AIEEE 2007 Practice Test 2
| Instructions 1. All questions are compulsory. 2. Every question carries 3 marks. 3. Do not write anything on answer sheet except in the marked area. 4. Every incorrect answer carries -1(negative) mark 5. The paper is of 2 hours duration Syllabus Physics - Heat, SHM and waves Chemistry - Electrochemistry , Hydrocarbons, Mathematics - Probability, Trigonometric equations and inverse trigonometric functions |
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Q1. Two holes of unequal diameters d1 and d2 (d1 > d2) are cut in a metal sheet. If the sheet is heated, Q2. In the previous question, the distance between the holes will Q3. A metal wire of length l and area of cross-section A is fixed between rigid supports at negligible tension. If this is cooled, the tension in the wire will be Q4. Two metal rods of the same length and area of cross-section are fixed end to end between rigid supports. The material of the rods have Yong modulii Y1 and Y2, and coefficients of linear expansion a1 and a2. The junction between the rods does not shift if the rods are cooled. Q5. Three rods of equal length are joined to form an equilateral triangle ABC. D is the midpoint of AB. The coefficient of linear expansion is a1 for AB, and a2 for AC and BC. If the distance DC remains constant for small changes in temperature, Q6. When the temperature of a body increases from t to t + Dt, its moment of inertia increases from I to I + DI. The coefficient of linear expansion of the body is a. The ratio Q8. In a vertical U-tube containing a liquid, the two arms are maintained at different temperatures, t1 and t2. The liquid columns in the two arms have height l1 and l2 respectively. The coefficient of volume expansion of the liquid is equal to Q9. A solid whose volume does not change with temperature floats in a liquid. For two different temperatures t1 and t2 of the liquid, fractions f1 and f2 of the volume of the solid remain submerged in the liquid. The coefficient of volume expansion of the liquid is equal to Q10. A solid with coefficient of linear expansion a just float in a liquid whose coefficient of volume expansion is g. If the system is heated, the solid will Q11. A gas at absolute temperature 300 K has pressure = 4 x 10–1 N/m2. Q12. The root-mean-square (rms) speed of oxygen molecules (O2) at a certain absolute temperature is v. If the temperature is doubled and the oxygen gas dissociates into atomic oxygen, the rms speed would be Q13. The average translational kinetic energy of O2 (molar mass 32) at a particular temperature is 0.048 eV. The average translational kinetic energy of N2 (molar mass 28) molecules in eV at the same temperature is Q14. A gas has volume V and pressure p. The total translational kinetic energy of all the molecules of the gas is Q15. A closed vessel is maintained at a constant temperature. It is first evacuated and then vapour is injected into it continuously. The pressure of the vapour in the vessel Q16. When an air bubble rises from the bottom to the surface of a lake, its radius becomes double. Find the depth of the lake, given that the atmospheric pressure is equal to the pressure due to a column of water 10 m high. Assume constant temperature and disregard surface tension Q17. Two containers of equal volume contain the same gas at pressures p1 and p2 and absolute temperatures T1 and T2 respectively. On joining the vessels, the gas reaches a common pressure p and a common temperature T. The ratio p/T is equal to Q19. In the pressure question, let V0 be the volume of each container. All other details remain the same. The number of moles of gas in the container at temperature 2T0 will be
Q21 A particle of mass 1 kg is moving in SHM with an amplitude 0.02 and a frequency of 60 Hz. The maximum force acting on the particle is Q38 A cylindrical tube open at both the ends, has a fundamental frequency ‘f’ in air. The tube is dipped vertically in air. The tube is dipped vertically in water so that half of it is in water. The fundamental frequency of the air column in now Q40 An organ pipe open at one end is vibrating in first overtone and is in resonance with another pipe open at both ends and vibrating in third harmonic. The ratio of length of two pipes is [ Chemistry ] Q41. In the reaction, H2(g) + I2(g) Q43 One mole of nitrogen and three moles of hydrogen are mixed in a 4 litre container. If 0.25 percent of nitrogen is coverd to ammonia by the following reaction N2(g) + 3H2(g) Q46 Iron filling and water were placed in a 5 litre tank and sealed The tank was heated to 1273 K. Upon analysis the tank was found to contain 1.10 gram of hydrogen and 42.5 gm of water vapour. If the reaction in the tank is represented by Q47 At 700 K, the equilibrium constant KP, for the reaction Q48 The value of KC for the reaction N2(g) + 3H2(g) Q49 The equilibrium constant for the reaction H2(g) + S(s) Q50 Inhibitor is ‑ Q51 KP for the reaction A(g) + 2B(g) Q53 If PCl5 is 80 % dissociation at 523 K. Calculate the vapour density of the equilibrium mixture at 523 K Q54 Ammonium carbamate when heated to 200 °C gives a mixture of vapours Q55 The volume of a closed reaction vessel in which the equilibrium Q56 H2(g) + I2(g) Q59 The value of KC for the reaction : Q60 Two moles of ammonia was introduced in an evacuated vessel of 1litre capacity. At high temperature the gas undergoes partial dissociation according to the equation Q61. Which sodium salt will be heated with soda lime to obtain propane – Q63 Which of the following compounds liberate methane when treated with excess of methyl magnesium iodide in dry ether Q64 Raney Nickel is a suitable catalyst for: ‑ Q65. Correct order of boiling point is ‑ Q66 In the complete combustion of Cn H2n + 2 , the number of oxygen rmoles required is Q68. The number of isomers of C6H14 are: Q69. Which of the following reaction pairs constitutes the chain propagation step in chlorination of methyl chloride?
