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Class 11 IIT JEE 2018 : Science

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Abhishek Bagal
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Page 1 1. PHYSICS : English & Hindi x and y displacements of a particle are given as x(t)5a sinvt and y(t)5a sin2vt. Its trajectory will look like : (1) (2) (3) (4) 1. 09 x y S , x(t)5a sinvt y(t)5a sin2vt, M , - , ? (1) (2) (3) (4) Page 2 2. PHYSICS : English & Hindi If a body moving in a circular path maintains constant speed of 10 ms21, then which of the following correctly describes relation between acceleration and radius ? 2. 09 U U U ( S ) 10 ms21 U U U , , U U ( ) U ? (1) (1) (2) (2) (3) (3) (4) (4) Page 3 3. A block of mass m510 kg rests on a horizontal table. The coefficient of friction between the block and the table is 0.05. When hit by a bullet of mass 50 g moving with speed v, that gets embedded in it, the block moves and comes to stop after moving a distance of 2 m on the table. 3. If a freely falling object were to acquire v after being dropped from height 10 H, then neglecting energy losses and taking g510 ms22, the value of H is close to : speed (1) 0.2 km (3) 0.4 km (2) (4) 4. ( U ) m510 kg U U 50.05 U 50 g v U U U , U 2 m S U L , H M U S v 10 U , - , (g510 0.3 km 0.2 km (3) 0.4 km (4) 4. ms22) (1) (2) 0.5 km A block of mass m50.1 kg is connected to a spring of unknown spring constant k. It is compressed to a distance x from its equilibrium position and released from rest. H U 0.3 km 0.5 km m50.1 kg ( S ) S U k S x U U U S U S x After approaching half the distance 2 from equilibrium position, it hits another block and comes to rest momentarily, while the other block moves with a velocity 3 ms 21. The total initial energy of the spring is : U M L , , U 3 ms21 U , U (2) (2) (1) 1.5 J (3) 0.3 J (4) 5. 09 PHYSICS : English & Hindi 0.6 J 0.8 J A uniform solid cylindrical roller of mass m is being pulled on a horizontal surface with force F parallel to the surface and applied at its centre. If the acceleration of the cylinder is a and it is rolling without slipping then the value of F is : (1) ma (3) (4) (2) x 2 (1) 1.5 J (3) 0.3 J (4) 5. U U U U U 0.6 J 0.8 J U U U U F U, U, U U U U U ( ) a U U , F m (1) ma 3 ma 2 (3) 3 ma 2 5 ma 3 (4) 5 ma 3 2 ma (2) 2 ma Page 4 6. 7. Consider a thin uniform square sheet made of a rigid material. If its side is a , mass m and moment of inertia I about one of its diagonals, then : (1) I> (2) ma 2 ma 2 <I< 24 12 (3) I5 (4) I5 8. ma 2 12 ma 2 24 7. T2 ; r3 (2) T ; r2 (4) T; (3) 6. ma 2 12 A very long (length L) cylindrical galaxy is made of uniformly distributed mass and has radius R (R<<L). A star outside the galaxy is orbiting the galaxy in a plane perpendicular to the galaxy and passing through its centre. If the time period of star is T and its distance from the galaxy s axis is r, then : (1) T;r r from a water tap of diameter 2 cm then p the Reynolds number for the flow is (density of water510 3 kg/m 3 and viscosity of water51023 Pa.s) close to : 5500 (2) 11,000 (4) 1100 (3) 550 , , U, U ( U) a , m U , I (1) I> (2) ma 2 ma 2 <I< 24 12 (3) I5 ma 2 12 (4) I5 ma 2 24 (1) T2 ; r3 (3) T;r (4) 8. ma 2 12 ( ) ( L) U , R (R<<L) U , U U U U U $ U , U U r U U T U (2) If it takes 5 minutes to fill a 15 litre bucket (1) 09 PHYSICS : English & Hindi T ; r2 T; r U U 2 cm p 15 U U U U 5 U ( , 5103 kg/m3 51023 Pa.s ) , U U (1) 5500 (3) 550 (2) (4) 11,000 1100 Page 5 9. 09 PHYSICS : English & Hindi If two glass plates have water between them and are separated by very small distance (see figure), it is very difficult to pull them apart. It is because the water in between forms cylindrical surface on the side that gives rise to lower pressure in the water in comparison to atmosphere. If the radius of the cylindrical surface is R and surface tension of water is T then the pressure in water between the plates is lower by : (1) T 4R (2) T 2R (3) 4T R (4) 2T R 9. U U ( U ) U U U U U , , U U U U ( U) U U U ( c U) R c U T , U ? (1) T 4R (2) T 2R (3) 4T R (4) 2T R Page 6 10. PHYSICS : English & Hindi An ideal gas goes through a reversible cycle a b c d has the V - T diagram shown below. Process d a and b c are adiabatic. 