ÊÒÁà ÁflôÊÊŸ. ÿᜠa, b, c ÊÒ U d apple Ê Ÿ apple Ê appleˇê òêèá U Ê. (English+Hindi) PHYSICS. 1. A physical quantity P is described by the relation

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1 PHYSICS ÊÒÁà ÁflôÊÊŸ 1. A physical quantity P is described by the relation 1 4 P = a b c d If the relative errors in the measurement of a, b, c and d respectively, are %, 1%, % and 5%, then the relative error in P will be : 8% () 1% % 5%. A car is standing 00 m behind a bus, which is also at rest. The two start moving at the same instant but with different forward accelerations. The bus has acceleration m/s and the car has acceleration 4 m/s. The car will catch up with the bus after a time of : 110 s 1. ÊÒÁà UÊÁ Ê P ÁŸêŸ œ mê UÊ Á U ÊÁ Ã Ë ÊÃË Ò 1 4 P = a b c d ÿᜠa, b, c ÊÒ U d apple Ê Ÿ apple Ê appleˇê òêèá U Ê %, 1%, % fl 5% Êapple ÃÊapple P apple Ê appleˇê òêèá U ÊappleªË 8% () 1% % 5%. Ê U U UË ÈÿË apple 00 m Ë appleu π«ë Ò ŒÊappleŸÊapple Ë ˇÊáÊ ª- ª ª ÁŒÁ Ê àfl UáÊ apple ø ŸÊ ÊÈM UÃapple Ò Ê àfl UáÊ m/s ÃÕÊ Ê U Ê àfl UáÊ 4 m/s Ò Á ßapple ÿ ÊŒ ÿ Ê U Ã È ø ÊÿappleªË? () 10 s 10 s 15 s 110 s () 10 s 10 s 15 s 1 IX - PHYSICS

2 . Two particles A and B of equal mass M are moving with the same speed v as shown in the figure. They collide completely inelastically and move as a single particle C. The angle θ that the path of C makes with the X-axis is given by :. ÊŸ Œ ÿ ÊŸ M apple ŒÊapple áê A ÃÕÊ B ÊŸ øê v apple ÁøòÊÊŸÈ Ê U ø U apple Ò fl ÍáÊ ÃÿÊ àÿêsõ ÉÊ^ UÃapple Ò ÃÕÊ ÉÊ^ apple ÊŒ áê C Ë Ã U ø Ãapple Ò ÊappleáÊ θ, Êapple áê C Ê Õ X- ˇÊ apple ŸÊÃÊ Ò, Êapple ÁŸêŸ ê 㜠apple ÁŒÿÊ ÊÿappleªÊ + tanθ= 1 + tanθ= 1 () tanθ= 1 () tanθ= 1 tanθ= 1 ( 1+ ) tanθ= 1 ( 1+ ) 1 tanθ= tanθ= 1 + IX - PHYSICS

3 4. The machine as shown has rods of length 1 m connected by a pivot at the top. The end of one rod is connected to the floor by a stationary pivot and the end of the other rod has a roller that rolls along the floor in a slot. As the roller goes back and forth, a kg weight moves up and down. If the roller is moving towards right at a constant speed, the weight moves up with a : 4. ÁøòÊ apple ÁŒπÊÿË ªÿË ÊËŸ Ë ŒÊapple U«Êapple, Á Ÿ Ë ê Êß 1 m Ò, apple UË Á UÊapple Êapple ÊÕ œè Uʪ Sà Á ÿê ªÿÊ Ò U«Ê ÊÁπ UË Á UÊ ÁSÕ U œè UË mê UÊ» Ê apple Êapple«Ê ªÿÊ Ò ÃÕÊ ŒÍ UË U«apple ÊÁπ UË Á appleu U UÊapple U ªÊ Ò Êapple Á» Ê U Ÿapple πê øapple apple ø ÃÊ Ò fl UÊapple U ʪapple Ë appleu ø ÃÊ Ò ÃÊapple kg Ê Ê U U ŸËøapple ø ÃÊ Ò ÿᜠUÊapple U ŒÊÁ ŸË ÁŒ ÊÊ apple ÊŸ øê apple ø ÃÊ Ò ÃÊapple fl Ê U ø appleªê, constant speed () decreasing speed increasing speed speed which is th of that of the 4 roller when the weight is 0.4 m above the ground ÊŸ øê apple () ÉÊ UÃË Èß øê apple ÃË Èß øê apple øê Êapple Á UÊapple U Ë øê Ê Ò fl 4 Ê U» Ê apple 0.4 m Ë øêß U Ò IX - PHYSICS

4 5. A conical pendulum of length 1 m makes an angle θ=45 w.r.t. Z-axis and moves in a circle in the XY plane. The radius of the circle is 0.4 m and its center is vertically below O. The speed of the pendulum, in its circular path, will be : (Take g=10 ms ) 5. ÊÊ fl (conical) ŒÊapple, Á Ë ê Êß 1 m Ò ÊÒ U Êapple Z- ˇÊ apple θ=45 apple ÊappleáÊ U Ò, XY à apple ªÊapple Ê Ê U Õ apple ø ÃÊ Ò ªÊapple Ê Ê U Õ Ë ÁòÊíÿÊ 0.4 m Ò ÊÒ U Ê apple 㜠Á ãœè O apple UË ŸËøapple Ò ŒÊapple Ë ªÁà ªÊapple Ê Ê U Õ apple ÊappleªË (g=10 ms ) 0.4 m/s () 4 m/s 0. m/s m/s 0.4 m/s () 4 m/s 0. m/s m/s 4 IX - PHYSICS

5 6. A circular hole of radius R is made in a 4 thin uniform disc having mass M and radius R, as shown in figure. The moment of inertia of the remaining portion of the disc about an axis passing through the point O and perpendicular to the plane of the disc is : 6. Œ ÿ ÊŸ M ÃÕÊ ÁòÊíÿÊ R flê apple ÊŸ Á«US apple R ÁòÊíÿÊ Ê ªÊapple Ê Ê U appleuœ, ÁøòÊÊŸÈ Ê U, Á ÿê 4 ªÿÊ Ò Á ŒÈ O apple ÊŸapple flê apple ÃÕÊ Á«US apple à apple ê flã ˇÊ apple Ê appleˇê, Á«US apple øapple È Êª Ê, «àfl ÊÉÊÍáÊ ÊappleªÊ () 19 MR 56 7 MR MR MR 56 () 19 MR 56 7 MR MR MR 56 5 IX - PHYSICS

6 7. The mass density of a spherical body is given by ρ (r)= k for r R and r ρ (r)=0 for r > R, where r is the distance from the centre. The correct graph that describes qualitatively the acceleration, a, of a test particle as a function of r is : 7. ªÊapple Ê Ê U Á á«u Ê Œ ÿ ÊŸ ÉÊŸàfl Ò ρ (r)= k r r R ÃÕÊ ρ (r)=0 r > R, Ê r apple 㜠apple ŒÍ UË Ò ÁŸêŸ apple apple ÊÒŸ Ê ª Ê$» UˡÊáÊ áê apple àfl UáÊ a Êapple r apple» Ÿ apple ªÈáÊÊà M apple Œ ÊÊ ÃÊ Ò? () () 6 IX - PHYSICS