Q70 Kolbe's reaction is convenient for the preparation of: Q71. For the formation of 27 gm of water, what volume of neopentane is required for the complete combustion: Q72. Acetylene and ethylene reacts with alk. KMnO4 to give ‑ Q73. Chloroform when heated with silver powder gives an alkyne. For the substitution of hydrogen atom by chlorine the reaction must be carried out with ‑ Q74. Acetylene on passing into excess of HOCl solution forms ‑ Q75. 10 ml of a certain hydrocarbon require 25 ml of oxygen for complete combustion and the volume of CO2 produced is 20 ml. What is the formula of hydrocarbon ‑ Q76. Lindlar's catalyst consists of ‑ Q77. 2‑Butyne and 1‑Butene show resemblance in all except ‑ Q78. Acetylene reacts with formaldehyde in the presence of sodium alkoxide to form mainly ‑ Q79. Acetylene reacts with 42% H2SO4 containing 1% HgSO4 to give: Q80. The alkene which on ozonolysis yields acetone is: [ Mathematics ] Q81 A car is parked by a driver amongst 25 cars in a row, not at either end. When he returns he finds that 10 places are empty. The probability that both the neighboring places of driver’s car are vacant is Q82 A is one of the six race horses which is to be ridden by one of the two jockeys B or C. It is 2 :1 that B rides A in which case all the horses are equally likely to win but if C rides, then A’s chances of wining are trebled. The odds against his winning are Q83 A and B play by throwing a pair of dice alternately. A wins if he throws 6 before B throws 7. If A starts the game their chances of wining the game are in the ratio Q86 Two cards are randomly selected from a deck of 52 playing cards. The probability that both the cards are greater than 3 and less than 8 is Q87 Probabilities of teams A, B and C wining are Q88 If two squares are chosen at random on a chess board, the probability that they have a side in common is Q89 A single letter is selected at random from the word PROBABILITY . The probability that it is a vowel is Q90 if P(A Ç B) = Q91 The probability that a leap year selected at random contains either 53 Sundays or 53 Mondays is Q92 A bag contains 50 tickets numbered 1, 2, 3 , ……., 50 of which five are drawn at random and arranged in ascending order of magnitude ( Q93 A box contains 10 mangoes out of which 4 are rotten. 2 mangoes are taken out together. If one of them is found to be good, the probability that the other is also good is Q94 Three letters, to each of which corresponds an envelope, are placed in the envelopes at random. The probability that all the letters are not placed in the right envelope is Q95 Two athletes A and B participate in a race along with other athletes. If the chance of A wining the race is 1/6 and that of B wining the same race is 1/8, then the chance that neither wins the race is Q96 Six coins are tossed simultaneously. The probability of getting at least 4 heads is Q97 Dialing a telephone number an old man forgets the last two digits remembering that these are different dialed at random. The probability that the number is dialed correctly is Q98 If A and B are two independent events, the probability that both A and B occur is 1/8 and the probability that neither of them occur is 3/8. The probability of the occurrence of A is Q99 If three vertices of a regular hexagon are chosen at random, then the chance that they form an equilateral triangle is Q100 10 apples are distributed at random among 6 persons. The probability that at least one of them will receive none is Q102. cos–1 [cos (2 cot–1 ( Q103. The equation Q104. Two angles of a triangle are cot–1 2 and cot–1 3. Then the third angle Q105. Complete set of values of x satisfying [tan–1 x] + [cot–1 x] = 2, where [.] denotes the greatest integer function, is Q106. Complete solution set of the equation [cot–1 x] + 2[tan–1 x] = 0, where [.] denotes the greatest integer function, is equal to Q107. The trigonometric equation sin–1 x = 2 sin–1 a, has a solution for: Q108. Q109. Q110. The value of Q111. The number of real solutions of Q112. If Q113. The value of x for which sin (cot–1 (1 + x)) = cos (tan–1 x) is Q114. The principal value of Q115. The period of the function f(x) = sin4 x + cos4 x is Q116. The value of Q117. If Q118. If sin (a + b) = 1, sin (a – b) = Q119. Number of solutions of the equation tan x + sec x = 2 cos x lying in the interval [0, 2p] is& Q120. In a triangle PQR, ÐR = p/2. If tan (P/2) and tan (Q/2) are the roots of the equation ax2 + bx + c = 0 (a ¹ 0) then
|
a2 
is equal to
pV only if the gas is monatomic
pV only if the gas is diatomic
pV only if the gas is diatomic
pV in all cases
m/s
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, what is the maximum acceleration of the particle doing the SHM 
2HI(g) the concentration of H2, I2 and HI at equilibrium are 8.0 , 3.0 and 28.0 moles are litres respectively. What will be the equilibrium constant ‑
2NH3(g), the partial pressures of H2 and N2 are 0.4 and 0.8 atmosphere, respectively. The total pressure of the entire system is 2.8atmosphere. What will be the value of Kp if all the concentration are given in atmosphere ? 
2NH3(g). What will be the equilibrium constant (Kc) in concentration units ? What will be the value of K for the following equilibrium ‑
N2(g) + 
H2(g) 
NH3(g).
2NH3(g) + CO2(g)
Fe3O4 (s) + 4H2(g)
2SO2(g) + O2(g) is 1.8 x 10‑3 kPa.
2NH3(g) is 0.50 at 400 °C. What will be the value of KP at 400 °C when concentration are expressed in mole litre‑1 and pressure in atmosphere ‑
H2S(g) ; is 18.5 at 935 K and 9.25 at 1000 K respectively. The enthalpy of the reaction will be ‑
3C(g) + D(g) ; is 0.05 atm. What will be its KC at 1000 K in terms of R ‑
R
2NH3 + CO2)
2SO3(g) sets is halved, Now‑
2HI(g)
C + D
2C at 400 °C . Calculate the value of KP
N2(g) + 3H2(g)
O2
O2
O2
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