PRACTICE TEST-3- PAPER-1

PRACTICE TEST THREE PAPER-1 Duration : 3 Hours Max. Marks : 180 GENERAL INSTRUCTIONS 1. The question paper consists of three parts (Physics, Chemistry and Mathematics). Each part consists of three sections and total number of questions are 60. Marking Scheme 2. For each question in Section 1, you will be awarded 2 marks if you darken the bubble corresponding to the correct answer each zero mark if no bubbles are darkened. No negative marks will be awarded for incorrect answers in this section. 3. For each question in Section 2, you will be awarded 4 marks if you darken all the bubble(s) corresponding to only the correct answer(s) and zero mark if no bubbles are darkened. In all other cases, minus one (–1) mark will be awarded. 4. For each question in Section 3, you will be awarded 4 marks if you darken the bubble corresponding to only the correct answer and zero mark if no bubbles are darkened. In all other cases, minus one (–1) mark will be awarded. PART-I (PHYSICS) SECTION-1 : (Only One option correct type) This section contains 10 multiple choice qustions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct. 1. A system consists of two point masses, A and B of masses 1 kg and 2 kg respectively. At an instant the kinetic energy of A with respect to the centre of mass is 2 Joules and the velocity of centre of mass is 2 m/ s. The kinetic energy of the system at this instant is : (A) 9 J (B) 11 J (C) 13 J (D) none of these 2. A convex lens is cut into two parts inaaz different ways that are arranged in four manners, as shown. Which arrangement will give maximum optical power ? (A) (B) (C) (D) 3. A vernier calipers which is used to measure length of a cylinder has 1mm marks on the main scale. It has 10 equal division on the vernier scale which match with 8 marks of main scale. If main scale reading is 4 and vernier reading is 5 then the length of cylinder is 1.25 N × 10–3 m then the value of N is : (A) 4 (B) 6 (C) 8 (D) 3 4. The potential energy (in S units) of a particle of mass 2 kg in a conservative field is U = 6x – 8y. If the initial velocity of the particle is → = – 1.5 ˆi + 2 ˆj then the total distance travelled by the particle in first two seconds is (A) 10 m (B) 12 m (C) 15 m (D) 18 m 5. The elongation in a metallic rod hinged at one end and rotating in a horizontal plane becomes four times of the initial value. The angular velocity of rotation becomes : (A) two times the initial value (B) half of initial value (C) one third of initial value (D) four times the initial value. 6. A triangular medium has varying refracting index n = n0 + ax, where x is the distance (in cm) along x–axis 4 from origin and n0 = 3 . A ray is incident normally on face OA at the mid–point of OA. The range of a so that light does not escape through face AB when it falls first time on the face AB (OA = 4 cm, OB = 3 cm and AB = 5 cm) : (Surrounding medium is air) 1 (A) a > 9 2 (B) a > 9 1 (C) a > 3 (D) None of these 7. A tugsten bulb radiates 2 W of energy.The filament of the bulb has surface area 2 mm2 and an emissivity of 0.9.The temperature of the bulb is: (Stefan’s Constant  = 5.6 × 10–8 S.I. units) (A) 3500K (B) 4210K (C) 2110K (D) 211K 8. In an x - ray tube, if the accelerating potential difference is changed, then: (A) the frequency of characteristic x  rays of a material will get changed (B) number of electrons emitted will change (C) the difference between 0 (minimum wavelength) and k (wavelength of k x  ray) will get changed (D) difference between k and k will get changed. 9. In a calm pond, water ( = 4/3) is filled uniformly upto 1 m depth. The maximum wavelength of the electromagnetic radiation incident normally from air onto the water surface, that will be strongly reflected is: [ assume: nground > nwater ] 16 8 4 (A) 3 m (B) 3 m (C) 3 m (D) 8 m 10. In an adiabatic expansion the product of pressure and volume : (A) decreases (B) increases (C) remains constant (D) first increases, then decreases. SECTION-2 : (One or more option correct type) This section contains 5 multiple choice qustions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE are correct. 