where c1and c C) 16 a 3 from where three distinct normals can be drawn, then

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NARAYANA IIT A/C ACADEMY VIJ-SPARK-AC (AMARAVATHI CAMPUS) BENZ CIRCLE VIJAYAWADA-10 CONTACT : 0866-497615, 8179880670 MODEL :- ADV OUTGOING SR-IZ DPT EX.

1 NARAYANA IIT A/C ACADEMY VIJ-SPARK-AC (AMARAVATHI CAMPUS) BENZ CIRCLE VIJAYAWADA-10 CONTACT : , MODEL :- ADV OUTGOING SR-IZ DPT EX.DT: MATHS Section- I (Single correct answer type questions) 1. The locus of a point such that the sum of it distances from the origin and the line x = is 4 units is A)A circle of radius 4 B) a parabola of latus rectum 8 C) Segments of two opposite parabola of laturecta 4 and 1 D) an ellipse or a parabola y 4a x c and x 4a y c where c1and c are variables, touch each other. Locus of. Parabola their point of contact is A) xy a B) xy 1 a C). The triangle formed by the tangent to the parabola y xy 4a D) a,4a, the ordinate and the x axis, has the greatest area equal to A)1 a B) 8 a C) 16 a D) 4. If (h,k) is a point on the axis of parabola x 1 y 1 x y xy a 4x at the point whose abscissa lies in the interval from where three distinct normals can be drawn, then A) h B) h 4 C) h 8 D) h 8 5. The tangents at P and Q on the parabola y 4x meet in T. S is the focus, SP, ST, SQ are equal to a, b, c, respectively. Then the roots of the equation ax bx c 0 are A)Real and different B) Real and equal C) Complex numbers D) Irrational 6. Minimum distance between the curves y 4x and x y 1x 1 0is A) 5 B) 1 C) 8 5 D) Coordinates of the vertices B and C of a triangle ABC are (,0) and (8,0) respectively. The vertex A is varying B C in such a way that 4 tan tan 1. The locus of A is x 5 y 1 B) x 5 y 1 C) x 5 y 1 D) x 5 y 1 A) PQ and QR are two focal chords of an ellipse and the eccentric angles of P,Q,R are,, respectively. Then tan tan is equal to A) cot B) cot C) cot D) 9. Equation of the largest circle with centre (1,0) that can be inscribed in the ellipse a cot x 4y 16, is A) x y 4x 7 0 B) x y x 5 0 C) x y 6x8 0 D) x y x If the tangent and normal to a rectangular hyperbola at a point cut off intercepts a1, a on x axis and b1,bon the Y-axis, then a1a b1 b is equal to A) B) 1 C) 0 D) -1 Section-II (One or more than one correct Answer Type Questions ) 11. If the quadrilateral formed by four tangents to the ellipse x 4y 1 is a square then A)The vertices of the square lie on is y x