10. 09 a b c d , V - T U d a b c L c The corresponding P - V diagram for the process is (all figures are schematic and not drawn to scale) : , , P - V U ( U S U U S U ) (1) (1) (2) (2) (3) (3) (4) (4) Page 7 11. In an ideal gas at temperature T, the average force that a molecule applies on the walls of a closed container depends on q T as T . A good estimate for q is : (1) 2 (3) 1 2 (4) 1 4 (2) 12. 13. 09 PHYSICS : English & Hindi 11. 1 , m U U U , T U, Tq U U U , q U (1) 2 (3) 1 2 (4) 1 4 (2) A simple harmonic oscillator of angular frequency 2 rad s21 is acted upon by an external force F5sint N. If the oscillator is at rest in its equilibrium position at t50, its position at later times is proportional to : 1 (1) sint 1 1 sin 2t 2 U 2 rad s21 U s , F5sint U (N) t50 U, , S U S , , S ? (2) sint 1 1 cos 2t 2 (1) sint 1 1 sin 2t 2 (3) cost 2 1 sin 2t 2 (2) sint 1 1 cos 2t 2 (4) sint 2 1 sin 2t 2 (3) cost 2 1 sin 2t 2 (4) sint 2 1 sin 2t 2 A bat moving at 10 towards a wall sends a sound signal of 8000 Hz towards it. On reflection it hears a sound of frequency f. The value of f in Hz is close to (speed of sound5320 ms21) 12. ms21 (1) 8258 (3) 8000 (2) (4) 8516 8424 13. 10 ms21 U U , U U 8000 Hz ( ) U ( ) U U f , , 320 ms21 , Hz f U (1) 8258 (3) 8000 (2) (4) 8516 8424 Page 8 14. 09 PHYSICS : English & Hindi A thin disc of radius b52a has a concentric hole of radius a in it (see figure). It carries uniform surface charge s on it. If the electric field on its axis at height h (h<<a) from its centre is given as Ch then value of C is : (1) s ae 0 (2) s 2ae0 (3) s 4ae0 (4) s 8ae0 14. US ( ) b U ( U ) a (b52a) S U c U s U h U, (h<<a), l Ch , C (1) s ae 0 (2) s 2ae0 (3) s 4ae0 (4) s 8ae0 Page 9 15. Shown in the figure are two point charges 1Q and 2Q inside the cavity of a spherical shell. The charges are kept near the surface of the cavity on opposite sides of the centre of the shell. If s1 is the surface charge on the inner surface and Q1 net charge on it and s2 the surface charge on the outer surface and Q2 net charge on it then : (1) (2) (3) (4) 16. 15. s1 0, Q1 0 U , U ( ) U U U - 1Q 2Q U U U U U , U U U U U U , U U ( c U ) U, c U s1 s2 U U Q1 Q2 s2 0, Q2 0 (1) s1 0, Q1 0 s2 0, Q2 5 0 (2) s1 0, Q1 5 0 s2 5 0, Q2 5 0 (3) s2 5 0, Q2 5 0 (4) s1 0, Q1 5 0 s1 0, Q1 5 0 s1 5 0, Q1 5 0 If the capacitance of a nanocapacitor is measured in terms of a unit u made by combining the electronic charge e , Bohr radius a0 , Planck s constant h and speed of light c then : (1) u5 e2 c ha0 (2) u5 e2 h ca0 (3) u5 (4) 09 PHYSICS : English & Hindi e 2 a0 hc hc u5 2 e a0 16. s2 0, Q2 0 s2 0, Q2 5 0 s1 0, Q1 5 0 s2 5 0, Q2 5 0 s1 5 0, Q1 5 0 s2 5 0, Q2 5 0 U U , u , U e , U- a0 , S U h c (1) u5 e2 c ha0 (2) u5 e2 h ca0 (3) u5 e 2 a0 hc (4) hc u5 2 e a0 Page 10 17. PHYSICS : English & Hindi Suppose the drift velocity vd in a material varied with the applied electric field E as vd ; E . Then V - I graph for a wire made of such a material is best given by : (1) (2) (3) (4) 17. 09 , , vd , l E U U U U , vd ; E - ( ), U , U V - I ? (1) (2) (3) (4) Page 11 18. A 10V battery with internal resistance 1V and a 15V battery with internal resistance 0.6V are connected in parallel to a voltmeter (see figure). The reading in the voltmeter will be close to : (1) 11.9 V (3) 13.1 V (2) (4) 19. 09 PHYSICS : English & Hindi 18. (1) (2) (3) (4) 12.5 V 24.5 V A proton (mass m) accelerated by a potential difference V flies through a uniform transverse magnetic field B. The field occupies a region of space by width d . If a be the angle of deviation of proton from initial direction of motion (see figure), the value of sin a will be : (1) B qd 2 mV (2) q B d 2mV (3) q Bd 2mV (4) Bd qV 2m U U U U , U U , , 10V 1V U U U U , 15V 0.6V U U ( U ) , U U U U ( U U ) U 19. 