FIITJEE RT II (CHAMPIONS_2 ND YEAR)

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1 FIITJEE RT II (CHAMPIONS_ ND YEAR) MAINS DATE: 7..8 Time: hours Maximum Marks: 6 INSTRUCTIONS: Instructions to the Candidates. This Test Booklet consists of 9 questions. Use Blue/Black ball Point Pen only for writing particulars and bubbling of OMR.. For each correct answer 4 Marks will awarded and for each wrong answer Mark will be deducted.. Attempt all questions. 4. In case you have not darkened any bubble you will be awarded mark for that question. 5. Use of calculator/logarithmic table is not permitted. Don t write / mark your answers in this question booklet. If you mark the answers in question booklet, you will not be allowed to continue the exam. NAME: ENROLLMENT NO.:

2 RT-II ( ND YEAR_CHAMP)-9-MPC-. The centre and radius of the circle with the segment of the line x + y = cut of by the coordinate axes as diameter are (A),, (B),, (C),, (, ),. The straight lines joining the origin to the points of intersection of the lines 4x + y = 4 with the curve (x ) + (y 4) = 5 (A) are coincident (B) are perpendicular (C) made equal angles with x-axis none of these. A straight line moves such that the algebraic sum of the perpendicular drawn to it from two fixed points is equal to k. Then the straight line always touches a fixed circle of radius (A) k (B) k (C) k none of these 4. The equation of the image of the circle x + y 6x 4y + = by the line mirror x + y = is (A) x + y + x + 4y + 4 = (B) x + y x + 4y + 4 = (C) x + y + x + 4y 4 = x + y + x 4y + 4 = 5. Let A be the centre of the circle x + y x 4y =. Suppose that the tangents at the point B(, 7) and D(4, ) on the circle meet at the point C. The area of the quadrilateral ABCD is (A) 75 sq. unit (B) 45 sq. unit (C) 5 sq. unit 5 sq. unit 6. An isosceles ABC is inscribed in a circle x + y = a with the vertex A at (a, ) and the base bangles B and C each equal to 75, then length of the base BC is (A) a (B) a (C) a 7. The point (, 4) lies inside the circle x + y 6x y + p = which does not touch or intersect the coordinate axes, then (A) < p < 9 (B) 5 < p < 9 (C) 9 < p < 5 p < p < 9 8. If the circle x + y + 4x + y + c = bisects the circumference of the circle x + y x + 8y d =, then c + d is equal to (A) 6 (B) 5 (C) A circle C of radius touches both x-axis and y-axis. Another circle C whose radius is greater than touches circle C and both the axes. Then the radius of circle C is (A) 6 4 (B) 6 4 (C) a

3 RT-II ( ND YEAR_CHAMP)-9-MPC-. An equation of a circle touching the axes of coordinates and the line x cos + y sin = is x + y gx + gy + g = where g = (A) (cos + sin + ) (B) (cos sin + ) (C) (cos + sin ) (cos sin ). The equation of the circle passing through the point (a, ) and whose radical axis is x = a with respect to the circle x + y = a, will be (A) x + y ax = (B) x + y + ax = (C) x + y + ay = x + y ay =. The equation to the sides AB, BC, CA of ABC are x + y =, 4x y + 4 = and x + y = 6, Circles are drawn on AB, BC, CA as diameters. The point of concurrence of the common chord is (A) centroid of the triangle (B) orthocentre (C) circumcentre incentre. A and B are two fixed points in a plane such that PA = k, and locus of point P is a circle, then k will PB not be equal to (A) (B) (C) 4. If a tangent drawn from the point (4, ) to the circle x + y = 8 touches it at a point A in the first quadrant, then the coordinates of another point B on the circle such that AB = 4 are (A) (, ) or (, ) (B) (, ) or (, ) (C) (, ) or (, ) (, ) or (, ) 5. The tangents to x + y = a having inclinations and intersect at P. If cot + cot =, then the locus of P is (A) x + y = (B) x y = (C) xy = none of these 6. A line segment AM = a moves in the XOY plane such that AM is parallel to the X-axis. If A moves along the circle x + y = a, then the locus of M is (A) x + y = 4a (B) x + y = ax (C) x + y = ay x + y = ax + ay 7. The circle passing through (, ) and touching the axis of x at (, ) also passes through the point (A) (5, ) (B) (, 5) (C) ( 5, ) (, 5) 8. If the radius of the circle (x ) + (y ) = and (x 7) + (y ) = 4 are increasing uniformly w.r.t time as. and.4 unit/sec; then they will touch each other at time equal to (A) 45sec (B) 9sec (C) sec 5sec