2 B)The vertices of the square lie on x y 7 C)The area of all such squares is constant D)Only two such squares are possible x, y, i 1,,,4 to the rectangular hyperbola xy = meet at the point (,4), then 1. If the normals at i i x A) x x x 1 4 y B) 1 y y y 4 4 x x x x 4 C) 1 4 y D) 1y y y P is a point which moves in the x-y plane such that the point P is nearer to the centre of a square than any of the sides. The four vertices of the square are a, a. The region in which P will move is bounded by parts of parabola of which one has the equation A) y a ax B) x a ay C) y ax a D) x a ay 14. The ends of a line segment are P(1,) and Q(1,1). R is a point on the line segment PQ such that PR:QR=1:. If R is an interior point of the parabola y 4x then 0,1 B),1 A) 1 C), D), 5 x y x y 15. From any point on the hyperbola 1, tangents are drawn to the hyperbola. The area cut a b a b off by the chord of contact on the region between the asymptotes is equal to ab B) ab C) ab D) 4ab A) Section-III Integer type answer questions 16. A trapezium is inscribed in the parabola y 4x such that its diagonals pass through the point (1,0) and each has length 5.If the area of traperzium be P then 4P-7 is equal to Three normals drawn from any point on the parabola y 4ax cut the line x = a in points whose ordinates are in arithmetic progression. If the slopes of the normals be m1, m and m then 18. The tangent at a point acos, bsin m 1 m is equal to m m x y of an ellipse 1, (a > b ) meets its auxillary circle in two a b points Q and R. If the chord QR subtends right angle at the centre and e be the eccentricity of the ellipse then e 1 sin is equal to 19. If S1and Sbe the foci of the hyperbola of four whose transverse axis length is 4 conjugate axis length is 6, S and S 4 be the foci of the conjugate hyperbola and the area of the quadrilateral S1SSS 4 is A then A 4 is 0. Let 1 be the area of a triangle PQR inscribed in an ellipse and be the area of the triangle P ' Q ' R ' whose vertices are the points lying on the auxiliary circle corresponding to the points P,Q,R respectively. If the eccentricity of the ellipse is 4 7 then the ratio 1 is equal to

What should be the separation between the slits (in 10-7 m) so that the successive maxima on the screen are separated by a distance of 0.1 mm?. A neutron having kinetic energy 1.

3 PHYSICS SECTION-1 (INTEGER ANSWER TYPE) 1. Suppose a monochromatic X-ray beam of wavelength 100 pm is sent through a Young s double slit and the interference pattern is observed on a photographic plate placed 40 cm away from the slit. What should be the separation between the slits (in 10-7 m) so that the successive maxima on the screen are separated by a distance of 0.1 mm?. A neutron having kinetic energy 1.5 ev collides with a hydrogen atom at rest. Neglect the difference in mass between the neutron and the hydrogen atom and assume that the neutron does not leave its line of motion. Find the possible kinetic energies of the neutron after the event.. Nuclei A and B convert into a stable nucleus C. Nucleus A is converted into C by emitting two -particles and -particles. Nucleus B is converted into C by emitting one -particle and five -particles. At time t = 0, nuclei of A are 4No and nuclei of B are No. Initially, the number of nuclei of C are zero. Half-life of A (into conversion of C) is 1 min and that of B is min. Find the time at which the rate of disintegration of A and B are equal (in minutes). 4. Consider a nuclear reaction AB C. A nucleus A moving with kinetic energy of 5 MeV collides with a nucleus B moving with kinetic energy of MeV and forms a nucleus C in the exited state with excitation energy MeV MeV. The kinetic energy of nucleus C just after its formation is p. Take masses of nuclei of A, B and C as 5 amu, 10 amu and amu, respectively and 1 amu 90 MeV / c. Find value of p 5. A stationary He ion emitted a photon corresponding to the first line of the Lyman series. The photon liberates electron from a stationary hydrogen atom in the ground state. The velocity of the liberated electron is.1 10 x unit. Find x (You can make necessary approximations) SECTION- (MORE THEN ONE CORRECT ANSWER) 6. The figure shows electronic wave function for a hydrogen atom. a) The quantum number of this state is 6 b) The wavelength of this electron is 6 r0. ( r 0 is radius of ground state) c) can go to ground state by emitting different photons d) On deexcitation it emits at least one line in infra red region of spectrum.

