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ISC Class XI Notes 2025 : Physics (New Horizon Gurukul (NHG), Bangalore)

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Apoorv Jain
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Arjuna JEE Main (2025) MANTHAN Physics Mechanical Properties of Solid Exercise -1 7. A force F is needed to break a copper wire having radius R. The force needed to break a copper wire of radius 2R will be ELASTIC BEHAVIOUR, LONGITUDINAL STRESS, YOUNG S MODULUS (a) F/2 1. An elastic rod will not change its length when it is: (b) 2F (a) Pulled along the rough surface (c) 4F (b) Pulled along the smooth surface (d) F/4 (c) Is hanging under gravity 8. A graph is shown between stress and strain for a metal. The part in which Hook s law holds good is (d) Freely falls vertically under gravity Stress 2. The length of an iron wire is L and area of cross-section is A. The increase in length is l on applying the force F on its two ends. Which of the statements is correct? (a) Increase in length is inversely proportional to its length L C A D B (b) Increase in length is proportional to area of cross-section A (c) Increase in length is inversely proportional to A O (d) Increase in length is proportional to Young s modulus Strain (a) OA (b) AB (c) BC (d) CD 9. The strain-stress curves of three wires of different materials are shown in the figure. P, Q and R are the elastic limits of the wires. The figure shows that Q P 3. Two wires have the same diameter and length. One is made of copper and the other of brass. They are connected together at one end. When free ends are pulled in opposite direction by same force (a) The wires will have same strain (b) The wires will have same stress (c) Both the wires will break at the same force Strain (d) Both wires will have same elongation 4. The ratio of the lengths of two wires A and B of same material is 1 : 2 and the ratio of their diameter is 2 : 1. They are stretched by the same force, then the ratio of increase in length will be R O Stress (a) 2 : 1 (b) 1 : 4 (a) Elasticity of wire P is maximum (c) 1 : 8 (d) 8 : 1 (b) Elasticity of wire Q is maximum 5. The area of cross-section of a wire of length 1.1 metre is 1 mm2. It is loaded with 1 kg. If Young s modulus of copper is 1.1 1011 N/m2, then the increase in length will be (g = 10 m/s2) (a) 0.01 mm (b) 0.075 mm (c) 0.1 mm (d) 0.05 mm (c) Elasticity of wire R is maximum (d) None of the above is true 10. A metal wire of length L area of cross-section A and Young modulus Y behaves as a spring of spring constant k, where k is equal to 6. If the temperature increases, the modulus of elasticity (a) Decreases (b) Increases (c) Remains constant (d) Becomes zero 1 (a) YL YA (b) A L (c) 2YA YA (d) L 2L 11. The figure shows a horizontal block that is suspended by two wires A and B are identical except their original length. Which wire was originally shorter? (Final lengths are equal) A 18. A uniform bar of length L and cross sectional area A is subjected to a tensile load F . Y be the Young s modulus and s be the Poisson s ratio then volumetric strain is F (a) (1 s ) (b) F ( 2 s ) AY AY F F (c) .s (1 2s ) (d) AY AY B 19. The mean distance between the atoms of iron is 3 10 10 m and interatomic force constant for iron is 7 N /m. The Young s modulus of elasticity for iron is (a) 2.33 105 N/ m2 (b) 23.3 1010 N/ m2 (c) 233 1010 N/ m2 (d) 2.33 1010 N/ m2 Uniform block (a) A (b) B (c) Both had equal length (d) Any one of them could be shorter 20. The dimensions of two wires A and B are the same. But their materials are different. Their load-extension graphs are shown. If YA and YB are the values of Young s modulus of elasticity of A and B respectively then A (a) load 12. An iron wire of negligible mass, length L and cross-section are A has one end fixed. A ball of mass m is attached to the other end of wire. The wire and ball are rotating with an angular velocity w in a horizontal plane. If DL is extension produced in wire, then the Young s modulus of wire is mL2 m 2 L2 (b) A L A L extension 2 m L m L (d) A L A L 13. The Young s modulus of wire of length L and radius r is Y. L r If the length and radius are reduced to and , then its 3 2 Young s modulus will be (a) Y (b) 3 Y (c) 3Y (d) 4Y 4 14. On increasing the length by 0.5 mm of a steel wire of length 4m and area of cross section 5 mm2, the force required is (Y = 11.90 1012 N/m2) (a) 4 103 N (b) 2 103 N (c) 7.4 103 N (d) 103 N (c) (c) 0.04 (b) YA < YB (c) YA = YB (d) YB = 2YA (a) l = L2 Dg L2 Dg (b) l = Y 2Y (c) l = L2 Dg L2 Dg (d) l = 8Y 4Y 22. The metal ring of initial radius r and cross-sectional area A is fitted onto a wooden disc of radius R > r. If young s modulus of the metal is Y, then the tension in the ring is (a) AYR (b) AY ( R r ) r r Y R r Yr (c) (d) A r AR TANGENTIAL STRESS AND STRAIN, SHEAR MODULUS 16. Two wires A and B are of same materials. Their length are in the ratio 3 : 4 and diameters are in the ratio 5 : 1 when stretched by force FA and FB respectively they get equal F increase in their lengths. The ratio of B is. FA (b) 0.03 (a) YA > YB 21. A rubber cord of length L is suspended vertically. Density of rubber is D and Young s modulus is Y. If the cord extends by a length l under its own weight then 15. A block of mass 500 kg is suspended by wire of length 70 cm. The area of cross-section of wire is 10 mm2. When the load is removed, the wire contracts by 0.5 cm. The Young s modulus of the material of wire will be (a) 10 1014 N/m2 (b) 4 1014 N/m2 (c) 8 1011 N/m2 (d) 7 1010 N/m2 (a) 0.01 B 23. Modulus of rigidity of diamond is (a) Too less (b) Greater than all matters (c) Less than all matters (d) Zero 24. Modulus of rigidity of a liquid (a) Non zero constant (b) Infinite (c) Zero (d) Can not be predicted 25. For a given material, the Young s modulus is 2.4 times that of rigidity modulus. Its Poisson s ratio is (a) 2.4 (b) 1.2 (c) 0.4 (d) 0.2 (d) 0.05 17. Four wires made of same material are stretched by the same load. Their dimensions are given below. The one which elongates more is (a) Length 1 m, diameter 1 mm (b) Length 2 m, diameter 2 mm (c) Length 3 m, diameter 3 mm (d) Length 0.5 m, diameter 0.5 mm 26. Shearing stress causes change in (a) Length (b) Breadth (c) Shape (d) Volume 2 27. A 3 cm long copper wire is stretched to increase its length by 0.3 cm. Find the lateral strain in the wire, if the Poisson s ratio for it is 0.26. (a) 0.013 (b) 0.018 (c) 0.026 (d) 0.016 38. The fractional change in volume per unit increase in pressure is called (a) Pressure coefficient (b) Volume coefficient (c) Bulk modulus (d) Compressibility 39. An increase in pressure required to decrease the 200 litres volume of a liquid by 0.004% in container is: (Bulk modulus of the liquid = 2100 MPa) (a) 188 kPa (b) 8.4 kPa (c) 18.8 kPa (d) 84 kPa 40. A metal wire elongates by hanging load on it, then fractional DV change in volume is proportional to V 28. Y, k, n represent respectively the young s modulus,bulk modulus and rigidity modulus of a body. If rigidity modulus is twice the bulk modulus, then (a) Y = 5k/18 (b) Y = 5n/9 (c) Y = 9k/5 (d) Y = 18k/5 29. For a material Y = 6.6 10 10 N/m 2 and bulk modulus K = 11 1010 N/m2, then its Poissons s ratio is (a) 0.8 (b) 0.35 (c) 0.7 (d) 0.4 30. If the poisson s ratio of a solid is 2/5, then the ratio of its young s modulus to the rigidity modulus is (a) 5/4 (b) 7/15 (c) 14/9 (d) 14/5 (a) lDl (b) Dl l (c) 2Dl (d) l Dl