7 8. A steel rail of length 5 m and area of cross section 40 cm is prevented from expanding along its length while the temperature rises by 10 C. If coefficient of linear expansion and Young s modulus of steel are K 1 and Nm respectively, the force developed in the rail is approximately : 10 7 N () N 10 9 N 10 5 N 8. 5 m ê Êß ÃÕÊ 40 cm ŸÈ SÕ Ê U apple ˇÊappleòÊ» Ë S UË Ë U UË Ê ê Êß apple ŸÈÁŒ Ê ÁflSÃÊ UáÊ UÊapple Ê ÊÃÊ Ò Á Ê ÃÊ ÊŸ 10 C ÊÿÊ ÊÃÊ Ò ÿᜠS UË Ê appleuπëÿ Ê U ªÈáÊÊ ÃÕÊ ÿ ª àÿêsõãê ªÈáÊÊ Ê K 1 ÃÕÊ Nm Ò ÃÊapple U UË apple à ÛÊ Ê ÁŸ Uà ʟ ÊappleªÊ 10 7 N () N 10 9 N 10 5 N 9. Two tubes of radii r 1 and r, and lengths l 1 and l, respectively, are connected in series and a liquid flows through each of them in stream line conditions. P 1 and P are pressure differences across the two tubes. If P is 4P 1 and l is l 1 4, then the radius r will be equal to : r 1 () r 1 4r 1 9. ŒÊapple ŸÁ ÿê Á Ÿ Ë ÁòÊíÿÊÿapple Ê r 1 fl r ÃÕÊ ê Êß ÿê, l 1 fl l Ò, Êapple üêappleáêë apple Êapple«Ê ªÿÊ Ò ÊÒ U Ÿ apple Œ fl œê UÊ appleuπëÿ flê apple ÃÊ Ò Ë ÃÕÊ ŒÍ UË Ÿ Ë apple Á UÊapple apple Ëø apple ŒÊ Êãà U Ê P 1 ÃÕÊ P Ò ÿᜠP Ê ÊŸ 4P 1 ÃÕÊ l Ê ÊŸ l 1 Êapple ÃÊapple ÁòÊíÿÊ 4 r Ê ÊŸ ÊappleªÊ r 1 r 1 () r 1 4r 1 r 1 7 IX - PHYSICS

8 10. For the P-V diagram given for an ideal gas, 10. ÊŒ Ê ªÒ Ê P-V Ê appleuπ ÁŒÿapple ªÿapple ÁøòÊ apple Œ ÊÊ ÿê ªÿÊ Ò out of the following which one correctly represents the T-P diagram? ÁŒÿapple ªÿapple Ê appleuπêapple apple apple ÊÒŸ- Ê Ë T-P Ê appleuπ Œ ÊÊ ÿappleªê? () () 8 IX - PHYSICS

9 11. N moles of a diatomic gas in a cylinder are at a temperature T. Heat is supplied to the cylinder such that the temperature remains constant but n moles of the diatomic gas get converted into monoatomic gas. What is the change in the total kinetic energy of the gas? () 0 1 nrt nrt 5 nrt 1. A block of mass 0.1 kg is connected to an elastic spring of spring constant 640 Nm 1 and oscillates in a damping medium of damping constant 10 kg s 1. The system dissipates its energy gradually. The time taken for its mechanical energy of vibration to drop to half of its initial value, is closest to : s ().5 s 5 s 7 s 11. Ám U ÊáÊÈ ªÒ apple N Êapple T ÃÊ ÊŸ U Á appleá«u U apple Œ Ò Á appleá«u U apple c Ê ß Ê U flêá Ã Ë ÊÃË Ò Á apple Ám U ÊáÊÈ ªÒ apple n Êapple U ÊáÊÈ ªÒ apple Á ŸÊ ÃÊ ÊŸ Œ apple Á UflÁà à Êapple ÊÃapple Ò ªÒ Ë È ªÁÃ Ê apple Á ÃŸÊ Á Uflà Ÿ ÊappleªÊ? () 0 1 nrt nrt 5 nrt kg Œ ÿ ÊŸ apple ªÈ U apple Êapple àÿêsõ ÁS ª, Á Ê ÁS ª ÁŸÿÃÊ 640 Nm 1 Ò, apple Êapple«Ê ªÿÊ Ò ÿ ªÈ U Ê fl ãœÿ Êäÿ, Á Ê fl ãœÿ ªÈáÊÊ 10 kg s 1 Ò, apple ŒÊapple Ÿ ªÁà UÃÊ Ò ÿ ÁŸ Êÿ œë appleu-œë appleu ŸË Ê ÿáãã UÃÊ Ò ÁŸ Êÿ apple ŒÊapple Ÿ Ë ÿê ÁòÊ Ê Êapple apple Ê UÁê ÊŸ apple ÊœÊ ÊappleŸapple apple ªŸapple flê apple ÿ Ê ÁŸ Uà ʟ ÊappleªÊ s ().5 s 5 s 7 s 9 IX - PHYSICS

10 1. A standing wave is formed by the superposition of two waves travelling in opposite directions. The transverse displacement is given by 5 yx (, t) 0.5 sin π = x cos(00 πt). 4 What is the speed of the travelling wave moving in the positive x direction? (x and t are in meter and second, respectively.) 160 m/s () 90 m/s 180 m/s 10 m/s 1. ŒÊapple à Uªapple, Êapple Áfl UËà ÁŒ ÊÊ apple ø U Ë Ò, apple äÿê UÊapple áê apple ªÊ Ë Ã Uª ŸÃË Ò Á Ê ŸÈ SÕ ÁflSÕÊ Ÿ ÁŸêŸ Ë UáÊ mê UÊ Á πê Ê ÃÊ Ò 5 yx (, t) 0.5 sin π = x cos(00 πt). 4 +x ˇÊ Ë Ã U» ø Ÿapple flê Ë ªÊ Ë Ã Uª Ë ªÁà ÊappleªË (ÿ Ê x fl t Ê Ë U U fl apple á«u apple Ò ) 160 m/s () 90 m/s 180 m/s 10 m/s 10 IX - PHYSICS

11 14. Four closed surfaces and corresponding charge distributions are shown below. 14. øê U Œ Îc U ÃÕÊ Ÿ apple Êflapple Ê ÁflãÿÊ Êapple ÁŸêŸ ÁøòÊ apple Œ ÊÊ ÿê ªÿÊ Ò Let the respective electric fluxes through the surfaces be Φ 1, Φ, Φ and Φ 4. Then : Φ 1 < Φ =Φ > Φ 4 () Φ 1 > Φ > Φ > Φ 4 Φ 1 =Φ =Φ =Φ 4 Φ 1 > Φ ; Φ < Φ 4 ÿᜠŸ apple Îc U apple h flòlèã ç Ä Ê Φ 1, Φ, Φ ÃÕÊ Φ 4 Êapple ÃÊapple Φ 1 < Φ =Φ > Φ 4 () Φ 1 > Φ > Φ > Φ 4 Φ 1 =Φ =Φ =Φ 4 Φ 1 > Φ ; Φ < Φ 4 11 IX - PHYSICS

12 15. A combination of parallel plate capacitors is maintained at a certain potential difference. 15. Êãà U å apple U œêá UòÊÊapple apple ÿêapple Ÿ Êapple ÁŸÁ øã Áfl flêãã U U UπÊ ªÿÊ Ò (ÁøòÊ ŒappleÁπÿapple) When a mm thick slab is introduced between all the plates, in order to maintain the same potential difference, the distance between the plates is increased by.4 mm. Find the dielectric constant of the slab. () A uniform wire of length l and radius r has a resistance of 100 Ω. It is recast into a wire of radius r. The resistance of new wire will be : 1600 Ω () 400 Ω 00 Ω 100 Ω mm Êapple appleu ªÈ U apple Êapple Ë œêá UòÊÊapple Ë å apple UÊapple apple Ëø «UÊ Ê ÊÃÊ Ò, ÃÊapple fl Ë Áfl flêãã U ŸÊÿapple UπŸapple apple Á å apple UÊapple apple Ëø Ë ŒÍ UË Êapple.4 mm apple ÊŸÊ «ÃÊ Ò ªÈ U apple Ê UÊflÒlÈÃÊ ÊappleªÊ () ê Êß l ÃÕÊ ÁòÊíÿÊ r apple ÊŸ ÃÊ U Ê Áà UÊappleœ 100 Ω Ò ß Êapple ÁòÊíÿÊ r apple ÃÊ U apple ÈŸ UÊ Ê ÊÃÊ Ò Ÿÿapple ÃÊ U Ê Áà UÊappleœ ÊappleªÊ 1600 Ω () 400 Ω 00 Ω 100 Ω 1 IX - PHYSICS

