1111000110 10 2 (a) Delhi - Bus (b) Chennai - Aeroplane (c) 1100110101112 (d) None of these (c) Bangalore - Car (d) Chennai - Boat 37. The person travelling to Delhi went by which of the fol- 48. Conversion of a hexadecimal number 3116 to its bi- lowing modes ? nary number equivalent is : (a) Bus (b) Train (c) Aeroplane (d) Car (a) 101010 2 (b) 1101012 38. Who among the following travelled to Delhi ? (c) 1100012 (d) 1001012 (a) R (b) S (c) T (d) none 49. Conversion of a binary number 11000112 to hexadeci- Directions (Q.39 to 40) : mal number is : Find out that number which will come next in the series: (a) 6316 (b) 5716 (c) 4716 (d) 4016 39. 2, 5, 9, 10, 13, 17, 18, 21, 25, 26, ? (a) 27 (b) 28 (c) 29 (d) 30 50. Conversion of a hexadecimal number 93FA16 to its 40. 3, 2, 6, 8, 18, 40, 72, 240 ? binary number equivalent is : (a) 360 (b) 320 (c) 440 (d) 432 (a) 1001001111 111010 2 (b) 1001001111 11101112 (c) 1100111111 100112 (d) 111110 0001112. www.impetusgurukul.com 18, Zone-II, M.P. Nagar, Bhopal  : 0755-4295319 NIT NEW TEST SERIES NT-01|3  Section - 3 (Mathematics) 18 18 (a) (3j + 4k) (b) (3 j  4k ) 51. Period of 2 sin 3  4 cos 3 is 10 3 25 (a) 2 / 3 (b)  / 4 (c)  / 2 (d)  / 3 18 (c) (3 j  4k ) (d) 3 j  4k 3 52. In a ABC, If c  a  b  ac, then B = 2 2 2 61. In a triangle PQR, 2 pq sin (1/2(P + Q - R) = (a)  / 6 (b)  / 4 (c)  / 3 (d) None 53. If a system of linear equations (a) p2  q2  r 2 (b) r 2  p2  q2 x  ay  a 2 z  0, x  by  b 2 z  0, (c) q2  r 2  p2 (d) r 2  p2  q2 [ x] x  cy  c 2 z has a non zero solution, then 62. The value of  {t} dt is (where [ ] - greatest integer, { } 0 (a) a + b + c = 0 (b) either a = b or b = c or a = c (c) a, b, c are in A.P. (d) none of these - fractional part) cos 6x  6 cos 4x  15 cos 2x  10 (a) [x] (b) 2[x] (c) 1/(2[x]) (d) [x]/2 54. The expression cos 5x  5 cos 3x  10 cos x is  /3  sec2 x etan x dx  F (k )  F (1) equal to d 63. Let F ( x )  e x. If (a) cos 2x (b) 2 cos x (c) cos2 x (d) 1 + cos x dx  /4 55. The circumcenter of the triangle formed by the lines then value of k is : xy  2 x  2 y  2  0 and x  y  2  0 is (a) (0, 0) (b) ( – 2, – 2) (c) (–1, – 1) (d) none (a) 1/ 3 (b) 3 (c)  3 (d) 1/ 3 log(2  x 2 )  log(2  x 2 ) 1 2 56. lim  k , the value of k is A x 0 x2 64. Let  , then An  0 1 (a) -1 (b) 2 (c) 1 (d) 0 1 2n 2 n 1 2n  1 n (c)   57. If the distance between the foci of an ellipse be equal to (a)   (b)   (d) 0 2 its minor axis, then its eccentricity is 0 1  0 1 0 1    (a) 1/2 (b) 1/ 2 (c) 1/3 (d) 1 / 3 x 2 x3 xn dy 58. The sum of the series 65. If y  1  x   ....  , then  2 ! 3! n! dx 3 5 7 2 2  2 2  2 2 ...   is equal to : 1.2 2.3 3.4 xn xn xn (a) 1 (b) 0 (c) -1 (d) 2 (a) y (b) y (c) y (d) y 1 n! n! n!  sin(a  1) x  sin x 66. The vector directed along the bisectors of the angle  for x0 c  x    f ( x)   c for x0 between the vectors a  7 i  4 j 4 k and 59.  ( x  bx 2 )1/ 2  x1/ 2  for x0  bx 3 / 2    c 3 6 b  2 i  j  2 k , where is given by is continuous at x = 0 then a =       (a) 3/2 (b) -3/2 (c) 1/4 (d) -1/4 (a) i  7 j 2 k (b) i  7 j 2 k       60. If a = 4 i + 6 j and b = 3j + 4k, then the components of a (c) i  7 j 2 k (d) i  7 j 2 k along b is 4| NIT NEW TEST SERIES NT-01 18, Zone-II, M.P. Nagar, Bhopal  : 0755-4295319 www.impetusgurukul.com 67. The area of a parallelogram whose diagonals coincide  x 1   x 1  with the following pair of vectors is 5 3. The vectors (a) ex 2   C (b) ex 2   C  x  1  x  1 are       3 i  2 j k , 3 i  j 4 k  x 2  1  x  1 e  2  C (a) ex  C x (c) (d)  x  1  x  1 3 1      (b) i  j k , 2 i  6 j 8 k 2 2   /2 cos x       74. dx  (c) 3 i  j 2 k , i  3 j 4 k 0 1  cos x  sin x (d) none of these π 1 π (a)  log 2 (b)  log 2 68. The area of the smaller region bounded by the curves 4 2 4 x2  y2  5 and y2  4x is : π 1 (c)  log 2 (d) none of these  1  1 4 2 (a)  (b)  4 6 4 6 1 1 I1   xe  x 3 x dx, I 2   e  x 3 x 2 2 dx, 1 5 2  1 5 2  75. If then (c) 2  sin 1  (d) 2  sin 1  0 0 3 2 5 3 2 5 (a) 3I1  2l2 (b) 2 I1  3l2 69. Line y = 2x + 2 cuts the circle x  y 1 2 2 in two dis- (c) 1  e 4 (d) 3e 4  2 tinct points. Equation of circle with these points as end of its diameter is : 76. If y = 2x + 5 and 4x + 5y + 1 = 0 are perpendicular then axes are inclined at an angle : (a) 5x  5 y  8x  4 y  3  0 2 2 (a) π/4 (b) π/3 (c) π/6 (d) tan -1 (5 / 2) (b) 5x  5 y  8x  4 y  3  0 2 2 100  5x 2  5 y 2  8x  4 y  3  0  (c) 77. If I  (1  cos 2x ) dx, then the value of I is 0 (d) 5x  5 y  8x  4 y  3  0 2 2 (a) 100 2 (b) 200 2 (c) 50 2 (d) None 70. The number of real solutions of the equation x 2  5 | x | 6  0 x4 x is : sin t dt, then F (x) equals 78. If F (x) = 2 (a) 1 (b) 2 (c) 0 (d) none 71. If x is a positive real number then the minimum value of (a) sin x 2  sin x (b) 4x3 sin x 2  2 x sin x (c) x 4 sin x 2  x sin x (d) None of these 1 x  3 is : x 79. The set of values of λ for which the real circles (a)  2 3 (b) 2 3 x2  y2  λ2 and x2  y 2  2 2x  2 2 y  λ  0 have exactly one common tangent, is : (c) 3 (d) 0 (a) {0, 5} (b) {-3, 5} (c) {-3, 0, 5} (d) {-3} 80. A bag A contains 2 white and 3 red balls and bag B (1  cos 2 x)(2  cos 2 x) contains 4 white and 5 red balls. One ball is drawn at 72. lim random from a randomly chosen bag and is found to be x0 x tan 3 x red. The probability that it was drawn from bag B was (a) -1/2 (b) 2 (c) 0 (d) -1 5 5 5 25 (a) (b) (c) (d) 14 16 18 52 x2  x  2 x 73. The value of integral  ( x 2  1) 2 e dx is : www.impetusgurukul.com 18, Zone-II, M.P. Nagar, Bhopal  : 0755-4295319 NIT NEW TEST SERIES NT-01|5 81. Urn A contains 6 red and 4 black balls and Urn B con- 89. The number of divisors of 9600 including 1 and 9600 tains 4 red and 6 black balls. One ball is drawn at ran- are dom from Urn A and placed in Urn B. Then one ball is (a) 60 (b) 58 (c) 48 (d) 46 drawn at random from Urn B and placed in Urn A. If one ball is now drawn at random from Urn A, the probability sin x  cos x sin x that it is found to be red, is 90. If π 4 x π 2 then  1  sin 2 x.e. cos x dx  32 21 19 (a) (b) (c) (d) None 55 55 55 (a) e sin x  C (b) e sin x cos x  C 82. If the equations ax2  bx c  0 and 5x 2  12x  13  0 (c)  e sin x  C (d) e cos x  C have a common