4 RT-II ( ND YEAR_CHAMP)-9-MPC-4 9. A circle with centre at the origin and radius equal to a meets the axis of x at A and B. P() and Q() are two points on this circle so that =, where is a constant. The locus of the point of intersection of AP and BQ is (A) x y ay tan = a (B) x + y ay tan = a (C) x + y + ay tan = a x y + ay tan = a. If two distinct chords, drawn from the point (p, q) on the circle x + y = px + qy (where pq ) are bisected by the x-axis, then (A) p = q (B) p = 8q (C) p < 8q p > 8q. If PQ and RS are the tangents at the extremities of a diameter PR of a circle of radius r such that PS and RQ intersect at a point X on the circumference of the circle, then r = (A) PQ RS (B) PQ RS (C) PQ RS PQ RS PQ RS. An isosceles right angled triangle is inscribed in the circle x + y = r. If the coordinates of an end of the hypotenuse are (a, b) the coordinates of the vertex are (A) ( a, b) (B) (b, a) (C) (b, a) ( b, a). An equation of the chord of the circle x + y = a passing through the point (, ) farthest from the centre is (A) x + y = (B) x y = (C) x y + 4 = x y + = 4. The lengths of the chords of the circle x + y x 6y 5 = which make an angle of 6 at (, ) and the locus of the midpoints of all such chords are (A) 5, 4(x + y x 6y) 5 = (B), (x + y x 6y) 5 = (C) 5, 4(x + y x 6y) 5 =, 4(x + y + x + 6y) 5 = 5. The equation of the straight line meeting the circle x + y = a in two points equal distance d from a point (x, y ) on the circumference is xx + yy = (A) a ad (B) a + d (C) a d 6. The slope m of a tangent through the point (7, ) to the circle (A) m 7m (B) m 7m 9 (C) x y 5 satisfies the equation m 7m 9m m 6

5 RT-II ( ND YEAR_CHAMP)-9-MPC-5 7. The locus of the middle points of portions of the tangents to the circle x y a terminated by the axes is 4 4 (A) (B) (C) x y a x y a x y a x y a 8. The equation to the circle touching the y-axis at the origin and passing through (b, c) is b x y x b c b x y y b c (A) (B) (C) bx y xb c bx y yb c 9. A line meets the coordinate axes in A and B. A circle is circumscribed about the triangle OAB. If m and n are the distances of the tangent to the circle at the origin from the points A and B respectively the diameter of the circle is (A) m (m + n) (B) m + n (C) n(m + n) m n x y r and. If the two circles x y x y 7 intersect in two distinct points then (A) < r < 8 (B) r < (C) r = r >. In a thermodynamic process, pressure of a fixed mass of gas is changed in such a manner that the gas releases joule of heat and 8 joule of work was done on the gas. If the initial internal energy of the gas was joule, then the final internal energy will be (A) joule (B) 8 joule (C) 4 joule 58 joule. An ideal gas with pressure P, volume V and temperature T is expanded isothermally to a volume V and a final pressure P I. The same gas is expanded adiabatically to a volume V, the final pressure is P A. In terms of the ratio of the two specific heats for the gas y, the ratio P I /P A is: (A) (B) (C). The temperature of a gas is doubled (i) on absolute scale (ii) on centigrade scale. The increase in root mean square velocity of gas will be (A) More in case (i) (B) More in case (ii) (C) Same in both case Information not sufficient