l ELASTIC POTENTIAL ENERGY 41. An iron bar of length L cross section A and Young s modulus Y is pulled by a force F , from both the ends so as to produce an elongation l . The elastic energy stored in the deformed rod will be: 31. A material has Poisson s ratio 0.30. If a uniform rod suffers a longitudinal strain of 3 10 4, then the percentage change in volume. (a) 0.05% (b) 0.02% (c) 0.01% (d) 0.08% (a) PRESSURE AND VOLUMETRIC STRAIN, BULK MODULUS OF ELASTICITY (c) 32. The isothermal elasticity of a gas is equal to (a) Density (b) Volume (c) Pressure (d) Specific heat 33. The adiabatic elasticity of a gas is equal to (a) density (b) volume (c) pressure (d) specific heat 34. The only elastic modulus that applies to fluids is (a) Young s modulus (b) Shear modulus (c) Modulus of rigidity (d) Bulk modulus 35. A ball falling in a lake of depth 200 m shows 0.1% decrease in its volume at the bottom. What is the bulk modulus of the material of the ball (a) 19.6 108 N/m2 (b) 19.6 10 10 N/m2 (c) 19.6 1010 N/m2 (d) 19.6 10 8 N/m2 36. What is the density of water at a depth where the pressure is 501 atm, given its density at the surface is 1.0 10 3 kg/m 3 ? Given : Bulk modulus of water K = 2.0 109 Pa. 1 atm = 1.01 105 Pa (a) 1 103 kg/m3 (b) 3.51 103 kg/m3 (c) 2.12 103 kg/m3 (d) 0.52 103 kg/m3 37. To what depth below the surface of sea should a ball be taken so as to decrease its volume by 0.4% [density of sea water = 1000 kg m 3, Bulk modulus of the ball = 9 108 Nm 2, g = 10 m/s2] (a) 5 102 m (b) 30 106 m 6 (c) 40 10 m (d) 36 101 m F 2L F 2L (b) AY 2 AY F2 2 A 2Y (d) None of these Extension 42. The diagram shows a force-extension graph for a rubber band. Consider the following statements force I. It will be easier to compress this rubber than expand it II. Rubber does not return to its original length after it is stretched III. The rubber band will get heated if it is stretched and released Which of these can be deduced from the graph (a) III only (b) II and III (c) I and III (d) I only 43. A wire suspended vertically from one of its ends is stretched by attaching a weight of 200 N to the lower end. The weight stretches the wire by 1 mm. Then the elastic energy stored in the wire is (a) 20 J (b) 0.1 J (c) 0.2 J (d) 10 J 3 45. If the tension on a wire is removed at once, then (a) It will break (b) Its temperature will reduce (c) There will be no change in its temperature (d) Its temperature will increases 44. A 5 metre long wire is fixed to the ceiling. A weight of 10 kg is hung at the lower end and is 1 metre above the floor. The wire was elongated by 1 mm. The energy stored in the wire due to stretching is (a) Zero (b) 0.05 joule (c) 100 joule (d) 500 joule 46. A wire is suspended by one end. At the other end, a weight equivalent to 20 N force is applied. If the increase in length is 1.0 mm, the increase in energy of the wire will be (a) 0.01 J (b) 0.02 J (c) 0.04 J (d) 1.00 J 4 Exercise -2 Single Correct Type Questions: (1 to 30) 1. A rod of length L kept on a smooth horizontal surface is pulled along its length by a force F. The area of cross-section is A and Young s modulus is Y. The extension in the rod is (a) (c) 2. 3. 