For B.Tech. Topic No. of Ques. Physics 20 Chemistry 10 Maths 40 (Algebra, Coordinate Geometry, Probability, Trigonometry, Calculus, Differential Equations, Vector, Statistics, Dynamics and Statistics) Timing 2:00 Hr. English 15 (Antonym, Synonyms, Spellings, Common Errors, One Word Substitutions, Sentence Completion, Preposition and Articles) TOTAL 90 About Online Test • This is a multiple choice test. • The total duration of the test is 120 minutes (i.e. Two Hours). • Total marks for the test will be 360 marks. Each correct answer will be awarded 4 marks. • There is negative marking for wrong choices selected. For each wrong answer 1 mark will be deducted. • Numbered list of all questions appears at the right side of the screen. • Keep a close watch on 'Time Left' while appearing for the test. • The timer of the test starts only once you click the 'Start' button. • Once you click 'Start' button, a question and the possible answer choices will appear. 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When he pulls his ¨ arms suddenly inside then ¨ (a) his angular velocity decreases ¨ ¨ (b) his moment of inertia decreases ¨ ¨ (c) his angular velocity remains constant ¨ (d) his angular momentum increases ¨ On decreasing the temperature of a liquid its rate of evaporation Q.10. A p-type crystal is ¨ (a) increases (a) positive ¨ ¨ (b) decreases (b) negative ¨ (c) first increases and then decreases ¨ (c) neutral ¨ ¨ (d) remains unaffected (d) may be positive or negative ¨ Bernoulli’s theorem is based upon Q.11. The resistance of a wire is R. If the length ¨ (a) conservation of energy of the wire is doubled, then its resistance ¨ (b) conservation of charge will be ¨ (c) conservation of momentum (a) 2R ¨ ¨ (d) none of these (b) 4R ¨ (c) 8R ¨ In an isochoric process (d) 16R ¨ ¨ (a) temperature remains constant ¨ (b) pressure remains constant Q.12. Diamagnetism exist in the substances on ¨ (c) volume remains constant account of ¨ (d) no exchange of heat takes place (a) paired electrons ¨ (b) unpaired electrons ¨ Temperature of two bodies are T1 and T2. (c) presence of protons ¨ If they are in thermal equilibrium then (d) presence of domains ¨ ¨ (a) T1 > >T2 ¨ (b) T1 > T2 Q.13. You are given a wire of length 50 cm and ¨ (c) T1 < T2 battery of negligible resistance. In which ¨ (d) T1 = T2 case the maximum amount of Heat is generated ? Of the following cases, velocity of sound (a) when the wire is connected across the ¨ at 30° will be least through battery directly (a) N2 (b) hen the wire is divided into two ¨ ¨ (b) O2 parts and both the parts are connected ¨ (c) SO2 across the battery in parallel ¨ (d) CO2 (c) when wire is divided into four parts ¨ ¨ and all the parts are connected across Two tuning forks have the frequencies battery in parallel 512 Hz and 516 Hz. Number of beats (d) None of these ¨ produced by these forks per second will be Q.14. The temperature of the sun is