11.9 12.5 13.1 24.5 V V V V V m U U , U ( m), S B U $ U d S U , U , U U a ( U ) , sin a (1) B qd 2 mV (2) q B d 2mV (3) Bd q 2mV (4) qV Bd 2m Page 12 20. A 25 cm long solenoid has radius 2 cm and 500 total number of turns. It carries a current of 15 A. If it is equivalent to a magnet of the same size and magnetization 20. (2) (3) (4) 21. 300 Am21 (3) 3H 1.67 H 6H 21. 3p Am21 (2) 30000 Am21 (4) 30000p Am21 (3) 30000p Am21 0.67 H (4) (1) 30000 Am21 (1) (2) / ), , 3p Am21 When current in a coil changes from 5 A to 2 A in 0.1 s, an average voltage of 50 V is produced. The self - inductance of the coil is : U 25 cm 2 cm U U 500 U U 15 A U U U , M (magnetic moment/volume), then ?M? is : (1) 09 PHYSICS : English & Hindi M ?M? ( 300 Am21 U l U , 0.1 s , 5 A 2 A , 50 V U , U S U (1) 0.67 H (3) 3H (2) (4) 1.67 H 6H Page 13 22. PHYSICS : English & Hindi In the circuits (a) and (b) switches S1 and S2 are closed at t50 and are kept closed for a long time. The variation of currents in the two circuits for t 0 are roughly shown by (figures are schematic and not drawn to scale) : (1) (2) (3) (4) 22. 09 U (a) (b) S S1 S2, t50 U U U , t 0 , U l U ( U ) , U ? ( U S U S U ) (1) (2) (3) (4) Page 14 23. An electromagnetic wave travelling in the x-direction has frequency of 231014 Hz and electric field amplitude of 27 Vm21. From the options given below, which one describes the magnetic field for this wave ? (1) 23. x- l U 231014 Hz l 27 Vm21 , , U U U ? (1) B ( x , t)5(331028 T) j sin 2 p(1.531028 x2231014 t) (2) (2) B ( x , t)5(931028 T) k (3) B ( x , t)5(931028 T) i (4) B ( x , t)5(931028 T) j You are asked to design a shaving mirror assuming that a person keeps it 10 cm from his face and views the magnified image of the face at the closest comfortable distance of 25 cm. The radius of curvature of the mirror would then be : (1) 30 cm (3) 60 cm (2) (4) 24 cm 224 cm B ( x , t)5(931028 T) k B ( x , t)5(931028 T) i sin 2 p(1.531028 x2231014 t) sin 1.531026 x2231014 t 24. B ( x , t)5(331028 T) j sin 2 p(1.531026 x2231014 t) sin 2 p(1.531028 x2231014 t) (4) sin 2 p(1.531028 x2231014 t) sin 2 p(1.531026 x2231014 t) (3) 09 PHYSICS : English & Hindi B ( x , t)5(931028 T) j sin 1.531026 x2231014 t 24. U 10 cm U U U U , - U U , 25 cm U , (1) 30 cm (3) 60 cm (2) (4) 24 cm 224 cm Page 15 25. A parallel beam of electrons travelling in x-direction falls on a slit of width d (see figure). If after passing the slit, an electron acquires momentum py in the y-direction then for a majority of electrons passing through the slit (h is Planck s constant) : (1) 26. ?py?d>h (4) ?py?d>>h (1) 18 (3) 308 (4) 27. 0.5 (3) 1.7 (2) (4) 26. 1.2 2.4 ?py?d>h (4) ?py?d>>h ?py?d<h U U 150 cm 5 cm 1 km U S 50 m U U ( U) , , U U, U U m U , u , u (1) 18 (3) 308 (4) 27. ?py?d ; h (2) (2) 608 (1) U U U d U U ( U ) U U , y- , py U , S U U U ( h ) (3) 158 de-Broglie wavelength of an electron accelerated by a voltage of 50 V is close to (?e?51.6310 219 C, m e59.1310 231 kg, h56.6310234 Js) : x- (1) ?py?d<h A telescope has an objective lens of focal length 150 cm and an eyepiece of focal length 5 cm. If a 50 m tall tower at a distance of 1 km is observed through this telescope in normal setting, the angle formed by the image of the tower is u, then u is close to : (2) 25. ?py?d ; h (2) (3) 09 PHYSICS : English & Hindi 158 608 U m U U U - U U 50 V (?e?51.6310 219 C, m e59.1310 231 kg, h56.6310234 Js) (1) 0.5 (3) 1.7 (2) (4) 1.2 2.4 Page 16 28. 29. 09 PHYSICS : English & Hindi If one were to apply Bohr model to a particle of mass m and charge q moving in a plane under the influence of a magnetic field B , the energy of the charged particle in the nth level will be : 28. B , U , m q U, U U ( ) , n S U (1) hqB n 2 pm (1) hqB n 2 pm (2) hqB n 4 pm (2) hqB n 4 pm (3) hqB n 8 pm (3) hqB n 8 pm (4) hqB n pm (4) hqB n pm In an unbiased n-p junction electrons diffuse from n - region to p - region because : (1) (2) (3) (4) holes in p - region attract them electrons travel across the junction due to potential difference electron concentration in n - region is more as compared to that in p - region only electrons move from n to p region and not the vice - versa 29. - n-p U n - p - U (1) (2) (3) (4) p - U ( ) U U U U U U n- p- U n p U (p n ) Page 17 30. Diameter of a steel ball is measured using a Vernier callipers which has divisions of 0.1 cm on its main scale (MS) and 10 divisions of its vernier scale (VS) match 9 divisions on the main scale. Three such measurements for a ball are given as : S.No. MS (cm) VS divisions 1. 