4 7. Light from a discharge tube containing hydrogen atoms falls on the surface of a piece of sodium. The K.E. of the fastest photoelectrons emitted from sodium is 0.7 ev. The work function of sodium is 1.8 ev then, a) the energy of the photons causing the photoelectric emission is.55 ev b) the quantum number of the two levels involved in the emission of these photons are 1 and 4 c) the change in the angular momentum of the electron in the hydrogen atom is h (in the above transition) d) assuming it to be at rest before transition, the recoil speed of the emitting hydrogen atom of mass is 0.85 m/s 8. If in hydrogen atom, radius of n th Bohr orbit in rn frequency of revolution of electron in n th orbit is fn and area enclosed by n th orbit is An, which of the following graphs is/are correct? a) b) c) d) 9. A photon collides with a stationary hydrogen atom in ground state inelastically. Energy of the colliding photon is 10. ev. After a time interval of the order of microsecond another photon collides with same hydrogen atom inelastically with an energy of 15 ev. What will be observed by the detector? a) photons of energy 10. Ev b) photons of energy 1.4 ev c) One photon of energy 0. ev and an electron of energy 1.4 ev d) One photons of energy 10. ev and an electron of energy 1.4 Ev 10. Mark out the correct statements(s). (a) In both fission and fusion processes, the mass of reactant nuclide is greater than the mass of product nuclide.

5 (b) In fission process, BE per nucleon of reactant nuclide is less than the binding energy per nucleon of product nuclide. (c) In fusion process, BE per nucleon of reactant nuclide is less than the binding energy per nucleon of product nuclide. (d) In fusion process, BE per nucleon of reactant nuclide is greater than the binding energy per nucleon of product nuclide. SECTION- (SINGLE CORRECT ANSWER) 11. In order to determine the value of E0 (the magnitude of ground state energy), a scientist shines photons ( light particles ) of various energies at a cloud of atomic hydrogen. Most of the hydrogen atoms occupy the ground state. A detector records the intensity of light transmitted through that cloud; second figure is a graph of part of the scientist s data, showing the intensity of the transmitted light as a function of the photon energy. A hydrogen atom s electron is likely to absorb a photon only if the photon gives the electron enough energy to knock it into a higher shell Laser Light detector Glass container of Atomic hydrogen Intensity photon enery (joules x10-18 ) According to this experiment, what is the approximate value of E0? a) 1.6 x joules b).1 x joules c). x10-18 joules d)6.4 x joules 1. A regular hexagonal lamina of side a made up of perfectly absorbing material is kept in a region where a parallel beam of light with intensity I having a large aperture falls on it. If the beam makes an angle of 0 with the normal to the plane of hexagon, then the force experienced by the hexagon will be (c velocity of light) A) 5aI 4c B) 9aI 4c C) ai c D) 6a I c

6 1. Electrons with de-broglie wavelength falls on the target in an x-ray tube. The cut- off wavelength of the emitted X-ray is a) mc h b) h mc c) m c h d) 14. A sample has two isotopes A and B with mass number 150. The masses of A and B are 50g and 0g respectively. A is radioactive and B is stable. A decays to C by emitting particles. The half life of A is hrs. The mass of the sample after 4hrs and number of particles emitted are a) 79 gm, b) 74 gm, c) 75 gm, 10 d) 79 gm, The energies of three photons from excited Hydrogen atoms was found to be 1.9eV, 10. ev and 1.1 ev. These photons must come from a) a single atom b) definitely two atoms c) definitely three atoms d) two or three atoms 16. In a screw gauge, least count of the pitch scale is 0.5mm and there are 50 divisions on its cap. When nothing is put between its jaws, 40 th division of circular scale coincides with reference line, with zero of circular scale lying above the reference line. When a plate is placed between the jaws, main scale reads divisions and circular scale reads 0 divisions. Thickness of the plate is A) 0.8 mm B) 1.1 mm C) 1. mm D) 1.6 mm 17. The pitch of a screw gauge is 1 mm and there are 100 divisions on its circular scale. When nothing is put in between its jaws, the zero of the circular scale lies 4 divisions below the reference line. When a steel wire is placed between the jaws, two main scale divisions are clearly visible and 67 divisions on the circular scale are observed. The diameter of the wire is (a).71 mm (b).67 mm (c).6 mm (d).65 mm 18. The percentage error in calculation of specific resistance, ρ = πr R / l, where r = radius of wire cm, l = length of wire cm, R = resistance of wire 64 ohm will be (A) (B) 10.0 (C) 5.8 (D) Backlash error is present in A) Vernier callipers B) Screw-Gauge and Vernier callipers C) Screw Gauge D) Vernier calipers and Spherometer