root, where a, b and c are the sides of a triangle ABC, then : 91. If x  2  22 / 3  21 / 3, then x3  6x2  6x  (a) ABC is acute angled (a) 3 (b) 2 (c) 1 (d) None of these (b) ABC is right angled x 1 ABC is (c) isosceles 92. If  f (t )dt  x   tf (t )dt , then f (1) (d) ABC is right angled isosceles 0 x 83. The probability that a marksman will hit a target is given (a) 1/2 (b) 0 (c) 1 (d) -1/2 as 1/5. Then his probability of at least one hit in 10 shots, is 93. The solution of |cos x| = cosx - 2sinx is 4 10 1 1 π (a) 1    (b) (c) 1 (d) None (a) x  nπ (b) x  nπ  5 510 510 4 π π  4 2 (c) x  nπ  (-1) n (d) x  (2n  1) π  , n 1 84. The value of tan cos 1  tan 1  is : 4 4  5 3 (a) 6/17 (b) 7/16 (c) 17/6 (d) None 94. If      then 85. The number of solutions cos 2   cos 2   cos 2   2 cos  cos  cos   (a) 1/2 (b) + 1 (c) – 1/2 (d) 0 tan 1 x ( x  1)  cos 1 x 2  x  1  0 of : 95. The number of arrangements that can be made taking (a) 0 (b) one (c) two (d) infinite 4 letters, at a time, out of the letter of the word ‘PASSPORT’ is : 86. The condition on a, b, c for which the system (a) 606 (b) 4464 (c) 4356 (d) 4644 x  2 y  3z  a 96. The minimum value of the intercept cut by a tangent to 3x  y  2 z  b x2 y2 x  5 y  8z  c the ellipse  1 between the coordinate axes a 2 b2 has a solution, is : is (a) 2a - b + c = 0 (b) b = c (c) 2a + c = 0 (d) b = 2a (a) a + b (b) a2  b2 87. If 2 cosx + sinx = 1, then value of 7 cosx + 6 sinx is equal to : (c) a 2  b2 (d) does not exist (a) 2 or 6 (b) 1 or 3 (c) 2 or 3 (d) none 97. The element of second row and third column in the 88. The system of equations 4x – 5y – 2z = 2 5x – 4y + 2z = 3 is  1 2 1 2x + 2y + 8z = 1   (a) Consistent (Unique Solution) inverse of  2 1 0 is : (b) Inconsistent   1 0 1  (c) Consistent (Infinite Solution) (d) None of these (a) -2 (b) -1 (c) 1 (d) 2 6| NIT NEW TEST SERIES NT-01 18, Zone-II, M.P. Nagar, Bhopal  : 0755-4295319 www.impetusgurukul.com 98. Sum of the series 107. AGONY (a) Pleasure (b) Bliss  1 1 1 1  (c) Ecstasy (d) Fear limn     ....   n  1 n  2 n  3 2 n  Direction for Q. 108 and Q. 109 : Choose the correct word which best expresses the meaning of the given word. is equal to 108. MAJESTIC (a) log 2 (b) loge 3 (a) Attractive (b) extra-ordinary (c) Grand (d) Interesting (c) loge 6 (d) None of these 109. NEMESIS (a) Victory (b) Adventure dy (c) Reward (d) Punishment 99. If 1 x 4 + 1  y 4 = k ( x 2  y 2 ) then dx is : Direction for Q. 110 : In the following sentences a blank has been given which can be filled correctly by one the four x 1 y 4 x 1 y 8 alternatives given under it. That is your answer. (a) (b) y 1 x 4 y 1 x8 110. My boss........ my request to increase my allowances. (a) refused (b) denied y 1 x8 y 1 x 4 (c) resisted (d) withheld (c) (d) x 1 y 8 x 1 y 4 Direction Question 111 and 112 :In each of the following ques- 100. If f : [1, 2] R is differentiable and f ( 2)  4, f  ( 2)  1 tion, a sentence is given with a black followed by four alternatives. Choose the word or pharse that most cor- lim xf ( 2)  2 f  ( x ) rectly complete the