0.5 8 2. 0.5 4 3. 0.5 6 If the zero error is 20.03 cm, then mean corrected diameter is : (1) 0.56 cm (3) 0.53 cm (2) (4) 09 PHYSICS : English & Hindi 0.59 cm 30. S U U (MSD) 0.1 cm , U (VS) 10 , 9 U U U ( U U ) 1. 2. 3. U cm 0.5 0.5 0.5 8 4 6 U U 20.03 cm, , 0.52 cm -o0o- (1) 0.56 cm (3) 0.53 cm (2) (4) 0.59 cm 0.52 cm -o0o- Page 1 1. A sample of a hydrate of barium chloride weighing 61 g was heated until all the water of hydration is removed. The dried sample weighed 52 g. The formula of the hydrated salt is : (atomic mass, Ba5137 amu, Cl535.5 amu) (1) 2. 3. BaCl2.4H2O (2) (3) (4) (3) 2. (2) Gas particles have negligible volume. (3) At high pressure, gas particles are difficult to compress. (4) Collisions of gas particles are perfectly elastic. ns np (n21)d (n22)f ns (n22)f (n21)d np ns (n21)d (n22)f np ns (n22)f np (n21)d 3. BaCl2.3H2O h U ? (1) A gas consists of many identical particles which are in continual motion. If the principal quantum number n56, the correct sequence of filling of electrons will be : (1) BaCl2.H2O (4) Which of the following is not an assumption of the kinetic theory of gases ? (4) (1) BaCl2.3H2O BaCl2.4H2O (3) Ba5137 amu, Cl535.5 amu) BaCl2.2H2O (4) (2) U U U U U U U 52 g U U ( U , 61 g (2) BaCl2.2H2O (1) 1. BaCl2.H2O (2) (3) 09 Chemistry : English & Hindi U M U S U U U U ^ S U n56 U U (1) ns np (n21)d (n22)f (3) ns (n21)d (n22)f np (2) (4) ns (n22)f (n21)d np ns (n22)f np (n21)d Page 2 4. After understanding the assertion and reason, choose the correct option. 4. Assertion : In the bonding molecular orbital (MO) of H2, electron density is increased between the nuclei. Reason : (1) (2) (3) (4) 5. (1) 1.493103 (3) 2.483104 nm (4) 6. (2) Assertion and reason are correct, but reason is not the correct explanation for the assertion. Assertion is incorrect, reason is correct. 2.483103 (3) (4) 5. (1) 35.0 torr and 0.480 (3) 30.5 torr and 0.389 (2) (4) 38.0 torr and 0.589 35.8 torr and 0.280 cA1cB U U U U S c U U U S c U U U U U c 360 kJ/mol 620 kJ/mol C - C U U ( 56.0231023, (1) 1.493103 nm (3) 2.483104 nm (2) (4) nm A solution at 208C is composed of 1.5 mol of benzene and 3.5 mol of toluene. If the vapour pressure of pure benzene and pure toluene at this temperature are 74.7 torr and 22.3 torr, respectively, then the total vapour pressure of the solution and the benzene mole fraction in equilibrium with it will be, respectively : : h56.62310234 J s) : nm 1.493104 nm : U U (1) Assertion and reason are correct and reason is the correct explanation for the assertion. Assertion is correct, reason is incorrect. U U The bonding MO is cA1c B, which shows destructive interference of the combining electron waves. The heat of atomization of methane and ethane are 360 kJ/mol and 620 kJ/mol, respectively. The longest wavelength of light capable of breaking the C - C bond is (Avogadro number56.0231023, h56.62310234 J s) : (2) 09 Chemistry : English & Hindi 6. 2.483103 nm 1.493104 nm U 1.5 U 3.5 U U U h U h U c 74.7 torr U 22.3 torr , c U 208C (1) 35.0 torr U 0.480 (3) 30.5 torr U 0.389 (2) (4) 38.0 torr 35.8 torr U U 0.589 0.280 Page 3 7. Gaseous N2O 4 dissociates into gaseous NO2 according to the reaction 7. N2O4(g) 2NO2(g) N2O4(g) 2NO2(g) U 1 atm U N2O4 0.2 U N2O4 (2) (2) (1) 1.56 g/L (3) 4.56 g/L (2) (3) (4) 6.22 g/L 106.25 mm Hg (3) 125 mm Hg 116.25 mm Hg 150 mm Hg (3) 4.56 g/L 3.11 g/L 6.22 g/L 1.1 V (1) U U U U (3) S U U U U s (Eext) Eext < 1.1 V Eext > 1.1 V, U (2) anode to cathode in both cases (1) 1.56 g/L Zn|Zn21 (1 M) ?? Cu21 (1 M) | Cu, cathode to anode in both cases follows first order kinetics. The pressure of a vessel containing