4. FL AY FL 2 AY (b) (a) (b) (c) (d) 2FL AY (d) Zero 7. A spherical ball contracts in volume by 0.01% when subjected to a normal uniform pressure of 100 atm. The Bulk modulus of its material is (a) 1.01 1011 Nm 2 (b) 1.01 1012 Nm 2 (c) 1.01 1010 Nm 2 (d) 1.0 1013 Nm 2 (c) 8. A steel rod has a radius 10 mm and a length of 1.0 m. A force stretches it along its length and produces a strain of 0.32%. Young s modulus of the steel is 2.0 1011 Nm 2. What is the magnitude of the force stretching the rod? (a) 100.5 kN (b) 201 kN (c) 78 kN (d) 150 kN 6. The load versus elongation graph for four wires of the equal length and same material is shown in figure. The thinnest wire is represented by line 2 FL 5 AY 3 FL 5 AY (b) (d) 3 FL 8 AY 8 FL 3 AY One end of a wire of length L and weight w is attached rigidly to a point in roof and a weight w1 is suspended from its lower end. If A is the area of cross-section of the wire then the stress in the wire at a height 3L 4 from its lower end is (a) Two exactly similar wires of steel and copper are stretched by equal forces. If the total elongation is 2 cm, then how much is the elongation in steel and copper wire respectively ? Given, Ysteel = 20 1011 dyne/cm2, Ycopper = 12 1011 dyne/cm2. (a) 1.25 cm; 0.75 cm (b) 0.75 cm; 1.25 cm (c) 1.15 cm; 0.85 cm (d) 0.85 cm; 1.15 cm 5. A uniform cylindrical rod of length L, cross-sectional area A and Young s modulus Y is acted upon by the forces as shown in figure. The elongation of the rod is (a) What is the percentage increase in length of a wire of diameter 2.5 mm, stretched by a force of 100 kg wt? Young s modulus of elasticity of wire = 12.5 1011 dyne/cm2 (a) 0.16% (b) 0.32% (c) 0.08% (d) 0.12% OC OD OA OB w1 A w1 + (b) A w1 + (c) (d) 9. 3w 4 A w1 + w2 A The stress versus strain graph for wires of two materials A and B are as shown in the figure. If YA and YB are the Young s moduli of the materials, then (a) (b) (c) (d) 5 w 4 YB = 2YA YA = 3YB YB = 3YA YA = YB 14. 10. A massless uniform rod is subjected to force F at its free end as shown in figure. The ratio of tensile stress at plane P1 to stress at P2 is Which of the following is the graph showing stressstrain variation for elastomers? (a) (b) (c) (d) (a) 1 : 2 2:1 (b) (c) 1 : 4 (d) 3 : 2 11. 12. Select the incorrect option (a) The Young s modulus and modulus of rigidity exist only for solids (b) The value of modulus of elasticity is independent of the magnitude of stress and strain (c) The value of modulus of elasticity depends only on the nature of material of the body (d) Only gases cannot exhibit a shearing stress Select the correct alternative(s) (a) Elastic forces are not always conservative (b) Elastic forces are always conservative (c) Elastic forces are conservative only when Hooke's law is obeyed (d) Elastic forces are not conservative 16. In the given figure, if the dimensions of the two wires are same but materials are different, then Young's modulus is A steel ring of radius r and cross-section area A is fitted on to a wooden disc of radius R (R > r). If y is Young s modulus of elasticity, then tension with which the steel ring is expanded is (a) (b) (c) (d) 13. 15. AyR r (a) (b) (c) (d) Ay ( R r ) r y(R r) Ar yr AR Stress vs strain graph for two different wires A and B is given. If YA and YB are Young s modulus of material then (a) YA = 3 YB (b) 3 YA = YB (c) YA = 3YB (d) 3YA = YB 6 More for A than B More for B than A Equal for A and B None of these 16. Calculate the work done, if a wire is loaded by 'Mg' weight and the increase in length is 'l' (a) Mgl (b) Zero (c) Mgl/2 (d) 2Mgl 18. A wire is suspended by one end. At the other end a weight equivalent to 20 N force is applied. If the increase in length is 1.0 mm, the increase in energy of the wire will be (a) 0.01 J (b) 0.02 J (c) 0.04 J (d) 1.00 J 19. A wire is suspended by one end. At the other end a weight equivalent to 20 N force is applied. The ratio of the increase in energy of the wire to the decrease in gravitational potential energy as load moves downwards by 1 mm, will be (a) 1 (b) 1/4 (c) 1/3 (d) 20. If s is stress and Y is Young s modulus of material, the energy stored per unit volume is (a) 2Y s (c) 2s2Y 21. 