11. Two concentric rings of radii R1 = m and R2= 4m are placed in y-z plane with their centres at origin. They have uniform charge –q and +Q = 2 2 q on the inner and outer rings respectively. Consider the electrostatic potential to be zero at infinity. Then x (A) The electric potential is zero at origin. (B) The electric field intensity is zero at r = 2 m. (C) A positive charged particle disturbed from origin along the x-axis will restore back to origin. (D) Where potential is maximum on the x-axis, field intensity is zero. 12. A steel wire is rigidly fixed at both ends. Its length, mass and cross sectional area are 1m, 0.1kg and 10-6 m2 respectively. Then the temperature of the wire is lowered by 20 oC. If the transverse waves are setup by plucking the wire at 0.25m from one end and assuming that wire vibrates with minimum number of loops possible for such a case. [Coefficient of linear expansion of steel = 1.21 × 10-5/oC and Young's modulus = 2 × 1011 N/m2] (A) The tension in the wire will be 48.4 N. (B) The number of loops will be 2. (C) The frequency of vibration will be 22 Hz. (D) The frequency of vibration will be 44 Hz. 13. Two metallic bodies separated by a distance 20 cm, are given equal and opposite charges of magnitude 0.88 C . The component of electric field along the line AB, between the plates, varies as E = 3 x2 + 0.4 N/C, where x (in meters) is the distance from one body towards the other body as shown. (A) The capacitance of the system is 10F (B) The capacitance of the system is 20F (C) The potential difference between A and C is 0.088 Volt. (D) The potential difference between A and C cannot be determined from the given data. 14. A single circular loop of wire with radius 0.02 m carries a current of 8.0 A. It is placed at the centre of a solenoid that has length 0.65 m, radius 0.080 m and 1300 turns. Solenoid Current carrying loop (A) The value of the current in the solenoid so that the magnetic field at the centre of the loop becomes zero, is equal to 44 mA. (B) The value of the current in the solenoid so that the magnetic field at the centre of the loop becomes zero, is equal to 100 mA. (C) The magnitude of the total magnetic field at the centre of the loop (due to both the loop and the solenoid) if the current in the loop is reversed in direction from that needed to make the total field equal to zero tesla, is 8p x 10–5 T. (D) The magnitude of the total magnetic field at the centre of the loop (due to both the loop and the solenoid) if the current in the loop is reversed in direction from that needed to make the total field equal to zero tesla, is 16p x 10–5 T. 15. Which of the following is not possible ? (A) (B) (C) (D) SECTION-3 : (Integer value correct Type) This section contains 5 questions. The answer to each question is a single digit integer, ranging from 0 to 9 (both inclusive) 16. A rough track ABCDE ends in a circular loop of radius R as shown in figure. A solid cylinder of radius 2 cm slides down the track from point A which is at height h = 13 cm. Find the maximum value of R (in cm) for the cylinder to complete the loop successfully. Friction is sufficient to provide pure rolling. Do not consider effect of collision at B. 17. Intensity v/s wavelength of x-rays graphs are given for two different target elements. If number of protons in an atom of target element-1 is 37. If number of protons in an atom of target element-2 is 95/n then find the value of n. 18. A particle collides with horizontal rough floor with a speed u at an angle 45º with vertical and after collision it moves vertically upward. Coefficient of restitution for normal impact is 1 , If the friction coefficient between 2 particle and surface is  find 3 . 19. The chain of length L is released from rest on a smooth incline with x = 0 as shown in the figure. 4 Determine velocity v of the chain when a half of the length has fallen. (Take L = 25 m) in m/s. (Neglect edge effect of inclined). 20. An ionisation counter is used to investigate the disintegration rate of a certain radioactive sample. At the start of the experiment, the counter gives 141 pulses in 20s. After 3 days it gives 100 pulses in 20s. Its half life is (in days). A nswers 1. (A) 2. (A) 3. (A) 4. (C) 5. (A) 6. (B) 7. (C) 8. (C) 9. (B) 10. (A) 11. (A ) 12. (A,B,C) 13. (A,C) 14. (B,D) 15. (A,C,D) 16. 6 17. 5 18. 2 19. v = 20. 6