measured (a) 1028 with ¨ (b) 4 (a) platinum resistance thermometer ¨ ¨ (c) 1/4 (b) gas thermometer ¨ ¨ (d) 1/1028 (c) vapour pressure thermometer ¨ ¨ (d) pyrometer ¨ Matter waves are (a) mechanical waves ¨ Q.15. For the production of x-rays of (b) electromagnetic waves ¨ wavelength 0.1 A, the minimum potential (c) quantum mechanical waves ¨ difference will be (d) none of these ¨ ¨ (a) 12.4 KV (c) Zn + Sn ¨ ¨ (D) Cu + Zn + Sn ¨ ¨ ¨ Q.22. Which of the following metal carbonate Q.16. If the elements of n > 4 were not exists in is decomposed on heating? nature, then possible number of elements (a) MgCO3 ¨ in nature were ¨ (b) Na2CO3 (a) 60 ¨ ¨ (c) K2CO3 (b) 32 ¨ ¨ (d) Rb2CO3 (c) 4 ¨ Q.23. The oxidation state of Mo in Mo2Cl8 is (d) 64 ¨ ¨ (a) +4 Q.17. An electron in an atom (Z = 4) is in first ¨ (b) –4 energy state. The ionization energy of the ¨ (c) +1 atom will be ¨ (d) +2 (a) 0 eV ¨ Q.24. Gamma rays are (b) − 13.6 eV ¨ (c) 13.6 eV ¨ ¨ (a) High energy electrons (d) 217.6 eV ¨ ¨ (b) Low energy electrons (c) High energy electromagnetic waves ¨ Q.18. Bohr’s Quantum condition is( where Iω ¨ (d) High energy positron is moment of inertia and ω is angular Q.25. Bakelite is obtained from phenol by velocity) (a) Iω = 2π/ nh ¨ reacting with (b) Iω = nh/ 2π ¨ ¨ (a) acetaldehyde (c) Iω2 = nh/ 2π ¨ ¨ (b) acetal (d) Iω = nh/ 4π ¨ ¨ (c) formaldehyde ¨ (d) chlorobenzene Q.19. N equal resistors are first connected in Q.26. Which of the following solution has the series and then connected in parallel. Ratio of maximum to the minimum high B.P.? resistance is ¨ (a) 0.1 M NaCl (a) N ¨ ¨ (b) 0.1 M urea 2 (b) N ¨ ¨ (c) 0.1 M BaCl2 2 ¨ ¨ (c) 1/N (d) 0.1 M Glucose ¨ (d) 1/N Q.27. In photography we use Q.20. Which of the following is true in case of ¨ (a) AgI ¨ longitudinal stationary waves? (b) NH3 ¨ ¨ (a) variation in pressure and density is (c) AgCl ¨ maximum at nodes (d) AgBr (b) variation in pressure is maximum and ¨ Q.28. variation in density is minimum at Natural gas is a mixture of nodes ¨ (a) CH4+C2H6+C3H8 (c) variation in pressure and density is ¨ ¨ (b) CO+H2+CH4 minimum at nodes ¨ (c) CO+H 2 (d) variation in pressure is minimum and ¨ ¨ (d) H2O+CO2 variation in density is maximum at Nodes Q.29. Bakelite is made by the action of ¨ (a) Phenol and formaldehyde Q.21. Brass is an alloy containing ¨ (b) Melamine and formaldehyde (a) Zn + Cu ¨ ¨ (c) Urea and formaldehyde (b) Cu + Sn ¨ (d) Ethylene glycol and phthalic acid ¨ (b) 124 KV (c) 6.2 KV (d) 62 KV Q.30. Among the following the strongest acid is (a) CH3COOH (b) Cl CH2 CH2 COOH (c) CH2Cl COOH (d) CH3CH2COOH Q.37. Let f(x) = 2 x + 1. Then the number of real values of x for which the three ¨ unequal numbers f(x), f(2x), f(4x) are in ¨ G.P. is ¨ (a) 1 ¨ ¨ (b) 0 ¨ (c) 2 ¨ Q.31. In a single throw with two dice, the odds (d) None of these ¨ against drawing 7 is ¨ (a) 1 : 6 Q.38. The system of simultaneous equations ¨ (b) 1 : 12 K x + 2 y – z = 