22. (b) s 2Y (d) s2 2Y A wire 2 m in length suspended vertically stretches by 10 mm when mass of 10 kg is attached to the lower end. The elastic potential energy gain by the wire is (take g = 10 m/s2) (a) 0.5 J (b) 5 J (c) 50 J (d) 500 J 27. A 2 m long rod of radius 1 cm which is fixed from one end is given a twist of 0.8 radians. The shear strain developed will be: (a) 0.002 (b) 0.004 (c) 0.008 (d) 0.016 28. The Young's modulus of the material of a wire is 6 1012 N/m2 and there is no transverse strain in it, then its modulus of rigidity will be (a) 3 1012 N/m2 (b) 2 1012 N/m2 (c) 1012 N/m2 (d) None of the above 29. The elastic energy stored in a wire of Yong's modulus Y is Strain 2 (a) Y Volume (b) Stress Strain Volume Stress 2 Volume (c) 2Y A wire of length L and cross-sectional area A is made of material of Young s modulus Y. The work done in stretching the wire by an amount x is YAx 2 YAx 2 (a) (b) 2L L 2 2YAx 4YAx 2 (c) (d) L L (d) 30. 1 Y Stress Strain Volume 2 The ratio of Young's modulus of the material of two wires is 2 : 3. If the same stress is applied on both, then the ratio of elastic energy per unit volume will be (a) 3 : 2 (b) 2 : 3 (c) 3 : 4 (d) 4 : 3 23. A steel wire of diameter 2 mm has a breaking strength of 4 105 N. What is the breaking force of similar steel wire of diameter 1.5 mm? (a) 2.3 105 N (b) 2.6 105 N 5 (c) 3 10 N (d) 1.5 105 N 24. Two wires of equal length and cross-sectional area are suspended as shown in figure. Their Young's modulli are Y1 = 2 1011 Pa and Y2 = 0.90 1011 Pa respectively. What will be the equivalent Young's modulus of combination? More Than Type Questions: (31 to 35) 31. The Young s modulus of steel is twice that of brass. Two wires of the same length and of the same area of cross-section, on of steel and another of brass are suspended from the same roof. If we want the lower ends of the wires to be at the same level, then the weight added to the steel and brass wires must be in the ratio of: (a) 1 : 2 (b) 2 : 1 (c) 4 : 1 (d) 1 : 1 (a) 2.90 1011 Pa (c) 1.34 1011 Pa 32. 25. (b) 1.45 1011 Pa (d) 4.25 1011 Pa What is the greatest length of copper wire that can hang without breaking? Breaking stress = 7.2 107 N/m2. Density of copper = 7.2 g/cc, g = 10 m/s2 (a) 100 m (b) 1000 m (c) 150 m (d) 1500 m (a) (c) 33. 26. The bulk modulus of a spherical object is B. If it is subjected to uniform pressure P, the fractional decrease in radius will be: The density of material of a wire is 6 g/cc. If to break the wire a stress of 107 N/m2 is required, then the length of the wire which will break by its own weight will be [Take g = 10 m/s2] (a) 121 m (b) 185 m (c) 133 m (d) 167 m 7 P B 3P B (b) (d) B 3P P 3B The following four wires are made of the same material. Which of them will have the largest extension when the same tension is applied? (a) Length = 50 cm, diameter = 0.5 mm (b) Length = 100 cm, diameter = 1 mm (c) Length = 200 cm, diameter = 2 mm (d) Length = 300 cm, diameter = 3 mm 34. In plotting stress versus strain curves for two materials P and Q, a student by mistake puts strain on the y-axis and stress on the x-axis as shown in the figure. Then the correct statements(s) is (are) (a) (b) (c) (d) 35. 38. Passage-II (39 and 40) In factories rods are suspended from roof with the help of wires for certain mechanical operations. These operations are always limited by the elastic property of suspension wires and the rod. A rod of length l is held horizontal by suspending it by two wires A and B of different materials but equal lengths having area of cross-sections 0.2 cm2 and 0.3 cm2. A weight W is hung from the rod. The value of YA = 12 1011 and YB = 36 1011. 