only N 2 O 5 was found to increase from 50 mm Hg to 87.5 mm Hg in 30 min. The pressure exerted by the gases after 60 min. will be (Assume temperature remains constant) : (4) 8. cathode to anode and anode to cathode 2N2O5(g) 4NO2(g)1O2(g) (1) (4) anode to cathode and cathode to anode The reaction (2) 300 K 3.11 g/L A variable, opposite external potential (Eext) is applied to the cell Zn|Zn21 (1 M) ?? Cu21 (1 M) | Cu, of potential 1.1 V. When Eext < 1.1 V and Eext > 1.1 V, respectively electrons flow from : (1) 9. N2O4 NO2 U At 300 K and 1 atm pressure, the degree of dissociation of N2O4 is 0.2. If one mole of N2O4 gas is contained in a vessel, then the density of the equilibrium mixture is : (4) 8. 09 Chemistry : English & Hindi (4) 9. U U U U S U U U 2N2O5(g) 4NO2(g)1O2(g) 30 min , N2O5 , 87.5 mm Hg 60 min ( ) : 50 mm Hg (1) 106.25 mm Hg (3) 125 mm Hg (2) (4) 116.25 mm Hg 150 mm Hg Page 4 10. The following statements relate to the adsorption of gases on a solid surface. Identify the incorrect statement among them : (1) Enthalpy of adsorption is negative (3) On adsorption, the residual forces on the surface are increased (2) (4) 11. Group 16 and period 6 (3) Group 16 and period 5 12. metal carbonate (3) metal sulphide (2) (4) 13. 11. 12. (3) Calgon s method (4) Ion exchange method Treatment with washing soda 13. U U, c U O c M U U S M , U U 5s2 5p4 S (1) 16 U 6 (3) 16 U 5 17 U 17 U 5 6 c , S U (1) U (3) U (4) Permanent hardness in water cannot be cured by : (2) U, c U U c U (2) metal hydroxide Boiling (3) (4) metal oxide (1) (2) Group 17 and period 6 (1) (1) (4) Group 17 and period 5 In the isolation of metals, calcination process usually results in : U c U U (2) On adsorption decrease in surface energy appears as heat (1) (4) 10. Entropy of adsorption is negative In the long form of the periodic table, the valence shell electronic configuration of 5s2 5p4 corresponds to the element present in : (2) 09 Chemistry : English & Hindi U U U S U U U (1) (3) (2) (4) U U Page 5 14. The correct order of thermal stability of hydroxides is : (1) (2) (3) (4) 15. 16. Fluorine 17. (4) pentagonal planar An aqueous solution of a salt X turns blood red on treatment with SCN2 and blue on treatment with K4[Fe(CN)6]. X also gives a positive chromyl chloride test. The salt X is : 18. (3) U U U . . . . U. (VSEPR) h U, XeOF4 (1) m U U (3) c U (4) U U CuCl2 Cu(NO3)2 (2) FeCl3 (4) Fe(NO3)3 Which molecule/ion among the following cannot act as a ligand in complex compounds ? (1) CO (3) CH4 (4) Mg(OH)2 < Sr(OH) 2 < Ca(OH) 2 < Ba(OH)2 X SCN2 U U K4[Fe(CN)6] U X U U U U X (2) (2) Mg(OH)2 < Ca(OH) 2 < Sr(OH) 2 < Ba(OH)2 U (2) octahedral Ba(OH)2 < Ca(OH) 2 < Sr(OH) 2 < Mg(OH)2 (1) (4) 16. Ba(OH)2 < Sr(OH) 2 < Ca(OH) 2 < Mg(OH)2 (2) trigonal bipyramidal square pyramidal (3) 15. Chlorine (2) (1) (4) Sulphur The geometry of XeOF4 by VSEPR theory is : (3) (3) Mg(OH)2 < Sr(OH) 2 < Ca(OH) 2 < Ba(OH)2 (3) (1) (2) Mg(OH)2 < Ca(OH) 2 < Sr(OH) 2 < Ba(OH)2 Nitrogen U U S (1) Ba(OH)2 < Ca(OH) 2 < Sr(OH) 2 < Mg(OH)2 (1) (4) 14. Ba(OH)2 < Sr(OH) 2 < Ca(OH) 2 < Mg(OH)2 The least number of oxyacids are formed by : (2) 09 Chemistry : English & Hindi 17. (1) CuCl2 (3) Cu(NO3)2 (4) 18. FeCl3 Fe(NO3)3 / U ? CN2 (1) CO Br2 (3) CH4 (2) (4) CN2 Br2 Page 6 19. The correct statement on the isomerism associated with the following complex ions, (a) (b) 20. 21. (1) U (b) (c) (2) (b) and (c) show geometrical and optical isomerism (3) (b) and (c) show only geometrical isomerism (4) 20. CH4 (2) CO (4) O3 CO 2 1.4 g of an organic compound was digested according to Kjeldahl s method and the ammonia evolved was absorbed in 60 mL of M/10 H 2 SO 4 solution. The excess sulphuric acid required 20 mL of M/10 NaOH solution for neutralization. The percentage of nitrogen in the compound is : (a) (a) U (b) U (b) U (c) U U (b) (c) U U U U, U , U U U (PAN) X , X (1) CH4 (3) CO 2 (2) (4) 21. [Ni(H2O)3(NH3)3]21 : CO O3 1.4 g U U (1) 3 60 mL, M/10, H2SO4 U U U , 20 mL, M/10, NaOH U (3) 10 (2) (2) (4) 22. U (a) and (b) show only geometrical isomerism Photochemical smog consists of excessive amount of X, in addition to aldehydes, ketones, peroxy acetyl nitrile (PAN), and so forth. X is : (3) [Ni(H2O)5NH3]21, [Ni(H2O)4(NH3)2]21 (a) and (b) show geometrical and optical isomerism (1) (a) (b) (2) (4) U [Ni(H2O)4(NH3)2]21 and [Ni(H2O)3(NH3)3]21 is : (3) 19. [Ni(H2O)5NH3]21, (c) (1) 09 Chemistry : English & Hindi 5 24 The optically inactive compound from the following is : (1) 2 - chloropropanal (3) 2 - chlorobutane (2) (4) (1) 3 (3) 10 (4) 22. 