6 RT-II ( ND YEAR_CHAMP)-9-MPC-6 4. A cylinder containing gas at 7 C is divided into two parts of equal volume each cc and at equal pressure by a piston of cross sectional area.85 cm. The gas in one part is raised in temperature to C while the other maintained at original temperature. The piston and wall are perfect insulators. How far will the piston move during the change in temperature? (A) cm (B) cm (C).5 cm.5 cm 5. A reversible adiabatic path on a P-V diagram for an ideal gas passes through state A where P=.7 5 N/m and v =.49 m. The ratio of specific heat of the gas is.4. The slope of path at A is : (A). 7 Nm 5 (B). 7 Nm 5 (C). 7 Nm 5. 7 Nm 5 6. Five moles of helium are mixed with two moles of hydrogen to form a mixture. Take molar mass of helium M = 4g and that of hydrogen M = g.if the internal energy of He sample of J and that of the hydrogen sample is J, then the internal energy of the mixture is (A) 9 J (B) 8.5 J (C) 7.4 J J 7 The figure, shows the graph of logarithmic reading of pressure and volume for two ideal gases A and B undergoing adiabatic process. From figure it can be concluded that (A) gas B is diatomic (C) gas A is monoatomic (B) gas A and B both are diatomic gas B is monoatomic & gas A is diatomic 8. A thermodynamic cycle takes in heat energy at a high temperature and rejects energy at a lowertemperature. If the amount of energy rejected at the low temperature is times the amount of work done by the cycle, the efficiency of the cycle is (A).5 (B). (C) A system is taken along the path ABCA as shown in P-V diagram. The heat released by the system in joule is (A) (B) (C) 5 P B A C V in litre

7 RT-II ( ND YEAR_CHAMP)-9-MPC-7 4. Match the following a. lsothermal process e. W = b. Adiabatic process f. du = c. lsobaric process g. Q = d. lsochoric process h. Q ; du (A) a e; b f; c-g; d-h (B) a-f; b-g; c-h; d-e (C) a-f; b-g; c-e; d-h a-g ; b-f; c-h; d-e 4. A continuous flow water heater (geyser) has an electrical power rating is kw and efficiency of conversion of electrical power into heat is 8%. If water is flowing through the device at the rate of cc/sec, and the inlet temperature is C, the outlet temperature will be (A). C (B).8 C (C) C 6.5 C 4. During an experiment an ideal gas obeys an additional equation of state P V = constant. The initial temperature and volume of gas are T and V respectively. When it expands to volume V, then its temperature will be : (A) T (B) T (C) T T 4. Monoatomic, diatomic and triatomic gases whose initial volume and pressure are same, are compressed till their volume becomes half the initial volume. (A) If the compression is adiabatic then monoatomic gas will have maximum final pressure. (B) If the compression is adiabatic then triatomic gas will have maximum final pressure. (C) If the compression is adiabatic then their final pressure will be same. If the compression is isothermal then their final pressure will be different. 44. A monoatomic gas initially at temperature T, is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand to a temperature T by releasing the piston suddenly. If L and L are lengths of the gas column before and after expansion respectively, then (A). L L (B) L L (C). 45. One mole of a gas expands obeying the relation as shown in the P-V diagram. The maximum temperature in this process is equal to (A) PV R (B) PV R (C) 9PV 8R L L 9PV 4R T T is L L