39. The weight is suspended to produce equal stress in two wires then the tensions in two wires are TA and TB respectively as P has more tensile strength than Q P is more ductile than Q P is more brittle than Q The Young s modulus of P is more than that of Q Two rods of different materials having coefficients of thermal expansion 1, 2 and Young s moduli Y1, Y2 respectively are fixed between two rigid massive walls. The rods are heated such that they undergo the same increase in temperature. There is no bending of the rods. If 1 : 2 = 2 : 3, the thermal stresses developed in the two rods are equal provided Y1 : Y2 is equal to (a) 2 : 3 (b) 1 : 1 (c) 3 : 2 (d) 4 : 9 (a) (c) Passage Type Questions: (36 to 40) Passage-I (36 to 38) Figure shows qualitatively the relation between the stress and the strain as the deformation gradually increases. It is observed that for a substantial range of stresses, the stress-strain relation is linear, and the specimen recovers to its original dimensions when load is removed. 36. For which range, during unloading the above curve will be retraced? (a) up to OA only (b) up to OB (c) up to C (d) Never retraced its path 37. In the above question, during loading and unloading the force exerted by the material are conservative up to? (a) OA only (b) OB only (c) OC only (d) OD only During unloading beyond B, say C, the length at zero stress is now equal to (a) less than original length (b) greater than original length (c) original length (d) can t be predicted 40. W W , 2 2 3 2 W, W 5 5 2 3 W, W 5 5 W 2 (d) , W 3 3 (b) In the above situation the weight W is hanging from a point which divides the length of rod in the ratio lA : lB as (a) 1 : 1 (b) 1 : 2 (c) 2 : 3 (d) 3 : 2 Match the Column Type Questions: (41 to 45) 41. Match the following: Column-I Column-II Molecules have large (A) kinetic energy and almost (p) Solids zero potential energy Molecules have kinetic (B) energy larger than potential (q) Liquids energy Molecules have kinetic (C) energy smaller than (r) Gases potential energy Matter particles are (D) (s) Plasma charged ions (a) A q, r; B p; C p; D s (b) A r; B q; C p; D s (c) A s; B r; C q; D p (d) None of these 8 42. Match the following: Column-I (A) (B) (C) (D) (a) (b) (c) (d) 43. Column-II Maximum deforming force upto which body shows perfect elastic behaviour when Elastic (p) removed and beyond fatigue which if force is increased body showing elastic behaviour Loss of electric property for longer Elastic (q) time due to continuous after effect use of body showing elastic behaviour Loss of elastic property for shorter duration and when Elastomer (r) deforming forces are removed body does not regain its original shape immediately The bodies which do not have stress directly Elastic (s) proportional to strain limit and have no plastic range. A q; B p; C p; D q, s A p; B r; C q; D s A q; B r; C s; D p None of these 44. A body is falling in viscus medium. The terminal velocity depends on various factors. Column-I Column-II Terminal velocity Directly depends on (A) (p) proportional acceleration due to to square gravity Terminal velocity depends on radius of Directly (B) (q) sphere falling in proportional viscous medium Lesser is Greater the density (C) (r) terminal and viscosity of fluid velocity Smaller is Greater than density of (D) (s) terminal solid velocity (a) A s; B q; C q; D p (b) A r; B q; C p; D s (c) A q; B p; C r; D p (d) None of these 45. Match the following: Column-I Column-II Uniform stress (A) (p) developed in the rod Non-uniform stresses (B) (q) developed in the road Compressive (C) (r) stress developed Tensile stresses (D) (s) developed (a) A p, r; B p, s; C p, s; D q, r (b) A r; B r, s; C p; D s (c) A q; B p; C p; D q (d) None of these Integer Type Questions: (46 to 50) 46. The bulk modulus of rubber is 9.8 108 N/m2. To what depth (in meter) a rubber ball be taken in a