13 17. The figure shows three circuits I, II and III which are connected to a V battery. If the powers dissipated by the configurations I, II and III are P 1, P and P respectively, then : 17. ÁŒÿapple ªÿapple ÁøòÊ apple ÃËŸ Á U Õ, I, II fl III Êapple V Ò U UË apple Êapple«Ê ªÿÊ Ò ÿᜠÁflãÿÊ I, II ÃÕÊ III Ê P 1, P ÃÕÊ P ÊÁÄà ÿÿ UÃapple Ò ÃÊapple P 1 > P > P P 1 > P > P () P 1 > P > P P > P 1 > P () P 1 > P > P P > P 1 > P P > P > P 1 P > P > P A negative test charge is moving near a long straight wire carrying a current. The force acting on the test charge is parallel to the direction of the current. The motion of the charge is : away from the wire () towards the wire parallel to the wire along the current parallel to the wire opposite to the current 18. áêêà UˡÊáÊ Êflapple Ê, Ëœapple ê apple ÃÊ U, Á apple œê UÊ U Ë Ò, apple ÁŸ U ø U Ê Ò UˡÊáÊ Êflapple Ê U ªŸapple flê Ê œê UÊ Ë ÁŒ ÊÊ apple Êãà U Ò Êflapple Ê Ë ªÁà ÊappleªË ÃÊ U apple ŒÍ U () ÃÊ U Ë Êapple U ÃÊ U apple Êãà U fl œê UÊ Ë ÁŒ ÊÊ apple ÃÊ U apple Êãà U fl œê UÊ Ë Áfl UËà ÁŒ ÊÊ apple 1 IX - PHYSICS

14 19. A uniform magnetic field B of 0. T is along the positive Z-direction. A rectangular loop (abcd) of sides 10 cm 5 cm carries a current I of 1 A. Out of the following different orientations which one corresponds to stable equilibrium? T Ê ÊŸ øèê Ëÿ ˇÊappleòÊ B œÿêà Z- ˇÊ Ë Ã U» ÁŒÁ ÊÃ Ò 10 cm ÃÕÊ 5 cm È Ê Êapple flê apple ÊÿÃÊ Ê U Ê Ê (abcd) apple 1 A œê UÊ I ÃË Ò ÁŸêŸ apple apple ÊÒŸ- Ê ÁŒª ÁflãÿÊ ÁSÕ U ÊêÿÊflSÕÊ Êapple ŒÁ Ê Ã UÃÊ Ò? () () 14 IX - PHYSICS

15 0. A sinusoidal voltage of peak value 8 V and angular frequency 0/s is applied to a series LCR circuit. Given that R=5 Ω, L=5 mh and C=1000 µf. The total impedance, and phase difference between the voltage across the source and the current will respectively be : 0. 8 V ûê Áfl fl ÃÕÊ 0 s 1 ÊappleáÊËÿ ÊflÎÁûÊ flê apple íÿêfl Ëÿ Áfl fl Êapple üêappleáêë LCR Á U Õ apple ªÊÿÊ ªÿÊ Ò ÁŒÿÊ Ò R=5 Ω, L=5 mh ÊÒ U C=1000 µf Á U Õ Ë È ÁÃ ÊœÊ ÃÕÊ dêappleã Áfl fl fl œê UÊ apple Ëø Ê Ã U Ê ÊappleªÊ Ω and tan () 7 Ω and Ω ÊÒ U 1 5 tan 10 Ω and 7 Ω and 1 8 tan 1 5 tan 1. The electric field component of a monochromatic radiation is given by E = E 0 i cos k z cos ωt Its magnetic field B is then given by : () 7 Ω ÊÒ U Ω ÊÒ U 7 Ω ÊÒ U 1 8 tan 1 5 tan 1. Á Ë fláêë ÿ ÁflÁ UáÊ apple flòlèã ˇÊappleòÊ ÉÊ U Êapple ÁŸêŸ Ê U apple ÿäã Á ÿê Ê ÃÊ Ò E = E 0 i cos k z cos ωt () E 0 j sin k z cos ωt c E 0 j sin k z sin ωt c E 0 j sin k z sin ωt c E 0 j cos k z cos ωt c apple øèê Ëÿ ˇÊappleòÊ B Ê ÊŸ ÊappleªÊ E 0 j sin k z cos ωt c () E 0 j sin k z sin ωt c E 0 j sin k z sin ωt c E 0 j cos k z cos ωt c 15 IX - PHYSICS

16 . In an experiment a convex lens of focal length 15 cm is placed coaxially on an optical bench in front of a convex mirror at a distance of 5 cm from it. It is found that an object and its image coincide, if the object is placed at a distance of 0 cm from the lens. The focal length of the convex mirror is : 7.5 cm () 0.0 cm 5.0 cm 0.5 cm. A single slit of width 0.1 mm is illuminated by a parallel beam of light of wavelength 6000 Å and diffraction bands are observed on a screen 0.5 m from the slit. The distance of the third dark band from the central bright band is : mm () 9 mm 4.5 mm 1.5 mm 4. A Laser light of wavelength 660 nm is used to weld Retina detachment. If a Laser pulse of width 60 ms and power 0.5 kw is used the approximate number of photons in the pulse are : [Take Planck s constant h= Js] 10 0 () ÿêappleª apple ŒÊÒ UÊŸ, 15 cm» Êapple ŒÍ UË apple ûê apple Êapple Ê Ê apple ø U ûê Œ áê apple Ê Ÿapple 5 cm ŒÍ UË U ÊˇÊËÿ ÁSÕÁà apple UπÊ ªÿÊ Ò ÿᜠflsãè Êapple apple apple 0 cm Ë ŒÍ UË U UπÊ Êÿapple ÃÊapple flsãè ÃÕÊ Ê ÁÃÁ ê ÊÃË Êapple ÊÃapple Ò ûê Œ áê Ë» Êapple ŒÍ UË ÊappleªË 7.5 cm () 0.0 cm 5.0 cm 0.5 cm. 0.1 mm øêò«êß Ë Á Ê UË 6000 Å Ã UªŒÒÉÿ apple Êãà U Á UáÊ È apple ÊÁ ÊÃ Ë ÊÃË Ò ÊÒ U Áflflà Ÿ Òá«U Êapple Á Ê UË apple 0.5 m ŒÍ U ÁSÕà Œapple U ŒappleπÊ ÊÃÊ Ò ÃÎÃËÿ ŒËåà Òá«U Ë apple 㜠Ëÿ ŒËåà Òá«U apple ŒÍ UË ÊappleªË mm () 9 mm 4.5 mm 1.5 mm nm à UªŒÒÉÿ Ë apple$ U Êß U Êapple appleuá UŸÊ ÁflÿÊapple Ÿ Êapple Êapple«Ÿapple apple Á ÿêappleª Á ÿê ÊÃÊ Ò ÿᜠ60 ms øêò«êß fl 0.5 kw ÊÁÄà apple apple$ U S 㜠(pulse) Ê ÿêappleª Á ÿê Êÿapple ÃÊapple S 㜠apple» Êapple UÊÚŸÊapple Ë ÅÿÊ ª ª ÊappleªË [å Ê ÁŸÿÃÊ h= Js] 10 0 () IX - PHYSICS

17 5. The acceleration of an electron in the first orbit of the hydrogen atom (n=1) is : () h π m r h 8π m r h 4π m r h 4πm r 6. Imagine that a reactor converts all given mass into energy and that it operates at a power level of 10 9 watt. The mass of the fuel consumed per hour in the reactor will be : (velocity of light, c is 10 8 m/s) 0.96 gm () 0.8 gm 4 10 gm gm 7. The current gain of a common emitter amplifier is 69. If the emitter current is 7.0 ma, collector current is : 9.6 ma () 6.9 ma 0.69 ma 69 ma 5. Êß«UÊapple Ÿ U ÊáÊÈ Ë Õ ˇÊÊ (n=1) apple ß appleä UÊÚŸ Ê àfl UáÊ ÊappleªÊ () h π m r h 8π m r h 4π m r h 4πm r 6. À ŸÊ ËÁ, U UË, ÊappleÁ ÁŒÿapple ªÿapple ÍáÊ Œ ÿ ÊŸ Êapple Ê apple Œ ÃË Ò fl 10 9 watt Ë ÊÁÄà Sà U U ø ÃË Ò UË apple ÉÊá appleu apple π à ÊappleŸapple flê apple ßZœŸ Ê Œ ÿ ÊŸ ÊappleªÊ ( Ê Ê Ê flappleª, c= 10 8 m/s) 0.96 gm () 0.8 gm 4 10 gm gm 7. ÿáÿc U à flœ Ê œê UÊ Ê 69 Ò ÿáœ à œê UÊ Ê ÊŸ 7.0 ma Êapple ÃÊapple ª Ê œê UÊ Ê ÊŸ ÊappleªÊ 9.6 ma () 6.9 ma 0.69 ma 69 ma 17 IX - PHYSICS