8 Volume (litres) RT-II ( ND YEAR_CHAMP)-9-MPC Three particles have speeds of u, u and u. Which of the following statements is correct? (A) The r.m.s. speed exceeds the mean speed by about u. (B) The mean speed exceeds the r.m.s. speed by about u. (C) The r.m.s. speed equals the mean speed. The r.m.s. speed exceeds the mean speed by more than u. 47. A diatomic gas of molecules weight gm/mole is filled in a container at 7 C. It is moving at a velocity m/s. If it is suddenly stopped, the rise in temperature of gas is : (A) 6 R (B) 6 R (C) 4 6 R 5 6 R 48. Two Carnot engines A and B are operated in succession. The first one, A receives heat from a source at T 8 K and rejects to a sink at TK. The second engine B receives heat rejected by the first engine and rejects to another sink at T K. If the work outputs of two engines are equal, then the value of T is (A) K (B) K (C) 55 K 7 K 49. The efficiency of a heat engine: (A) is independent of the temperature of the source and the sink (B) is independent of the working substance (C) can be % is not affected by the thermal capacity of the source or the sink 5. An ideal gas heat engine operates between 7 C and 7 C, it absorbs 6 x 4 calories at the higher temperature, the amount of heat rejected to sink is (A) 4.8 x 4 cal (B).5 x 4 cal (C).6 x 4 cal. x 4 cal 5. The heat energy absorbed by a system in going through a cyclic process shown in figure is (A) J (B) J (C) 4 J 7 J Pressure (kpa) 5. A gas is expanded from volume V to V under three different processes. Process is isobaric process, process is isothermal and process is adiabatic. Let U, U and U be the change in internal energy of the gas in these three processes. Then (A) U > U > U (B) U < U < U (C) U < U < U U < U < U P P V V V

9 RT-II ( ND YEAR_CHAMP)-9-MPC-9 5. In a thermodynamic process, pressure of a fixed mass of gas is changed in such a manner that the gas releases joule of heat and 8 joule of work was done on the gas. If the initial internal energy of the gas was joule, then the final internal energy will be (A). joule (B) 8 joule (C) 4 joule 58 joule 54. An ideal gas with pressure P, volume V and temperature T is expanded isothermally to a volume V and a final pressure P I. The same gas is expanded adiabatically to a volume V, the final pressure is P A. In terms of the ratio of the two specific heats for the gas y, the ratio P I /P A is: (A) (B) (C) 55. A gas for which 4/, is heated at constant pressure. What percentage of the total heat supplied is used up for external work? (A).5 % (B) 5 % (C) 5 % 7 % 56. The efficiency of an ideal gas with adiabatic exponent ' ' for the shown cyclic process would be In In (A) (B) / / In In (C) / / 57. A cyclic process ABCD is shown in the V-T diagram. Which of the following curves represent the same proess? (A) (B) (C)

10 RT-II ( ND YEAR_CHAMP)-9-MPC- 58. One mole of an ideal monoatomic gas in taken through the thermodynamic process shown in the P- V diagram. The heat supplied to the system is (A) PV (B) PV 5 P V PV (C) 59. The system shown in the adjacent figure is thermally insulated. An ideal gas is filled in the cylinder having pressure P > atmospheric pressure P (> atmospheric pressure). The spring of force constant k is initially unstretched. The piston of mass m and area S is frictionless. In equilibrium, the piston rises by distance x. Then, which of the following is not correct. kx mg (A) Final pressure of the gas is P S S (B) Work done by the gas is greater than kx mgx (C) Decrease in internal energy is kx mgx P sx None of the above 6. A certain amount of a diatomic gas undergoes a certain polytropic process in which it absorbs joule heat and performs 5 joule work. The process can be described by the formula. 5 / 5 / 5 / 5 (A) PV C (B) PV C (C) PV C PV C 6. Identify the wrong statement in the following (A) Atomic radius of the elements increases as one moves down the first group of the periodic table (B) Atomic radius of the elements decreases as one moves across from left to right in the nd period of the periodic table (C) Amongst isoelectronic species, smaller the positive charge on the cation, smaller is the ionic radius amongst isoelectronic species, greater the negative charge on the anion, larger is the ionic radius