1, (K – 1) y – 2 z = 2, ¨ (c) 1 : 5 ( K + 2 ) z = 3 have a unique solution if K ¨ (d) 5 : 1 is (a) – 2 ¨ Q.32. Two cards are drawn at random from a (b) 0 ¨ pack of 52 cards. The probability of (c) – 1 ¨ getting at least a spade and an ace is (d) 1 ¨ ¨ (a) 1/34 ¨ (b) 8/221 Q.39. The number of values of a for which ¨ (c) 1/26 (a²–3a + 2) x² + (a² – 5 a + 6) x + a² – 4 = 0 ¨ (d) 2/51 is an identity in x is (a) 0 ¨ Q.33. A five digit number is formed by the (b) 2 ¨ digits 1, 2, 3, 4, 5 without repetition. Find (c) 1 ¨ the probability that the number formed is (d) 3 ¨ divisible by 4 : ¨ (a) 1/5 Q.40. Set A has 3 elements and set B has 4 ¨ (b) 6/5 elements. The number of injections that ¨ (c) 4/5 can be defined from A to B is ¨ (d) None of these (a) 144 ¨ (b) 12 ¨ Q.34. A bag contains 30 balls numbered from 1 (c) 64 ¨ to 30. One ball is drawn at random. The (d) 24 ¨ probability that the number of the ball drawn will be a multiple of 3 or 7 is : Q.41. The value of cos 15° is equal to ¨ (a) 14/30 (a) [(√3 +1)/2√2] ¨ ¨ (b) 40/900 (b) [(√3 -1)/2√2] ¨ ¨ (c) 13/30 (c) 2 – √3 ¨ ¨ (d) None of these (d) 2 + √3 ¨ Q.35. A probability that a leap year selected at Q.42. The value of tan 10° + tan 35° + tan 10°. random contains either 53 sundays or 53 tan 35° is equal to: mondays, is : (a) 0 ¨ ¨ (a) 2/7 (b) 1/2 ¨ ¨ (b) 4/7 (c) – 1 ¨ ¨ (c) 3/7 (d) 1 ¨ ¨ (d) 1/7 Q.36. The number of 6 digit numbers that can Q.43. The value of Ö 3 cosec 20° – sec 20° is be made with the digits 0, 1, 2, 3, 4 and 5, equal to : so that even digit occupy odd places is (a) 2 ¨ ¨ (a) 24 (b) 1 ¨ ¨ (b) 36 (c) 4 ¨ ¨ (c) 48 (D) None of these ¨ ¨ (d) None of these Q.44. In a right angled ABC, a = 2, b = 1+ Ö (c) constant ¨ 3, (d) information insufficient ¨ Ð C = 60° then the side c is equal to : ¨ (a) Ö 3–1 Q.52. The maximum value of x y subject to ¨ (b) Ö 2+1 x + y = 8 is ¨ (c) Ö 6 ¨ (a) 8 ¨ (D) None of these ¨ (b) 16 ¨ (c) 20 Q.45. If in a triangle PQR, sin P, sin Q, sin R are ¨ (d) 24 in A.P. Then : ¨ (a) the altitudes are in A.P. Q.53. ∫ [ cos 2x / cos x ] dx is equal to ¨ (b) the altitudes are in H.P. (a) 2 sin x + log ( sec x – tan x ) + c ¨ ¨ (c) the medians are in G.P. (b) 2 sin x – log ( sec x – tan x ) + c ¨ ¨ (d) the medians are in A.P. (c) 2 sin x + log ( sec x + tan x ) + c ¨ (d) 2 sin x – log ( sec x + tan x ) + c ¨ Q.46. The distance between the parallel lines y = 2x + 4 and 6x = 3y + 5 is : Q.54. If √( x + y ) + √( y – x ) = c where c is ¨ (a) 17/Ö 3 a constant then d2y/dx2 is equal to ¨ (b) 1 ¨ (a) 2 / c ¨ 2 (c) 3/Ö 5 ¨ (b) – 2 / c ¨ 2 (d) 17Ö 5 / 15 ¨ (c) 2 / c ¨ (d) None of these Q.47. The line segment joining the points (– 3, – 4) and (1 , – 2) is divided by Q.55. The area of the region bounded by y - axis in the ratio y = | x – 1 | and y = 1 is ¨ (a) 1 : 3 ¨ (a) 1 ¨ (b) 2 : 3 ¨ (b) 2 ¨ (c) 3 : 1 ¨ (c) 1/2 ¨ (d) 3 : 2 ¨ (d) None of these Q.48. The curve represented by x=3(cos t + sin t), Q.56. If a, b, c are three non zero vectors then y = 4 ( cos t – sin t ) is the equation a . b = a . c implies (a) Ellipse ¨ ¨ (a) b = c (b) Parabola ¨ ¨ (b) a is orthogonal to b – c (c) Hyperbola ¨ ¨ (c) both (i) and (ii) (d) Circle ¨ ¨ (d) None of these Q.49. Which of the following is the equation of Q.57. If i, j and k are unit orthonormal vectors a plane? then i .