18 8. A signal is to be transmitted through a wave of wavelength λ, using a linear antenna. The length l of the antenna and effective power radiated P eff will be given respectively as : (K is a constant of proportionality) () l λ, P eff = K λ λ l, P eff = K 8 λ λ 16 l, P eff = K λ λ l, P eff = K 5 λ 1 8. à UªŒÒÉÿ λ Ë Ã Uª mê UÊ Œapple Ê Êapple appleuπëÿ ã appleuÿê apple ÊÁ Uà UŸÊ Ò ã appleuÿê Ë ê Êß l ÃÕÊ ÊflË à Á à ÊÁÄà P eff Ê Ê ÊŸ ÊappleªÊ (K ÊŸÈ ÊÁà ÁSÕ UÊ (constant of proportionality) Ò) () l λ, P eff = K λ λ l, P eff = K 8 λ λ 16 l, P eff = K λ λ l, P eff = K 5 λ 1 18 IX - PHYSICS

19 9. In a meter bridge experiment resistances are connected as shown in the figure. Initially resistance P=4 Ω and the neutral point N is at 60 cm from A. Now an unknown resistance R is connected in series to P and the new position of the neutral point is at 80 cm from A. The value of unknown resistance R is : 9. Á Ë Ë U U appleãè ÿêappleª apple ŒÊÒ UÊŸ, Áà UÊappleœÊapple Êapple ÁøòÊÊŸÈ Ê U Êapple«Ê ªÿÊ Ò ÊÈM apple Áà UÊappleœ P=4 Ω ÃÕÊ Ÿ Á ãœè N, Á ãœè A apple, 60 cm Ë ŒÍ UË U Ò ôêêã Áà UÊappleœ R Êapple P apple ÊÕ üêappleáêë apple Êapple«Ê ÊÃÊ Ò Á apple Ÿ Á ãœè Ë Ÿß ÁSÕÁà Á ŒÈ A apple 80 cm ŒÍ U Êapple ÊÃË Ò ôêêã Áà UÊappleœ R Ê ÊŸ ÊappleªÊ 5 Ω () 6 Ω 7 Ω 0 Ω 5 Ω () 6 Ω 7 Ω 0 Ω 19 IX - PHYSICS

20 0. In an experiment to determine the period of a simple pendulum of length 1 m, it is attached to different spherical bobs of radii r 1 and r. The two spherical bobs have uniform mass distribution. If the relative difference in the periods, is found to be s, the difference in radii, r 1 r is best given by : 1 cm () 0.1 cm 0.5 cm 0.01 cm - o 0 o - 0. ÿêappleª apple, 1 m ê Êß Ë U ŒÊapple Ê ÊflÃ Ê ÁŸ Ê Ÿapple appleãè Êapple r 1 ÃÕÊ r ÁòÊíÿÊ Êapple apple ª- ª ªÊapple Ê Ê U Êapple apple Êapple«Ê ÊÃÊ Ò ŒÊappleŸÊapple ªÊapple Ê Ê U Êapple Êapple apple Œ ÿ ÊŸ Áflà UáÊ ÊŸ Ò ÿᜠÊflÃ Ê Êapple Ê Ê appleˇê à U s ÊÿÊ ªÿÊ Êapple ÃÊapple Ÿ Ë ÁòÊíÿÊ Êapple apple ãã U, r 1 r Ê ÁŸ Uà ʟ ÊappleªÊ 1 cm () 0.1 cm 0.5 cm 0.01 cm - o 0 o - 0 IX - PHYSICS

21 CHEMISTRY U ÊÿŸ ÊÊSòÊ 1. An ideal gas undergoes isothermal expansion at constant pressure. During the process : enthalpy increases but entropy decreases. () enthalpy remains constant but entropy increases. enthalpy decreases but entropy increases. Both enthalpy and entropy remain constant.. 50 ml of 0. M ammonia solution is treated with 5 ml of 0. M HCl. If pk b of ammonia solution is 4.75, the ph of the mixture will be :.75 () The electron in the hydrogen atom undergoes transition from higher orbitals to orbital of radius 11.6 pm. This transition is associated with : Lyman series () Balmer series Paschen series Brackett series 1. ÊŒ Ê ªÒ ÁSÕ U ŒÊ U ÃÊ Ëÿ Ê UáÊ UÃË Ò ß apple ãõòà Ë ÃË Ò UãÃÈ ã UÊÚ Ë ÉÊ UÃË Ò () ãõòà Ë ÁSÕ U U ÃË Ò UãÃÈ ã UÊÚ Ë ÃË Ò ãõòà Ë ÉÊ UÃË Ò UãÃÈ ã UÊÚ Ë ÃUË Ò ãõòà Ë ÃÕÊ ã UÊÚ Ë ŒÊappleŸÊapple Ë ÁSÕ U U ÃË Ò. 0. M ÊappleÁŸÿÊ Áfl ÿÿ apple 50 ml Êapple 0. M HCl apple 5 ml apple ÊÕ Á Î Ã Á ÿê ÊÃÊ Ò ÿᜠÊappleÁŸÿÊ Áfl ÿÿ apple pk b Ê ÊŸ 4.75 Êapple ÃÊapple Á üêáê Ê ph ÊappleªÊ.75 () Êß«UÊapple Ÿ U ÊáÊÈ apple ß appleä UÊÚŸ ìêã U ÊÚÁ U apple 11.6 pm ÁòÊíÿÊ flê apple ÊÚÁ U à áê UÃÊ Ò ß áê Ê ê 㜠Á apple Ò fl Ò Êß ÒŸ üêappleáêë () Ê U üêappleáêë Ê ÊŸ üêappleáêë apple apple U üêappleáêë 1 IX - CHEMISTRY

22 4. At 00 K, the density of a certain gaseous molecule at bar is double to that of dinitrogen (N ) at 4 bar. The molar mass of gaseous molecule is : 8 g mol 1 () 56 g mol 1 11 g mol 1 4 g mol 1 5. What quantity (in ml) of a 45% acid solution of a mono-protic strong acid must be mixed with a 0% solution of the same acid to produce 800 ml of a 9.875% acid solution? 0 () To find the standard potential of M + /M electrode, the following cell is constituted : Pt/M/M + (0.001 mol L 1 )/Ag + (0.01 mol L 1 )/Ag The emf of the cell is found to be 0.41 volt at 98 K. The standard potential of half reaction M + +e M at 98 K will be : 0.8 Volt () 0. Volt 1.8 Volt 0.66 Volt K U; Ê U U Uπapple Á Ë ªÒ Ëÿ áêè Ê ÉÊãÊàfl, 4 Ê U U Uπapple «UÊߟÊß UÊapple Ÿ (N ) apple ÉÊŸàfl Ê ŒÍŸÊ Ò ªÒ Ëÿ áêè Ê Êapple U Œ ÿ ÊŸ Ò 8 g mol 1 () 56 g mol 1 11 g mol 1 4 g mol 1 5. ÊappleŸÊapple ÊappleÁ U ê apple 45% Á «U Áfl ÿÿ Ë Á ÃŸË ÊòÊÊ (ml apple ) Ë ê apple 0% Áfl ÿÿ apple ÊÕ Á ÊÿË ÊŸË øêá Á 9.875% Á «U Áfl ÿÿ Ê 800 ml Ÿ Êÿ? 0 () M + /M ß ÒÄ UÊapple«U apple ÊŸ Áfl fl Êapple ÁŸ Ê Ÿapple apple Á ÁŸêŸ apple ŸÊÿÊ ªÿÊ Pt/M/M + (0.001 mol L 1 )/Ag + (0.01 mol L 1 )/Ag apple Ê ß..». 98 K,U 0.41 V ÊÿÊ ªÿÊ 98 K U, M + +e M, h Á Á ÿê Ê ÊŸ Áfl fl ÊappleªÊ 0.8 V () 0. V 1.8 V 0.66 V ) IX - CHEMISTRY