sentences. then x 2 is equal to x 2 111. Chuck came to Britain from the U.S.A. nearly three years (a) 1 (b) 2 (c) – 2 (d) none ago. Next Monday it will be exactly three years so on Monday he........... in Britain for exactly three years. SECTION - 4 ENGLISH (a) will be (b) will have Been Directions for Q.101 to Q.103 : There are four sentences in (c) will had been (d) none of these each of the following questions. One of the sentences 112. Phone me after 8 ‘O’ clock.............. dinner by then is correct, and the rest are incorrect. You are to select (a) we will finish (b) we will finished the correct sentence in each question : 101. (a) She is either right nor wrong. (c) we had finished (d) None of these (b) She is nor right or wrong. Direction Question 113 and 114 : In each of the following (c) She is neither right or wrong. questions, a related pair of words or phase is followed (d) She is niether right nor wrong. by four pairs of words or pharse, selected the pair that 102. (a) He went to Nepal five years ago. best expresses a relationship similar to that expressed (b) He went to Nepal five years back. in the original pair. (c) He went to Nepal five years before. 113. Coin : Mint (d) He went to Nepal five years past. (a) Grain : Field (b) Hay : Stable 103. (a) Before leaving home, it began to rain. (c) Wine : Brewary (d) Book : Publisher (b) As since I was leaving home, it began to rain. (c) As I was leaving home, it began to rain. 114. Traitor : Disloyalty (d) When leaving home, it began to rain. (a) Executioner : Reliability (b) Rebel : Defiance Directions for Q.104 & Q.105 : A part of the each of the following (c) Manager : Administration (d) Hope : Pessimism sentences is italicized from the answer choices which follow Direction for Q. 115 to Q. 120 : Fill in the blanks : pick up one which can substitute the italicized part correct. 115. The people................... you socialise are called friends. 104. Despite of his age his skill at tennis is good. (a) with whom (b) who (a) Despite his age his skill at tennis (c) with who (d) whom (b) Despite his age his skill of tennis 116. Every one of them............... to the music every day. (c) Despite his age his skill in tennis (a) Listen (b) Listening (d) No change (c) Listens (d) None of these 105. Take his statements with a grain of salt. 117. I didn’t work hard when I was................ school. (a) happily (b) with reservations (a) in (b) on (c) at (d) by (c) in proper spirit (d) exaggerated 118. Where are you......................? Directions for Q.106 & Q.107 : For each of the following words (a) from (b) by (c) of (d) to in CAPITAL letters pick up correct antonym from the 119. Which of these is an adjective in “It is......................” answer choices : (a) Hard (b) Hardly 106. LAUD (c) Hardship (d) Harden (a) seize (b) praise 120. I have been working here.....................six months. (c) denounce (d) patronise (a) since (b) by (c) for (d) in www.impetusgurukul.com 18, Zone-II, M.P. Nagar, Bhopal  : 0755-4295319 NIT NEW TEST SERIES NT-01|7