( j ´ k) + j. (K ´ i) + k. ( i ´ j) ¨ (a) l x + my = n is equal to ¨ (b) z = 0 ¨ (a) 1 ¨ (c) 2x + 3y = 0 ¨ (b) 3 ¨ (d) y = – x ¨ (c) – 3 ¨ (d) 0 Q.50. The eccentricity of the ellipse 2 2 9x + 5y – 30y = 0 is Q.58. The points with position vectors 10 i + 3j, ¨ (a) 1/3 12 i – 5 j & a i + 11j are collinear if a is ¨ (b) 2/3 equal to ¨ (c) 3/4 ¨ (a) – 8 ¨ (d) None of these ¨ (b) 4 ¨ (c) 8 Q.51. The function f(x) = 1 / x on its domain is ¨ (d) 12 (a) increasing ¨ (b) decreasing ¨ (c) 60˚ ¨ (d) None of these ¨ ¨ Q.65. Forces 7, 5 and 3 acting on a particle are ¨ in equilibrium. The angle between the ¨ last pair of forces is ¨ (a) 120˚ ¨ Q.60. If a, b and c are three non-coplanar (b) 90˚ ¨ (c) 60˚ ¨ vectors then (a + b + c).{(a + b) ´ (a + c )} (d) 30˚ ¨ equals ¨ (a) 0 Q.66. The mean marks of 100 students were ¨ (b) [a b c] found to be 40. Later on, it was ¨ (c) 2 [a b c] discovered that a score of 53 was misread ¨ (d) – [a b c] as 83. The correct mean is Q.61. A train of length 200 m. travelling at 30 (a) 35.3 ¨ (b) 36.9 ¨ m./sec. overtakes another of length 300 (c) 41.2 ¨ m. travelling at 20 m. /sec. The time taken (d) 39.7 ¨ by the first train to pass the second is ¨ (a) 30 sec. Q.67. The measure which takes into account all ¨ (b) 50 sec. the data items is ¨ (c) 10 sec. (a) Mean ¨ ¨ (d) 40 sec. (b) Median ¨ Q.62. The resultant of the forces 4, 3, 4 and 3 (c) Mode ¨ (d) None of these ¨ units acting along sides AB, BC, CD and DA of square ABCD of side a Q.68. The scores of a batsman in ten innings are respectively is 38, 70,48, 34, 42, 55, 63, 46, 54, 44. The ¨ (a) a null force mean deviation about the median is (b) a force of magnitude 5√2 through ¨ (a) 9.2 ¨ centre of square (b) 8.6 ¨ ¨ (c) a couple of moment 7 a (c) 7.4 ¨ ¨ (d) none of these (d) 6.6 ¨ Q.63. A man wishes to cross a river to an Q.69. The sum of 10 items is 12 and sum of their exactly opposite point on the other bank, squares is 18.Therefore the standard if he can swim with twice the velocity of deviation will be the current, then the inclination to the (a) 5/3 ¨ current of the direction in which he (b) 3/5 ¨ should swim is (c) 9/25 ¨ ¨ (a) 1 : 1 (d) 25/9 ¨ ¨ (b) √2 : 1 ¨ (c) 1 : √2 Q.70. One of the methods of determining mode is ¨ (d) 3 : 2 (a) Mode = 2 Median – 3 Mean ¨ (b) Mode = 2 Median + 3 Mean ¨ Q.64. A rod can turn freely about one of its ends (c) Mode = 3 Median – 2 Mean ¨ which is fixed. At the other end, a (d) Mode = 3 median + 2 Mean ¨ horizontal force equal to half of the weight of the rod is acting. In the position x 1– x Q.71. The minimum value of 