23 7. A gas undergoes change from state A to state B. In this process, the heat absorbed and work done by the gas is 5 J and 8 J, respectively. Now gas is brought back to A by another process during which J of heat is evolved. In this reverse process of B to A : 10 J of the work will be done by the gas. () 6 J of the work will be done by the gas. 10 J of the work will be done by the surrounding on gas. 6 J of the work will be done by the surrounding on gas. 8. Adsorption of a gas on a surface follows Freundlich adsorption isotherm. Plot of log m x versus log p gives a straight line with slope equal to 0.5, then : ( m x is the mass of the gas adsorbed per gram of adsorbent) Adsorption is independent of pressure. () Adsorption is proportional to the pressure. Adsorption is proportional to the square root of pressure. Adsorption is proportional to the square of pressure. 7. ªÒ flsõê A apple flsõê B Êapple ÊÃË Ò ß apple, ªÒ mê UÊ ÊÊappleÁ à c Ê ÃÕÊ Á ÿê ªÿÊ Êÿ Ê 5 J ÃÕÊ 8 J Ò ªÒ Êapple ŒÍ appleu mê UÊ ÈŸ A flsõê apple ÊÃapple Ò ß apple J c Ê ÁŸ ÃË Ò B apple A apple ß À appleu apple ªÒ mê UÊ 10 J Êÿ Á ÿê ÊÿappleªÊ () ªÒ mê UÊ 6 J Êÿ Á ÿê ÊÿappleªÊ ªÒ U Á Uflapple Ê mê UÊ Á ÿê ªÿÊ Êÿ 10 J ÊappleªÊ ªÒ U Á Uflapple Ê mê UÊ Á ÿê ªÿÊ Êÿ 6 J ÊappleªÊ 8. Á Ë Îc U U ªÒ Ê Áœ ÊÊapple áê,» ÊÚÿã«UÁ Áœ ÊÊapple áê ÃÊ Ê ŸÈ UáÊ UÃÊ Ò log p apple ÁflL h log m x Ê å Ê U U appleuπê ŒappleÃÊ Ò Á Ê S Êapple 0.5 apple UÊ U ÊÿÊ ªÿÊ, à ( m x, Áà ª Ê Áœ ÊÊapple mê UÊ Áœ ÊÊappleÁ à ªÒ Ê Œ ÿ ÊŸ Ò) Áœ ÊÊapple áê, ŒÊ U ÊÁüÊà Ÿ Ë Ò () Áœ ÊÊapple áê, ŒÊ apple ÊŸÈ ÊÃË Ò Áœ ÊÊapple áê, ŒÊ apple flª Í apple ÊŸÈ ÊÃË Ò Áœ ÊÊapple áê, ŒÊ apple flª apple ÊŸÈ ÊÃË Ò IX - CHEMISTRY

24 9. The rate of a reaction quadruples when the temperature changes from 00 to 10 K. The activation energy of this reaction is : (Assume activation energy and preexponential factor are independent of temperature; ln =0.69; R=8.14 J mol 1 K 1 ) 107. kj mol 1 () 5.6 kj mol kj mol kj mol A solution is prepared by mixing 8.5 g of CH Cl and g of CHCl. If vapour pressure of CH Cl and CHCl at 98 K are 415 and 00 mmhg respectively, the mole fraction of CHCl in vapour form is : (Molar mass of Cl=5.5 g mol 1 ) 0.16 () The electronic configuration with the highest ionization enthalpy is : [Ne] s p 1 () [Ne] s p [Ne] s p [Ar] d 10 4s 4p 9. ÃÊ 00 apple 10 K Á UflÁà à ÊappleŸapple apple Á Á ÿê Ë Œ U øê U ªÈŸÊ Êapple ÊÃË Ò ß Á Á ÿê Ë Á ÿáê Ê Ò : (ÿ ÊŸ U øá ÿapple Á Á ÿáê Ê ÃÕÊ Ë Ä ÊappleappleŸappleÁã Êÿ»Ò Ä U U ÃÊ U ÁŸ U Ÿ Ë Ò; ln =0.69; R=8.14 J mol 1 K 1 ) 107. kj mol 1 () 5.6 kj mol kj mol kj mol g CH Cl ÃÕÊ g CHCl Êapple Á Ê U Áfl ÿÿ ÃÒÿÊ U Á ÿê ÊÃÊ Ò ÿᜠ98 K U CH Cl ÃÕÊ CHCl apple flêc ŒÊ Ê 415 ÃÕÊ 00 mmhg Êapple ÃÊapple flêc M apple ÁSÕà CHCl Ê Êapple Ê Ò (Cl Ê Êapple U Œ ÿ ÊŸ=5.5 g mol 1 ) 0.16 () ëøã ÊÿŸŸ ãõòà Ë flê Ê ß appleä UÊÁŸ ÁflãÿÊ Ò [Ne] s p 1 () [Ne] s p [Ne] s p [Ar] d 10 4s 4p 4 IX - CHEMISTRY

25 1. The following reaction occurs in the Blast Furnace where iron ore is reduced to iron metal : Fe O (s)+ CO(g) Fe(l)+ CO (g) Using the Le Chatelier s principle, predict which one of the following will not disturb the equilibrium? Removal of CO () Removal of CO Addition of CO Addition of Fe O 1. Which one of the following is an oxide? KO () BaO SiO CsO 1. flêàÿê ^Ë (é ÊS U» UŸapple Ê) apple ÁŸêŸ Á Á ÿê ÊappleÃË Ò Á apple Êÿ UŸ ÿs øáÿã Êapple U Êÿ UŸ œêãè ŸÃÊ Ò; Fe O (s)+ CO(g) Fe(l)+ CO (g) apple- ÊÊÃÒÁ Á hêãã Ê ÿêappleª U apple ʪÈÁÄà ËÁ Á ÁŸêŸ apple apple ÊÒŸ Ê Êêÿ Êapple ÊÁflà Ÿ Ë appleuªê? CO Êapple ÁŸ Ê U UÊ ŒappleŸÊ () CO Êapple ÁŸ Ê U UÊ ŒappleŸÊ CO Êapple Á Ê ŒappleŸÊ Fe O Êapple Á Ê ŒappleŸÊ 1. ÁŸêŸ apple apple ÊÒŸ Ê, ÊÚÄ Êß«U Ò? KO () BaO SiO 14. Which of the following is a set of green house gases? CH 4, O, N, SO () O, N, CO, NO O, NO, SO, Cl CO, CH 4, N O, O CsO 14. ÁŸêŸ apple apple ÊÒŸ Ê ª ËŸ Ê ªÒ Êapple Ê ÈìÊÿ Ò? CH 4, O, N, SO () O, N, CO, NO O, NO, SO, Cl CO, CH 4, N O, O 5 IX - CHEMISTRY