7 0. The period of oscillation of a simple pendulum is T L / g. L is about 10 cm and is known to 1 mm accuracy. The period of oscillation is about 0.5 s. The time of 100 oscillations is measured with a wristwatch of 1 sec resolution. The percentage error in the determination of g will be (A) % (B) 5% (C) 6% (D) 8%

8 PHYSICS MATHS NARAYANA IIT A/C ACADEMY VIJ-SPARK-AC (AMARAVATHI CAMPUS) BENZ CIRCLE VIJAYAWADA-10 CONTACT : , MODEL :- ADV OUTGOING SR-IZ DPT EX.DT: KEY C C C A B A A B C C B,C A,B,C A,B,C,D A,C D B,C A,D A,B,C,D D A,C,D B B A A D C C A C B HINTS PHYSICS 1. Given = 10 pm = m D = 40 cm = m = 0.1 mm = m = D/d d = D = m. In one dimensional elastic collision of two bodies of equal masses, the initial velocities of bodies are interchanged after collision. Therefore, velocity of the neutron after collision is zero. Hence it has zero energy.. Given ANA = BNB ln ln T T At Bt 4Aoe No e A B AB e t 8 t ln8 ln A B ln ln t 6 min 1

9 4. 5. Energy of a photon emitted for transition n to n 1 is given by 1 1 E 1.6. ev... 1 n n 1 This transition energy is shared between recoiling helium ion and photon From conservation of energy. E jf K. E.... Where K.E. is kinetic energy of recoiling atom and hf is energy of photon From conservation of momentum, P Photon P He... E E 1 1 mc E 1.6 ev 40.8 ev mv eV 7.eV v.1 10 m/ s x Number of waves in the given diagram is. Hence n = r r 0 6r 0 Possible transmissions in de excitation a. e, 1, 1 7. h KEmax W The energy corresponds to transmission 4 in hydrogen

10 8. a) r n n b) r n Log log n r 1 c) Area A n n 4 LogA log n n 9. The first photon will excite the hydrogen atom (in ground state) in fist excited state (as EE1 10. ev ). Hence, during de-excitation a photon of 10. ev will be released. The second photon of energy 15ev can ionise the atom. Hence the balance energy 1.4 ev is retained by the electron. 10. All the statements are very conceptual statements related to different decays x J photon knocks a ground state electron into the first excited state. 18 EE1 1.6x E x E ground state energy =.1x10-18 J 0 1. Radiation pressure = Area of hexagon = 1. h ke P h hc m m 0 P 14. Mass left =1.5gm gm 150 = 79gm No of particles emitted = = An excited H-atom cannot emit 1.9ev, 10.ev and 1.1ev simultaneously

11 0.5mm 16. c Least count of screwguage = 5 div mm It has negative zero error e mm R= x 0.5mm + 0 x 0.01 = 1. mm True value = = 1. mm. 17. P = 1 mm, N = 100 Least count, C = P/N = 1 mm/100 = 0.01 mm The instrument has a positive zero error e = + NC = +4(0.01) = mm Main scale reading is (1 mm) = mm Circular scale reading is 67(0.01) = 0.67 mm observed reading is R o = =.67 mm or R t =.6 mm (c) 18. rr l % 19. Conceptual 0. g4 L T g L T g L T The percentage error L in L 100 1% L

12 T The percentage error in T 100 % T Thus, the percentage error in g g L T % g L T

QUESTION BANK ON. CONIC SECTION (Parabola, Ellipse & Hyperbola)

QUESTION BANK ON. CONIC SECTION (Parabola, Ellipse & Hyperbola) QUESTION BANK ON CONIC SECTION (Parabola, Ellipse & Hyperbola) Question bank on Parabola, Ellipse & Hyperbola Select the correct alternative : (Only one is correct) Q. Two mutually perpendicular tangents