5 24 2 - chloropentane (1) 2 - chloro - 2 - methylbutane (3) 2 - U (2) 2 - U U (4) 2 - U - 2 - U 2 - U U Page 7 Chemistry : English & Hindi 09 23. 23. A is : A (1) (1) (2) (2) (3) (3) (4) 24. (4) A compound A with molecular formula C 10 H 13 Cl gives a white precipitate on adding silver nitrate solution. A on reacting with alcoholic KOH gives compound B as the main product. B on ozonolysis gives C and D. C gives Cannizaro reaction but not aldol condensation. D gives aldol condensation but not Cannizaro reaction. A is : (1) (4) 24. A C10H13Cl , U U U U A KOH U U M B B - U U U C D C U , U U D U , U U A (1) (2) (3) C6H52CH22CH22CH22CH22Cl (2) (3) (4) C6H52CH22CH22CH22CH22Cl Page 8 25. In the presence of a small amount of phosphorous, aliphatic carboxylic acids react with chlorine or bromine to yield a compound in which a - hydrogen has been replaced by halogen. This reaction is known as : (1) Wolff - Kischner reaction (3) Hell - Volhard - Zelinsky reaction (2) (4) 26. (2) (3) (4) 25. S U S U U U U a - U U U (1) - U (3) - U- S (2) Etard reaction Rosenmund reaction Arrange the following amines in the order of increasing basicity. (1) 09 Chemistry : English & Hindi (4) 26. U U U U U (1) (2) (3) (4) Page 9 27. Match the polymers in column-A with their main uses in column-B and choose the correct answer : 27. Column - B Paints and lacquers (ii) Rain coats (iii) Manufacture of toys (iv) Computer discs -A -B U Column - A (A) Polystyrene (i) (B) Glyptal (C) Polyvinyl Chloride (D) Bakelite (1) (A) - (ii), (B) - (i), (C) - (iii), (D) - (iv) (3) (A) - (ii), (B) - (iv), (C) - (iii), (D) - (i) (2) (4) 28. (2) (3) (4) (B) (C) (A) - (iii), (B) - (i), (C) - (ii), (D) - (iv) (D) (A) - (iii), (B) - (iv), (C) - (ii), (D) - (i) glucose and fructose in equimolar amounts galactose and fructose in equimolar amounts (1) (2) (3) (4) 28. glucose only glucose and galactose in equimolar amounts is used as : 29. (3) Analgesic (3) (1) Cu 21 (2) Pb21 (4) Co21 (3) (2) Antacid As31 -oOo- (4) 30. (i) (ii) (iii) (iv) - B U U U U US (A) - (ii), (B) - (i), (C) - (iii), (D) - (iv) (A) - (iii), (B) - (i), (C) - (ii), (D) - (iv) (A) - (ii), (B) - (iv), (C) - (iii), (D) - (i) (A) - (iii), (B) - (iv), (C) - (ii), (D) - (i) M ? (1) Antihistamine The cation that will not be precipitated by H2S in the presence of dil HCl is : U U U U 29. Insecticide (4) - A S U U S U U (1) U U (2) U U U (3) (4) U U (1) (2) 30. (A) Complete hydrolysis of starch gives : (1) 09 Chemistry : English & Hindi U S U U HCl S , (1) (2) (3) (4) Cu 21 Pb21 As31 Co21 -oOo- H2S Page 1 1. In a certain town, 25% of the families own a phone and 15% own a car ; 65% families own neither a phone nor a car and 2,000 families own both a car and a phone. Consider the following three statements : (a) (b) 1. 5% families own both a car and a phone. 40,000 families live in the town. (1) Only (a) and (b) are correct. (3) Only (b) and (c) are correct. Then, (4) 2. (1) 3. 17 (2) 2 2 (3) 3 2 2 (4) 5 2 2 root of this equation : U k e R, then the real (1) does not exist. (2) exists and is equal to (3) exists and is equal to 2 (4) exists and is equal to 1. 3. 1 . 2 1 . 2 U 40,000 U U U (a) (b) (2) (a) (c) (4) (a), (b) (c) (b) (c) {v e C/?v242i?[r} m U U , {z e C/?z21?[?z1i?} m U U , r (1) If 213i is one of the roots of the equation 2x329x21kx21350, (c) (3) 2. U 35% U U (1) All (a), (b) and (c) are correct. 5% U U (b) , Only (a) and (c) are correct. The largest value of r for which the region represented by the set {v e C/?v242i?[r} is contained in the region represented by the set {z e C/?z21?