26 15. The group having triangular planar structures is : BF, NF, CO () CO, NO, SO NH, SO, CO NCl, BCl, SO 15. fl ª È Á apple ÁòÊ ÊappleáÊ Ã Ëÿ UøŸÊflÊ apple Ò, Ò BF, NF, CO () CO, NO, SO NH, SO, CO NCl, BCl, SO 16. XeF 6 on partial hydrolysis with water produces a compound X. The same compound X is formed when XeF 6 reacts with silica. The compound X is : XeF () XeF 4 XeOF 4 XeO 17. The number of P OH bonds and the oxidation state of phosphorus atom in pyrophosphoric acid (H 4 P O 7 ) respectively are : four and four () five and four five and five four and five 16. XeF 6, apple ÊÕ Ê Á Ê - ÉÊ UŸ UŸapple U, ÿêò᪠X ŒappleÃÊ Ò ÿ Ë ÿêò᪠X à ŸÃÊ Ò XeF 6 Á Á Ê apple ÊÕ Á Á ÿê UÃÊ Ò ÿêò᪠X Ò XeF () XeF 4 XeOF 4 XeO 17. Êÿ UÊapple» ÊS» ÊappleÁ U Á «U (H 4 P O 7 ) apple P OH Ê ãœêapple Ë ÅÿÊ ÃÕÊ» ÊS» Êapple U U ÊáÊÈ Ë ÊÚÄ Ë UáÊ flsõê Ê Ò øê U ÃÕÊ øê U () Ê ø ÃÕÊ øê U Ê ø ÃÕÊ Ê ø øê U ÃÕÊ Ê ø 6 IX - CHEMISTRY

27 18. Which of the following ions does not liberate hydrogen gas on reaction with dilute acids? Ti + () V + Cr + Mn The correct sequence of decreasing number of π-bonds in the structures of H SO, H SO 4 and H S O 7 is : 18. ÁŸêŸ ÊÿŸÊapple apple apple ÊÒŸ Ê ÃŸÈ ê Êapple apple Á Á ÿê UŸapple U Êß«UÊapple Ÿ ªÒ Ÿ Ë ÁŸ Ê ÃÊ? Ti + () V + Cr + Mn H SO, H SO 4 ÃÕÊ H S O 7 Ë UøŸÊ apple π- Ê ãœêapple Ë ÉÊ UÃË ÅÿÊ Ê Ë Ò H SO > H SO 4 > H S O 7 () H SO 4 > H S O 7 > H SO H S O 7 > H SO 4 > H SO H S O 7 > H SO > H SO 4 H SO > H SO 4 > H S O 7 () H SO 4 > H S O 7 > H SO H S O 7 > H SO 4 > H SO H S O 7 > H SO > H SO 4 0. [Co (CO) 8 ] displays : one Co Co bond, six terminal CO and two bridging CO () one Co Co bond, four terminal CO and four bridging CO no Co Co bond, six terminal CO and two bridging CO no Co Co bond, four terminal CO and four bridging CO 0. [Co (CO) 8 ] Á ÿäã UÃÊ Ò Co Co Ê ãœ, U U UÁ Ÿ CO ÃÕÊ ŒÊapple appleãè œÿ CO () Co Co Ê ãœ, øê U U UÁ Ÿ CO ÃÕÊ øê U appleãè œÿ CO Co Co Ê ãœ Ÿ Ë, U U UÁ Ÿ CO ÃÕÊ ŒÊapple appleãè œÿ CO Co Co Ê ãœ Ÿ Ë, øê U U UÁ Ÿ CO ÃÕÊ øê U appleãè œÿ CO 7 IX - CHEMISTRY

28 1. A compound of molecular formula C 8 H 8 O reacts with acetophenone to form a single cross-aldol product in the presence of base. The same compound on reaction with conc. NaOH forms benzyl alcohol as one of the products. The structure of the compound is : 1. ÿêò᪠Á Ê áêè ÍòÊ C 8 H 8 O Ò, Á UÊapple»apple ŸÊappleŸ apple ˇÊÊ U Ë ÁSÕÁà apple Á Á ÿê U apple Ë Ê - À«UÊapple à ÊŒ ŸÊÃÊ Ò fl Ë ÿêò᪠Ê㌠NaOH apple ÊÕ Á Á ÿê U apple apple Á À Êapple ÊÚ, Êapple ŸŸappleflÊ apple à ÊŒÊapple apple apple Ò, ŸÊÃÊ Ò ÿêòáª Ë UøŸÊ Ò () () 8 IX - CHEMISTRY

29 . Which of the following compounds is most reactive to an aqueous solution of sodium carbonate?. ÁŸêŸ apple apple ÊÒŸ Ê ÿêòáª, ÊappleÁ«Uÿ Ê Êapple Ÿapple U apple Ëÿ Áfl ÿÿ apple ÁÃ, flê Áœ Á Á ÿê ÊË Ò? () (). In the following structure, the double bonds are marked as I, II, III and IV. ÁŸêŸ UøŸÊ apple, Ám Ê ãœêapple Êapple I, II, III ÃÕÊ IV apple ÁøÁqà Á ÿê ªÿÊ Ò Geometrical isomerism is not possible at site (s) : III () I I and III III and IV íÿêá ÃËÿ ÊflÿflÃÊ ß SÕÊŸ/ߟ SÕÊŸÊapple apple fl Ÿ Ë Ò III () I I ÃÕÊ III III ÃÕÊ IV 9 IX - CHEMISTRY

30 4. The major product of the following reaction is : 4. ÁŸêŸ Á Á ÿê Ê ÈÅÿ à ÊŒ Ò () () 10 IX - CHEMISTRY

31 5. The incorrect statement among the following is : α-d-glucose and β-d-glucose are anomers. () α-d-glucose and β-d-glucose are enantiomers. Cellulose is a straight chain polysaccharide made up of only β-d-glucose units. The penta acetate of glucose does not react with hydroxyl amine. 6. Which of the following is a biodegradable polymer? 5. ÁŸêŸ apple apple ª à ՟ Ò α-d-ç Í Êapple ÃÕÊ β-d-ç Í Êapple appleÿêapple U Ò () α-d-ç Í Êapple ÃÕÊ β-d-ç Í Êapple ÁÃÁ ê M Ò apple Í Êapple È oî π Ê Ê Ë Ò UÊß«U Ò Êapple apple fl β-d-ç Í Êapple Êapple apple ŸÊ Ò Ç Í Êapple Ê appleã UÊ Ë appleu U, Êß«UÊÁÄ apple ËŸ apple ÊÕ Á Á ÿê Ÿ Ë UÃÊ Ò 6. ÁŸêŸ apple apple ÊÒŸ Ê ÒflÁŸêŸŸËÿ È Ò? () () 11 IX - CHEMISTRY

32 7. The increasing order of the boiling points for the following compounds is : CH5OH (I) CH5OCH (IV) CH5Cl (II) (III) < (IV) < (II) < (I) () (IV) < (III) < (I) < (II) (II) < (III) < (IV) < (I) (III) < (II) < (I) < (IV) CH5CH (III) 8. Which of the following compounds will show highest dipole moment? 7. ÁŸêŸ ÿêò᪠Êapple apple ÄflÕŸÊ Êapple Ê ÃÊ È Ê Ò CH5OH (I) CH5OCH (IV) CH5Cl (II) (III) < (IV) < (II) < (I) () (IV) < (III) < (I) < (II) (II) < (III) < (IV) < (I) (III) < (II) < (I) < (IV) CH5CH (III) 8. ÁŸêŸ ÿêò᪠Êapple apple apple Á Ê Ámœ Èfl ÊÉÊÍáÊ flê Áœ ÊappleªÊ? (I) (II) (I) (II) (III) (IV) (III) (IV) (I) (I) () (II) () (II) (III) (III) (IV) (IV) 1 IX - CHEMISTRY

33 9. In the following reaction sequence : 9. ÁŸêŸ Á Á ÿê apple The compound I is : ÿêò᪠I Ò () () 0. Among the following compounds, the increasing order of their basic strength is : (I) (II) 0. ÁŸêŸ ÿêòáª Ê apple apple ˇÊÊ UËÿ Ê âÿ Ê ÃÊ È Ê Ò (I) (II) (III) (IV) (I) < (II) < (IV) < (III) () (I) < (II) < (III) < (IV) (II) < (I) < (IV) < (III) (II) < (I) < (III) < (IV) (III) (IV) (I) < (II) < (IV) < (III) () (I) < (II) < (III) < (IV) (II) < (I) < (IV) < (III) (II) < (I) < (III) < (IV) 1 IX - CHEMISTRY