4 + 4 , x ε R is of equilibrium, the rod is inclined to the (a) 1 ¨ vertical at an angle (b) 2 ¨ ¨ (a) 30˚ (c) 4 ¨ ¨ (b) 45˚ (d) None of these ¨ Q.59. If | a | = 7, | b | = 11, | a + b | = 10√3 then |a – b| is equal to (a) 10 (b) √10 (c) 2√10 (d) 20 Q.72. The sum of all odd proper divisors of 360 Q.80. Choose the letter of the correctly spelt word. (a) pernicious is ¨ (b) parnicious (a) 77 ¨ ¨ (c) pernishes (b) 78 ¨ ¨ (d) pernecious (c) 81 ¨ ¨ (d) None of these ¨ Q.81. Choose the letter of the correctly spelt word. (a) marrygible Q.73. If f(x) = cos2 x + sec2 x , its value always is ¨ (b) marriageable ¨ ¨ (a) less than 1 (c) marriagable ¨ ¨ (b) equal to 1 (d) marriageble ¨ ¨ (c) between 1 and 2 ¨ (d) greater than or equal to 2 Q.82. Choose the most suitable One Word‘A workman who fits and repairs pipes’ Q.74. (sin θ + i cos θ)4 is equal to ¨ (a) Mechanic ¨ (a) cos 4 θ – i sin 4 θ ¨ (b) Blacksmith ¨ (b) sin 4 θ + i cos 4 θ (c) Plumber ¨ ¨ (c) sin 4 θ – i cos 4 θ (d) Technocrat ¨ ¨ (d) cos 4 θ + i sin 4 θ Q.83. Choose the most suitable One WordQ.75. If tan p θ = tan q θ then the values of θ ‘Study of books in regard to their form a series in outward form, authors, subjects, ¨ (a) A.P. editions, etc.’ ¨ (b) G.P. ¨ (a) autobiography ¨ (c) H.P. ¨ (b) biography ¨ (d) None of these ¨ (c) bibliography ¨ (D) philately Q.76. Choose the appropriate Antonym of Q.84. Fill in the blank selecting correct 'Undertaking’ ¨ Preposition from the alternatives given (a) Resignation ¨ below sentence (b) Trial ¨ He aspires ….. the post of a professor. (c) Refusal ¨ ¨ (a) about (d) Denial ¨ (b) for ¨ (c) to Q.77. Choose the appropriate Antonym of ¨ (d) on 'Sympathy’ ¨ (a) Enmity Q.85. Fill in the blank selecting correct ¨ (b) Cruelty Preposition from the alternatives given ¨ (c) Abhorrence below sentence ¨ (d) Apathy I do not know how to manage ……. four hundred francs. Q.78. Choose the appropriate Synonym of (a) with ¨ 'ABASH’ (b) without ¨ ¨ (A) Strike (c) by ¨ ¨ (b) Deduct (d) for ¨ ¨ (c) Forsake ¨ (d) Confound Q.86. Fill in the blank selecting correct Preposition from the alternatives given Q.79. Choose the appropriate Synonym of below sentence ‘HARASS’ ‘I am fond …………… vegetables.’ (a) rave ¨ (a) into ¨ (b) shelter ¨ (b) since ¨ (c) torment ¨ (c) of ¨ (d) pierce ¨ (d) for ¨ Q.87. Fill in the blank with a suitable Article ‘The man is ……… social animal.’ (a) a (b) an (c) the (d) None of these ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ Q.89. Fill in the blank with a suitable Article ¨ ‘Cold on …… Himalayas is terrible.’ ¨ (a) a ¨ ¨ (b) an ¨ (c) the ¨ (d) None of these ¨ ¨ ¨ Q.90. Complete the sentence: ¨ ¨ All of us should abide ______ the laws of our country. ¨ (a) on ¨ ¨ (b) to ¨ ¨ (c) by ¨ ¨ (d) in ¨ Q.88. Fill in the blank with a suitable Article ‘Mohan gave me ……… useful book.’ (a) a (b) an \ (c) the (d) None of these *** * ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨ ¨