[?z1i?}, is equal to : U , 25% U U 15% U ; 65% U U U U , 2,000 U U U U U (a) 35% families own either a car or a phone. (c) (2) 09 MATHEMATICS : English & Hindi 17 (2) 2 2 (3) 3 2 2 (4) 5 2 2 213i, U 2x329x21kx21350, k e R , U S (1) l (2) l (3) l 2 (4) l 1 U U 1 2 U U 1 2 U U Page 2 4. The least value of the product xyz for which the determinant x 1 1 1 y 1 1 1 z 4. 2 16 2 (4) 21 (3) 5. x 1 1 1 y 1 1 1 z U , 22 2 216 2 (4) 21 28 A 5 0 21 1 0 ? , - (1) A42I5A21I (1) A42I5A21I (3) A21I5A(A22I) (3) A21I5A(A22I) (4) 1120 (3) 1880 26.5 (3) 29.5 28 31 A31I5A(A32I) L 15 15 U , L , U (1) 1120 (3) 1880 (4) 7. A32I5A(A2I) 15 (2) 1960 (1) (4) 6. 1240 Let the sum of the first three terms of an A.P. be 39 and the sum of its last four terms be 178. If the first term of this A.P. is 10, then the median of the A.P. is : (2) (4) A31I5A(A32I) (1) (4) (2) A32I5A(A2I) The number of ways of selecting 15 teams from 15 men and 15 women, such that each team consists of a man and a woman, is : (2) 7. 5. xyz (2) (3) 28 0 21 If A 5 , then which one of the 1 0 following statements is not correct ? (2) 6. (1) 22 2 (2) U is non-negative, is : (1) 09 MATHEMATICS : English & Hindi 1240 1960 U 39 U 178 U 10 , U (1) 26.5 (3) 29.5 (2) (4) 28 31 Page 3 8. If the coefficients of the three successive terms in the binomial expansion of (11x)n are in the ratio 1 : 7 : 42, then the first of these terms in the expansion is : (1) 6 th (3) 8 th (2) (4) 9. 10. 9 th (3) 7775 30 r516 (r 1 2)(r 2 3) is equal to : 30 r516 (r 1 2)(r 2 3) 7775 e x 2 cosx 2 sin x (2) (3) 5 4 (2) is equal to : 10. 4 2 2 2 2 e x 2 cosx 2 lim sin 2 x (1) 3 (2) 3 2 (3) 5 4 (4) y 5 2 sint22t cost at t 5 7770 x 0 2 p , is : 4 11. x52 cost12t sint, y52 sint22t cost t5 (1) 4 U (3) (4) U U 2 U (2) U U 7780 (4) The distance, from the origin, of the normal to the curve, x52 cost 1 2t sint, (4) 9. (3) 3 2 (3) 7770 3 (2) U 7785 (1) (1) (3) (1) x 0 11. U U 7780 2 (4) (1) (4) 7785 lim (11x)n m S U 1 : 7 : 42 , S U (2) (1) (4) 8. 7 th The value of (2) 09 MATHEMATICS : English & Hindi p 4 2 2 2 2 U Page 4 12. If Rolle s theorem holds for the function f (x)52x 3 1bx 2 1cx, x e [21, 1], at the 12. 21 (4) 23 (3) 13. 14. f (x)52x31bx21cx, x e [21, 1] x5 1 2 2b1c U U 1 (2) 1 point x 5 , then 2b1c equals : 2 (1) 09 MATHEMATICS : English & Hindi (1) 2 Let the tangents drawn to the circle, x21y2516 from the point P(0, h) meet the x-axis at points A and B. If the area of DAPB is minimum, then h is equal to : 1 (2) 21 (4) 23 (3) U U , 2 (1) 4 3 P(0, h) x21y2516 U S U x- A B U DAPB , h U U (2) 3 3 (1) 4 3 (3) 3 2 (2) 3 3 (4) 4 2 (3) 3 2 (4) 4 2 The integral to : dx 3 5 (x 1 1) 4 (x 2 2) 4 (1) x 11 4 4 1C x 22 (2) x 22 4 4 1C x 11 (3) 4 x 11 4 2 1C 3 x 22 (4) 4 x 22 4 2 1C 3 x 11 is equal 13. 14. 1 dx 3 5 (x 1 1) 4 (x 2 2) 4 (1) x 11 4 4 1C x 22 (2) x 22 4 4 1C x 11 (3) 4 x 11 4 2 1C 3 x 22 (4) 4 x 22 4 2 1C 3 x 11 1 1 1 1 1 1 1 U U Page 5 15. x For x > 0, let f ( x ) 5 1 log t dt . Then 11t 15. 17. x>0 1 f (x) 1 f x 1 (log x )2 4 (1) 1 (log x )2 4 (2) 1 (log x )2 2 (2) 1 (log x )2 2 (3) log x (3) log x (4) 1 log x 2 4 (4) 1 log x 2 4 (1) 3 5 (2) 3 4 (3) 1 3 (4) 4 3 If y(x) is the solution of the differential dy 5 x 2 14x29 , x 22 dx and y(0)50, then y(24) is equal to : equation ( x12) (1) 0 (3) 21 (2) (4) 1 2 16. 17. log t dt 11t , U U (1) The area (in square units) of the region bounded by the curves y12x 2 50 and y13x251, is equal to : x f (x) 5 1 1 f ( x ) 1 f is equal to : x 16. 09 MATHEMATICS : English & Hindi y12x250 y13x251 m U U h ( ) U U (1) 3 5 (2) 3 4 (3) 1 3 (4) 4 3 y(x), U dy 5 x 2 14x29 , x 22 U dx y(0)50, , y(24) U U ( x12) (1) 0 (3) 21 (2) (4) 1 2 Page 6 18. The points 0, 8 , (1, 3) and (82, 30) : 3 (1) form an obtuse angled triangle. (3) form a right angled triangle. (2) (4) 19. 20. 18. form an acute angled triangle. (3) U U U S L, P(1, 2) U U U U U P U m L1 U L U (22, 1) U , L L1 U (1) 4 12 , 5 5 (1) 4 12 , 5 5 (2) 11 29 , 20 10 (2) 11 29 , 20 10 (3) 3 17 , 10 5 (3) 3 17 , 10 5 (4) 3 23 , 5 10 (4) 3 23 , 5 10 If y13x50 is the equation of a chord of the circle, x 2 1y 2 230x50, then the equation of the circle with this chord as diameter is : x 21y 2 13x19y50 (2) x 21y 2 23x19y50 (4) x 21y 2 13x29y50 (3) x 21y 2 23x29y50 20. (82, 30) (4) 19. 