11 RT-II ( ND YEAR_CHAMP)-9-MPC- 6. Correct order of Ist ionization potential among following elements Be, B, C, N, O is (A) B < Be < C < O < N (B) B < Be < C < N < O (C) Be < B < C < N < O Be < B < C < O < N 6. The decreasing order of ph value of the following salts in aqueous solution is (A) (NH 4 ) SO 4 > NaCl > NaCN (B) NaCN > NaNO > (NH 4 ) SO 4 (C) NaCl > NaCN > (NH 4 ) SO 4 NaCl > (NH 4 ) SO 4 > NaCN 64. The solubility product of Ag CrO 4 is x mol. The solubility of Ag CrO 4 is (A) 5 x (B) x 4 (C).5 x 4 x 65. In the reaction, PCl 5 PCl + Cl, the amounts of PCl 5, PCl and Cl at equilibrium are mole each and the total pressure is atm. The equilibrium constant K p is : (A). atm (B). atm (C). atm 6. atm 66. Consider the following equilibrium: A(g) + B(g) C(g) + D(g) At the approach of equilibrium, concentrations of A, B and C are.5m, M and.5m respectively. At the start of reaction, C was absent but D was present (initial concentration of D =.5M). Identify the correct statement: (A) The concentration of D at equilibrium is 4.5M (B) K c =4M KC (C) = 5 [A] [B] [C] [D] at equilibrium Addition of Helium at constant pressure to the equilibrium mixture would push equilibrium backward 67. Which order reaction obeys the expression t / = in chemical kinetics is K x a (A) (B) (C) The solubility s and solubility product K sp for PbI are related as 4 (A) S K sp (B) S K sp 4 (C) S K sp 4 S K sp The precipitate of CaF (K sp =.7 x ) is obtained when equal volumes of the following are mixed: (A) 4 M Ca M F (B) MCa + + MF (C) 5 M Ca + + MF MCa MF

12 RT-II ( ND YEAR_CHAMP)-9-MPC- 7. In a mixture of CH COOH and CH COONa, the ratio of salt to acid concentration is increased by ten folds. The ph of the solution will increase by : (A) Zero (B) (C) 7. The compressibility factor for a real gas at high pressure is : Pb (A) (B) (C) RT Pb RT RT Pb 7. Two closed vessel A and B of equal volume containing air at pressure P and temperature T are connected to each other through a narrow open tube. If the temperature of one is now maintained at T and other at T (where T > T ) then that what will be the final pressure? T PT PT P (A) (B) (C) P T T T T T T T 7. The correct order of temperature of a real gas is : (I) Boyle s temperature (II) Critical temperature (III) Inversion temperature (A) III > I > II (B) I > II > III (C) II > I > III I > III > II 74. The following equilibria are given by N H NH ; K N O NO; K H O HO; K The equilibrium constant of the reaction NH 5 O NO HO in terms of K, K and K is (A) KK K (B) KK K (C) KK K KK K 75. A + B AB [A ] [B] da dt.. x Ms.. x Ms..4 8 x Ms Order of reaction with respect to A and B are respectively : (A), (B), (C),,