34 MATHEMATICS ªÁáÊà 1. The function f : N N defined by x f ( x) = x 5 5, where N is the set of natural numbers and [x] denotes the greatest integer less than or equal to x, is : one-one and onto. () one-one but not onto. onto but not one-one. neither one-one nor onto.. The sum of all the real values of x satisfying the equation (x 1)(x +5x 50) =1 is : 16 () The equation Im iz + 1 = 0, z C, z i z i represents a part of a circle having radius equal to : () x 1.» Ÿ f : N N, f ( x) = x 5 mê UÊ 5 Á U ÊÁ à Ò, Ê N, Ê Î Ã ÅÿÊ Êapple Ê ÈìÊÿ Ò ÃÕÊ [x], x apple ÿê apple ÊŸ ûê ÍáÊÊZ Ò, Êapple Ò Ë ÃÕÊ Êë UÊŒ Ò () Ò Ë Ò UãÃÈ Êë UÊŒ Ÿ Ë Ò Êë UÊŒ Ò UãÃÈ Ò Ë Ÿ Ë Ò Ÿ ÃÊapple Ò Ë Ò ÊÒ U Ÿ Ë Êë UÊŒ Ò. Ë UáÊ (x 1)(x +5x 50) =1 Êapple ÃÈc U UŸapple flê apple x apple Ë flêsãáfl ÊŸÊapple Ê ÿêappleª Ò 16 () Ë UáÊ Im iz + 1 = 0, z C, z i z i flîûê apple ʪ Êapple ÁŸM Á à UÃË Ò, Á Ë ÁòÊíÿÊ Ò () IX - MATHEMATICS

35 4. For two matrices A and B, let A+B=B and A+B=I, where B is the transpose of B and I is identity matrix. Then : 5A+10B=I () 10A+5B=I B+A=I A+6B=I 4. ŒÊapple Ê ÿí Êapple A ÃÕÊ B apple Á ÊŸÊ A+B=B ÃÕÊ A+B=I Ò, Ê B Ê ÿí B Ê Á UflÃ Ò ÃÕÊ I Ãà Ê ÿí Ò, ÃÊapple 5A+10B=I () 10A+5B=I B+A=I A+6B=I 5. If x=a, y=b, z=c is a solution of the system of linear equations x+8y+7z=0 9x+y+z=0 x+y+z=0 such that the point (a, b, c) lies on the plane x+y+z=6, then a+b+c equals : 1 () The number of ways in which 5 boys and girls can be seated on a round table if a particular boy B 1 and a particular girl G 1 never sit adjacent to each other, is : 5 6! () 6 6! 7! 5 7! 5. ÿᜠx=a, y=b, z=c ÒUÁπ Ë UáÊ ÁŸ Êÿ x+8y+7z=0 9x+y+z=0 x+y+z=0 Ê apple Ê Ò Á Á ŒÈ (a, b, c) à x+y+z=6 U ÁSÕà Ò, ÃÊapple a+b+c UÊ U Ò 1 () «Êapple ÃÕÊ «Á ÿêapple Êapple ªÊapple apple$ apple øê UÊapple Êapple U ß Ê U Á UÊŸapple, Á ÁflÁ Êc U «Ê B 1 ÃÕÊ ÁflÁ Êc U «Ë G 1 Ë Ë ÊÕ Ÿ Ò U apple, apple à UË Êapple Ë ÅÿÊ Ò 5 6! () 6 6! 7! 5 7! IX - MATHEMATICS

36 7. The coefficient of x 5 in the binomial 10 x+ 1 x 1 expansion of 1 1, x x + 1 x x where x 0, 1, is : 1 () If three positive numbers a, b and c are in A.P. such that abc=8, then the minimum possible value of b is : () 9. Let S n = n If 100 S n n =n, then n is equal to : 199 () x+ 1 x 1 x x+ 1 x x apple Ám Œ ÁflSÃÊ U apple x 5 Ê ªÈáÊÊ Ò 1 () , Ê x 0, 1, 8. ÿᜠÃËŸ œÿêà ÅÿÊ a, b ÃÕÊ c Ê Ã U üêapple Ë apple Ò Á Ÿ apple Á abc=8 Ò, ÃÊapple b Ê ãÿíÿã fl ÊŸ Ò () 4 9. ÊŸÊ S n = n n 100 S n =n Ò, ÃÊapple n UÊ U Ò 199 () ÿᜠIX - MATHEMATICS

37 10. The value of k for which the function tan 4x 4 tan 5x π, 0 < x < f ( x) = 5 π k +, x = 5 is continuous at () π x =, is : 10. k Ê fl ÊŸ Á apple Á» Ÿ tan 4x 4 tan 5x π, 0 < x < f ( x) = 5 π k +, x = 5 x () π = U Ãà Ò, Ò If x= y+ y and d y dy ( x 1) x k y 0, dx dx + λ + = then λ+k is equal to : () ÿᜠx y y = + ÃÕÊ d y dy ( x 1) x k y 0 dx dx + λ + = Ò, ÃÊapple λ+k UÊ U Ò () IX - MATHEMATICS

38 1. The function f defined by f (x)=x x +5x+7, is : increasing in R. () decreasing in R. decreasing in (0, ) and increasing in (, 0). increasing in (0, ) and decreasing in (, 0). 1. Let f be a polynomial function such that f (x)=f (x) f (x), for all x R. Then : 14. If f ()+f ()=8 () f () f ()=0 f () f ()=4 f () f ()+f ()=10 x 4 4 f = x +, x, x + 4 f ( x ) d x = A log 1 x+ B x + C, the ordered pair (A, B) is equal to : (where C is a constant of integration) 8, and then 1. f (x)=x x +5x+7 mê UÊ Á U ÊÁ û Ÿ f R apple flœ ÊŸ Ò () R apple OÊ ÊŸ Ò (0, ) apple OÊ ÊŸ ÃÕÊ (, 0) apple flœ ÊŸ Ò (0, ) apple flœ ÊŸ ÃÕÊ (, 0) apple OÊ ÊŸ Ò 1. ÊŸÊ È Œ» Ÿ f apple Ê Ò Á Ë x R apple Á f (x)=f (x) f (x) Ò, ÃÊapple 14. ÿᜠf ()+f ()=8 () f () f ()=0 f () f ()=4 f () f ()+f ()=10 x 4 4 f =+ x, x x+ 4 f ( x ) d x = A log 1 x+ B x + C Á à ÿèç (A, B) UÊ U Ò ( Ê C Ê Ÿ ø U Ò) ÃÕÊ Ò, ÃÊapple () 8, 8, 8, () 8, 8, 8, 8, 5 IX - MATHEMATICS

39 15. If 1 dx k =, ( ) k + 5 x x+ 4 equal to : 1 () 4 then k is 15. ÿáœ Ò dx 1 1 () 4 ( ) x x+ 4 k = k + 5 Ò, ÃÊapple k UÊ U 16. If lim n a 1 (n+ 1) a a a n 1 = 60 [(na++ 1) (na++ )... + (na+ n) ] for some positive real number a, then a is equal to : 7 () Á Ë œÿêà flêsãáfl ÅÿÊ a apple Á ÿᜠlim n a 1 (n 1) a a a n 1 = 60 + [(na++ 1) (na++ )... + (na+ n) ] Ò, ÃÊapple a UÊ U Ò 7 () IX - MATHEMATICS

40 17. A tangent to the curve, y=f (x) at P(x, y) meets x-axis at A and y-axis at B. If AP : BP=1 : and f =1, then the curve also passes through the point : () 1, 4 1, 4 1, 8 1, A square, of each side, lies above the x-axis and has one vertex at the origin. If one of the sides passing through the origin makes an angle 0 with the positive direction of the x-axis, then the sum of the x-coordinates of the vertices of the square is : 1 () fl y=f (x) apple Á ŒÈ P(x, y) U S Ê appleuπê x- ˇÊ Êapple A U ÃÕÊ y- ˇÊ Êapple B U Ê UÃË Ò ÿᜠAP : BP=1 : ÃÕÊ f =1 Ò, ÃÊapple fl ÁŸêŸ Á ŒÈ apple Ë Êapple U ÊÃÊ Ò () 1, 4 1, 4 1, 8 1, flª, Á Ë àÿapple È Ê Ò, x- ˇÊ apple U ÁSÕÃ Ò ÃÕÊ Á Ê ÊË Í Á ŒÈ U Ò ÿáœ ß Ë Í Á ŒÈ apple Êapple U ÊÃË Èß È Ê, x- ˇÊ Ë œÿêà ÁŒ ÊÊ apple 0 Ê ÊappleáÊ ŸÊÃË Ò, ÃÊapple flª apple ÊË Á ŒÈ Êapple apple x-áÿœapple ÊÊ Êapple Ê ÿêappleª Ò 1 () 1 7 IX - MATHEMATICS