8 0, , (1, 3) 3 (1) (2) lie on a straight line. Let L be the line passing through the point P(1, 2) such that its intercepted segment between the co-ordinate axes is bisected at P. If L1 is the line perpendicular to L and passing through the point (22, 1), then the point of intersection of L and L1 is : (1) 09 MATHEMATICS : English & Hindi y13x50, x21y2230x50 U , , , , U (1) x 21y 2 13x19y50 (3) x 21y 2 23x29y50 (2) (4) x 21y 2 23x19y50 x 21y 2 13x29y50 Page 7 21. 22. If the tangent to the conic, y265x 2 at (2, 10) touches the circle, x21y218x22y5k (for some fixed k) at a point (a, b) ; then (a, b) is : (1) 6 10 , 2 17 17 (2) 8 2 , 2 17 17 (3) 4 1 , 2 17 17 (4) 7 6 , 2 17 17 An ellipse passes through the foci of the hyperbola, 9x 224y 2 536 and its major and minor axes lie along the transverse and conjugate axes of the hyperbola respectively. If the product of eccentricities 21. 22. 1 , then which of the 2 following points does not lie on the ellipse ? of the two conics is 23. 09 MATHEMATICS : English & Hindi (1) ( (2) y265x2 (2, 10) U S U x21y218x22y5k ( k ) (a, b) U S U , (a, b) (1) 6 10 , 2 17 17 (2) 8 2 , 2 17 17 (3) 4 1 , 2 17 17 (4) 7 6 , 2 17 17 , U 9x224y2536 U U S , - 1 2 U S ? ) (1) ( 39 , 3 2 (2) 39 , 3 2 (3) 1 3 13 , 2 2 (3) 1 3 13 , 2 2 (4) 13 , 6 2 (4) 13 , 6 2 13 , 0 If the points (1, 1, l) and (23, 0, 1) are equidistant from the plane, 3x14y212z11350, then l satisfies the equation : (1) 3x 2 210x1750 (3) 3x 2 110x21350 (2) (4) 3x 2 110x1750 3x 2 210x12150 23. 13 , 0 ) (23, 0, 1) 3x14y212z11350 US , l, U c U U (1, 1, l) (1) 3x 2 210x1750 (3) 3x 2 110x21350 (2) (4) 3x 2 110x1750 3x 2 210x12150 Page 8 24. If the shortest distance between the lines y 11 x 21 z 5 5 , (a 21) and a 21 1 x1y1z115052x2y1z13 is a value of a is : 25. (1) 16 2 19 (2) 19 2 16 (3) 32 19 (4) 19 32 Let a and b be two unit vectors such ( ) c 5 a 1 2 b 1 3 a 3 b , then equal to : (1) 55 (2) 51 (3) 43 (4) 37 (1) (2) (3) (4) 20 C10 2 10 25. (1) 2 16 19 (2) 2 19 16 (3) 32 19 (4) 19 32 26. 55 (2) 51 (3) 43 (4) 37 2 20 ( ) , U U 10 P(X) P(X) A B U , S , , A B U U (1) (3) C10 b (1) ( 2 10 2 1 ) 20 5 3 , a (2) 2 10 a 1 3 c 5 a 12 b 13 a 3 b ( 2 10 2 1 ) 2 20 y 11 x 21 z 5 5 , (a 21) 1 a 21 x1y1z115052x2y1z13 U is Let X be a set containing 10 elements and P(X) be its power set. If A and B are picked up at random from P(X), with replacement, then the probability that A and B have equal number of elements, is : U 5 3 . If that 26. 24. 1 , then 3 09 MATHEMATICS : English & Hindi (4) X 20 C10 2 10 ( 210 2 1 ) 2 20 ( 210 2 1 ) 2 10 20 C10 2 20 Page 9 27. A factory is operating in two shifts, day and night, with 70 and 30 workers respectively. If per day mean wage of the day shift workers is ` 54 and per day mean wage of all the workers is ` 60, then per day mean wage of the night shift workers (in `) is : (1) 66 (3) 74 (2) (4) 28. 29. (4) (758, 458) (3) 74 75 (1) (158, 1058) (3) (458, 758) (4) , x > 1, 69 ABC , (2) 29. (4) 65 tan21 156 tan21(5) The contrapositive of the statement If it is raining, then I will not come , is : (1) If I will come, then it is not raining. (3) If I will not come, then it is not raining. If I will not come, then it is raining. If I will come, then it is raining. -o0o- C5608 (1058, 158) (758, 458) f ( x ) 5 2tan21 x 1 sin21 (2) p (4) 65 tan21 156 (3) 30. , x > 1 11x 2x 2 p 2 (1) p a 521 3 b , f (5) U U p 2 (2) (4) 66 , ( A, B) U U (458, 758) 2x If f ( x ) 5 2tan21 x 1 sin21 1 1 x2 then f (5) is equal to : (2) 28. (158, 1058) 4 (1) (4) (1058, 158) (3) 30. 75 (2) (1) U U , U , 70 30 U U U U ` 54 U ` 60 , U U U (` ) (2) a 5 2 1 3 and C5608. b Then the ordered pair ( A, B) is equal to : (3) 27. 69 In a DABC, (1) 09 MATHEMATICS : English & Hindi 4 tan21(5) U , (1) , U (3) , U (2) (4) , U , U -o0o-

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