13 RT-II ( ND YEAR_CHAMP)-9-MPC- 76. In which of the following equilibrium, the value of K p is less than K c? (i) N O 4 NO (ii) N + O NO (iii) N H NH (iv) SO4 O SO Correct option is : (A) i, ii (B) ii, iii (C) i, iii iii, iv 77. If the equilibrium constants of the two reactions, NH N + H and N H NH are K and K respectively at 5C, then the relation between K and K is : (A) K K (B) K (C) K K K K K 78. The vapour density of PCl 5 is 4.5 but when heated to C, its vapour density is reduced to 6. The degree of dissociation of PCl 5 at this temperature will be : (A) 6.8% (B) 68% (C) 46% 64% 79. For the reaction, PCl 5 (g) PCl (g) + Cl (g), the forward reaction at constant temperature is favoured by : (i) introducing an inert gas at constant volume (ii) introducing chlorine gas at constant volume (iii) introducing an inert gas at constant pressure (iv) increasing the volume of the container Correct option is : (A) i, ii (B) ii, iii (C) iii, iv i, iv 8. When g CaCO was put into litre flask and heated to 8C, 5% of CaCO remained unreacted at equilibrium. K p for decomposition of CaCO is : (A).45 atm (B).45 atm (C).45 atm.45 atm 8. Cl P Cl bond angles in PCl 5 molecule are : (A) and 9 (B) 6 and 9 (C) 6 and and 8. During the reduction C H 4 + O CO + H O ; The hybridized state of carbon changes from (A) sp to sp (B) sp to sp (C) sp to sp sp to sp

14 RT-II ( ND YEAR_CHAMP)-9-MPC-4 8. Among the following species identify isostructural pairs NF NO BF, H O PF 5 I II III IV V (A) (I, II) and (III, IV) (B) (I, V) and (II, III) (C) (I, IV) and (II, III) (I, IV) and (V, III) 84. The structure of PF 4 Cl will be (A) Trigonal bipyramidal with Cl at equatorial position (B) Trigonal bipyramidal with Cl at axial position (C) Square pyramidal Pentagonal 85. The molecule of hydrogen atom is formed due to the overlapping of orbitals of two hydrogen atoms. Which of the following types of overlapping takes place in the formation of H molecule? (A) (B) (C) All of these 86. The correct order of increasing O O bond length is (A) O O O (B) O O O (C) O O O O O O 87. Which of the following arrangements of molecules is correct on the basis of their dipolemoment (A) BF > NF > NH (B) NF > BF > NH (C) NH > NF > BF NH > BF > NF 88. In which of the following ionisation process, the bond order has increased and the magnetic power has changed? (A) N N (B) C C (C) NO NO O O 89. N accepts electron and coverts into N, where the electron goes? (A) Anti bonding molecular orbital (B) bonding molecular orbital (C) bonding molecular orbital antibonding molecular orbital. 9. Bond energies in NO, NO and NO are such as (A) NO NO NO (B) NO NO NO (C) NO NO NO NO NO NO

15 RT-II ( ND YEAR_CHAMP)-9-MPC-5 FIITJEE RT II (CHAMPIONS_ ND YEAR) MAINS_ANSWERS DATE: 7..8 MATHEMATICS PHYSICS CHEMISTRY. C. B. C 4. A 5. A 6. B 7. B 8. B 9. B. B. A. B. B 4. A 5. C 6. B 7. A 8. B 9. B. D. A. B. A 4. A 5. C 6. C 7. A 8. C 9. B. A. B. A. A 4. A 5. C 6. D 7. D 8. A 9. B 4. B 4. B 4. B 4. A 44. D 45. C 46. A 47. A 48. C 49. B 5. A 5. Bonus 5. A 5. B 54. A 55. B 56. Bonus 57. B 58. D 59. D 6. C 6. C 6. A 6. B 64. B 65. A 66. C 67. B 68. D 69. B 7. B 7. B 7. B 7. A 74. A 75. A 76. D 77. C 78. B 79. C 8. A 8. A 8. A 8. C 84. A 85. A 86. B or A 87. C 88. C or D 89. A 9. C

(D) (A) Q.3 To which of the following circles, the line y x + 3 = 0 is normal at the point ? 2 (A) 2

(D) (A) Q.3 To which of the following circles, the line y x + 3 = 0 is normal at the point ? 2 (A) 2 CIRCLE [STRAIGHT OBJECTIVE TYPE] Q. The line x y + = 0 is tangent to the circle at the point (, 5) and the centre of the circles lies on x y = 4. The radius of the circle is (A) 3 5 (B) 5 3 (C) 5 (D) 5