41 19. A line drawn through the point P(4, 7) cuts the circle x +y =9 at the points A and B. Then PA PB is equal to : 5 () The eccentricity of an ellipse having centre at the origin, axes along the co-ordinate axes and passing through the points (4, 1) and (, ) is : () If y=mx+c is the normal at a point on the parabola y =8x whose focal distance is 8 units, then c is equal to : () ÿᜠÁ ŒÈ P(4, 7) apple πë øë ªß appleuπê, flîûê x +y =9 Êapple Á ŒÈ Êapple A ÃÕÊ B U Ê UÃË Ò, ÃÊapple PA PB UÊ U Ò 5 () ŒËÉÊ flîûê Á Ê apple ãœ Í Á ŒÈ Ò, ˇÊ ÁŸŒapple ÊÊ ˇÊ Ò ÃÕÊ Êapple Á ŒÈ Êapple (4, 1) ÃÕÊ (, ) apple Êapple U ÊÃÊ Ò, Ë à apple Œ ÃÊ (eccentricity) Ò () ÿᜠy=mx+c Ufl ÿ y =8x apple Á ŒÈ U Á Ò Á Ë ŸÊÁ apple ŒÍ UË 8 ß Êß Ò, ÃÊapple c UÊ U Ò () IX - MATHEMATICS

42 . If a variable plane, at a distance of units from the origin, intersects the coordinate axes at A, B and C, then the locus of the centroid of ABC is : = 1 x y z () + + = x y z = 1 x y z = 9 x y z. ø U Ã, Á Ë Í Á ŒÈ apple ŒÍ UË ß Êß Ò, ÁŸŒapple ÊÊ ˇÊÊapple Êapple A, B ÃÕÊ C U Ê UÃÊ Ò, ÃÊapple ABC apple apple Œ Ê Á ŒÈ Õ Ò = 1 x y z () + + = x y z = 1 x y z = 9 x y z x y + z +λ. If the line, = = lies in 1 1 the plane, x 4y+z=, then the shortest distance between this line and the line, () 1 0 x 1 y z = = is : x y + z +λ = = 1 1. ÿᜠappleuπê,, à x 4y+z= apple ÁSÕà Ò, ÃÊapple ß appleuπê ÃÕÊ appleuπê x 1 y z = = apple Ëø Ë ãÿíÿã ŒÍ UË Ò () IX - MATHEMATICS

43 4. If the vector b = j+ 4 k is written as the sum of a vector b 1, parallel to a = i+ j and a vector b, perpendicular to a, then b 1 b is equal to : i + j 9 k 4. ÿᜠÁŒ Ê b = j+ 4 k Êapple ÁŒ Ê a = i+ j apple Ê Ã U ÁŒ Ê b 1 ÃÕÊ ÁŒ Ê a apple flã ÁŒ Ê b apple ÿêappleª apple M apple Á πê Ê, ÃÊapple b 1 b UÊ U Ò i + j 9 k () 9 6 i 6 j + k () 9 6 i 6 j + k 9 6 i + 6 j k 9 6 i + 6 j k i j + 9 k i j + 9 k 5. From a group of 10 men and 5 women, four member committees are to be formed each of which must contain at least one woman. Then the probability for these committees to have more women than men, is : () ÈL ÃÕÊ 5 Á Ê Êapple apple Í apple apple øê U ŒSÿÊapple Ë apple Ë appleá UÿÊ ŸÊŸË Ò Á Ÿ apple àÿapple apple apple Á Ê fl ÿ Êapple ߟ appleá UÿÊapple apple Á Ê Êapple Ë ÅÿÊ ÈL Êapple Ë ÅÿÊ apple Áœ ÊappleŸapple Ë ÊÁÿ ÃÊ Ò () IX - MATHEMATICS

44 6. Let E and F be two independent events. The probability that both E and F happen is 1 1 and the probability that neither E nor F happens is 1 is :, then a value of P(E) P(F) 6. ÊŸÊ E ÃÕÊ F ŒÊapple Sflà òê ÉÊ UŸÊ Ò E ÃÕÊ F ŒÊappleŸÊapple apple ÉÊ UŸapple Ë ÊÁÿ ÃÊ 1 1 ÉÊ UŸapple Ë ÊÁÿ ÃÊ 1 Ò ÃÕÊ Ÿ E ÊÒ U Ÿ Ë F apple Ò, ÃÊapple P(E) P(F) Ê ÊŸ Ò 4 4 () () The sum of 100 observations and the sum of their squares are 400 and 475, respectively. Later on, three observations,, 4 and 5, were found to be incorrect. If the incorrect observations are omitted, then the variance of the remaining observations is : appleˇêáêêapple Ê ÿêappleª ÃÕÊ Ÿ apple flªêapplez Ê ÿêappleª Ê 400 ÃÕÊ 475 Ò ÊŒ apple ÃËŸ appleˇêáê, 4 ÃÕÊ 5 ª Ã Ê ª ÿᜠª à appleˇêáêêapple Êapple UÊ ÁŒÿÊ Ê ÃÊapple Êapple appleˇêáêêapple Ê UáÊ Ò 8.5 () () IX - MATHEMATICS

45 8. A value of x satisfying the equation sin[cot 1 (1+x)]=cos[tan 1 x], is : 1 () Ë UáÊ sin[cot 1 (1+x)]=cos[tan 1 x] Êapple ÃÈc U UŸapple flê Ê x Ê ÊŸ Ò 1 () The two adjacent sides of a cyclic quadrilateral are and 5 and the angle between them is 60. If the area of the quadrilateral is 4, then the perimeter of the quadrilateral is : 1.5 () ø Ëÿ-øÃÈ È Ë ŒÊapple ÇŸ È Ê ÃÕÊ 5 Ò ÃÕÊ Ÿ apple Ëø Ê ÊappleáÊ 60 Ò ÿáœ ß øãè È Ê ˇÊappleòÊ» 4 Ò, ÃÊapple ß Ê Á U Ê Ò 1.5 () IX - MATHEMATICS

46 0. Contrapositive of the statement If two numbers are not equal, then their squares are not equal, is : If the squares of two numbers are equal, then the numbers are equal. () If the squares of two numbers are equal, then the numbers are not equal. If the squares of two numbers are not equal, then the numbers are not equal. If the squares of two numbers are not equal, then the numbers are equal. - o 0 o - 0. ÕŸ ÿᜠŒÊapple ÅÿÊ ÊŸ Ÿ Ë Ò, ÃÊapple Ÿ apple flª ÊŸ Ÿ Ë Ò Ê ÁÃœŸÊà (Contrapositive) Ò ÿᜠŒÊapple ÅÿÊ Êapple apple flª ÊŸ Ò, ÃÊapple ÅÿÊ ÊŸ Ò () ÿᜠŒÊapple ÅÿÊ Êapple apple flª ÊŸ Ò, ÃÊapple ÅÿÊ ÊŸ Ÿ Ë Ò ÿᜠŒÊapple ÅÿÊ Êapple apple flª ÊŸ Ÿ Ë Ò, ÃÊapple ÅÿÊ ÊŸ Ÿ Ë Ò ÿᜠŒÊapple ÅÿÊ Êapple apple flª ÊŸ Ÿ Ë Ò, ÃÊapple ÅÿÊ ÊŸ Ò - o 0 o - 1 IX - MATHEMATICS