lake so that its volume is decreased by 0.1%? (g = 9.8 m/s2) Match the following: Column-I Column-II Ratio of longitudinal Modulus of (A) or tensile stress to (p) Rigidly longitudinal strain Ratio of normal or Poisson s (B) hydrostatic stress to (q) ratio volumetric strain Ratio of lateral Bulk (C) strain to longitudinal (r) modulus strain Ratio of tangential Young s (D) (s) stress to shear strain modulus (a) A s; B r; D q; D p (b) A r; B s; C p; D q (c) A q; B s; C p; D r (d) None of these 9 47. If the work done by stretching a wire by 1 mm is 2 J, the work necessary for stretching another wire of the same material but with double the radius of cross section and half the length by 1 mm is (in joule)? 48. The approximate depth of an ocean is 2700 m. The compressibility of water is 45.4 10 11 Pa 1 and density of water is 103 kg/m3, then the fractional compression of water will be obtained at the bottom of the ocean is 1.2 10 x, then value of x is (g = 10 m/s2) 49. Two identical rods are pulled as shown in figure (1) and (2). The surfaces are smooth. If l1 and l2 are the elongations in two cases respectively, then find l2 . l1 50. 10 A tube has two area of cross-sections as shown in figure. The diameters of the tube are 8 mm and 12 mm. Find range of water falling on horizontal surface, if piston is moving with a constant velocity of 0.25 m/s, h = 1.25 m (g = 10 m/s2) Exercise -3 (PYQ s) 9. The density and breaking stress of a wire are 6 104 kg/m3 and 1.2 108 N/m2 respectively. The wire is suspended from a rigid support on a planet where acceleration due to gravity is 1rd/3 of the value on the surface of earth. The maximum length of the wire with breaking is ______ m (take, g = 10 m/s2) [05 April, 2024 (Shift-I)] 10. A wire of cross sectional area A, modulus of elasticity 2 1011 Nm 2 and length 2 m is stretched between two vertical rigid supports. When a mass of 2 kg is suspended at the middle it sags lower from its original position making angle q = 1/100 radian on the points of support. The value of A is _____ 10 4 m2 (consider x << L). (given : g = 10 m/s2) [06 April, 2024 (Shift-II)] T1 Strain, Stress, Young s Modulus of Elasticity 1. Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R) [27 Jan, 2024 (Shift-II)] Assertion (A): The property of body, by virtue of which it tends to regain its original shape when the external force is removed, is Elasticity. Reason (R): The restoring force depends upon the bonded inter atomic and inter molecular force of solid. In the light of the above statements, choose the correct answer 2L from the options given below: (a) (b) (c) (d) (A) is false but (R) is true (A) is true but (R) is false Both (A) and (R) are true and (R) is the correct explanation (A) Both (A) and (R) are true but (R) is not the correct explanation of (A) 2kg 11. Two persons pull a wire towards themselves. Each person exerts a force of 200 N on the wire. Young s modulus of the material of wire is 1 1011 N m 2. Original length of the wire is 2 m and the area of cross section is 2 cm2. The wire will extend in length by ______ mm. [09 April, 2024 (Shift-I)] 2. A wire of length L and radius r is clamped at one end. If its other end is pulled by a force F, its length increases by l. If the radius of the wire and the applied force both are reduced to half of their original values keeping original length constant, the increase in length will become. [29 Jan, 2024 (Shift-II)] (a) 3 times (b) 3/2 times (c) 4 times (d) 2 times 12. A 100 m long wire having cross-sectional area 6.25 10 4m2 and Young s modulus is 1010 Nm 2 is subjected to a load of 250 N, then the elongation in the wire will be: [24 Jan, 2023 (Shift-I)] 3. Two metallic wires P and Q have same volume and are made up of same material. If their area of cross sections are in the ratio 4 : 1 and force F1 is applied to P, an extension of Dl is produced. The force which is required to produce same extension in Q is F2. (a) 6.25 10 3 m (c) 6.25 10 m (d) 4 10 3 m 13. Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A: Steel is used in the construction of buildings and bridges. Reason R: Steel is more elastic and its elastic limit is high. In the light of above statements, choose the most appropriate answer from the options given below [24 Jan, 2023 (Shift-II)] (a) Both A and R are correct but R is NOT the correct explanation of A (b) A is not correct but R is correct (c) Both A and R are correct and R is the correct explanation of A (d) A is correct but R is not correct 4. Young s modules of material of a wire of length L and crosssectional area A is Y. If the length of the wire is doubled and cross-sectional area is halved then Young s modules will be: [30 Jan, 2024 (Shift-I)] Y (a) (b) 4Y (c) Y (d) 2Y 4 5. Each of three blocks P, Q and R shown in figure has a mass of 3 kg. Each of the wire A and B has cross-sectional area 0.005 cm 2 and Young s modulus 2 10 11 N m 2. Neglecting friction, the longitudinal strain on wire B is ________ 10 4. (Take g = 10 m/s 2) [30 Jan, 2024 (Shift-I)] P A Q 14. As shown in the figure, in an experiment to determine Young s modulus of a wire, the extension-load curve is plotted. The curve is a straight line passing through the origin and makes an angle of 45 with the load axis. The length of the wire is 62.8 cm and its diameter is 4 mm. The Young s modulus is found to be x 104 Nm 2. The value of x is______ [25 Jan, 2023 (Shift-I)] B Extension (m) R 6. A solid circular disc of mass 50 kg rolls along a horizontal floor so that its center of mass has a speed of 0.4 m/s. The absolute value of work done on the disc to stop it is ______ J. (b) 4 10 4 m 6 [29 Jan, 2024 (Shift-II)] F The value of 1 is: _______ . F2 x [31 Jan, 2024 (Shift-I)] 7. One end of a metal wire is fixed to a ceiling and a load of 2 kg hangs from the other end. A similar wire is attached to the bottom of the load and another load of 1 kg hangs from this lower wire. Then the ratio of longitudinal strain of upper wire to that of the lower wire will be ___. 45 Load (N) 15. A force is applied to a steel wire A , rigidly clamped at one end. As a result elongation in the wire is 0.2 mm. If same force is applied to another steel wire B of double the length and a diameter 2.4 times that of the wire A , the elongation in the wire B will be (wires having uniform circular cross sections) [30 Jan, 2023 (Shift-II)] (a) 6.06 10 2 mm (b) 2.77 10 2 mm (c) 3.0 10 2 mm (d) 6.9 10 2 mm [Area of cross section of wire 0.005 cm2, Y = 2 1011 Nm 2 and g = 10 ms 2] [1 Feb, 2024 (Shift-II)] 8. An elastic spring under tension of 3 N has a length a. Its length is b under tension 2 N. For its length (3a 2b), the value of tension will be _____ N. [04 April, 2024 (Shift-I)] 11 16. Under the same load, wire A having length 5.0 m and cross section 2.5 10 5 m2 stretches uniformly by the same amount as another wire B of length 6.0 m and a cross section of 3.0 10 5 m2 stretches. The ratio of the Young s modulus of wire A to that of wire B will be: [31 Jan, 2023 (Shift-II)] (a) 1 : 4 (b) 1 : 1 (c) 1 : 10 (d) 1 : 2 24. The elongation of a wire on the surface of the earth is 10 4 m. The same wire of same dimensions is elongated by 6 10 5 m on another planet. The acceleration due to gravity on the planet will be _________ms 2. (Take acceleration due to gravity on the surface of earth = 10 ms 2) [26 June, 2022 (Shift-I)] 25. A wire of length L is hanging from a fixed support. The length changes to L1 and L2 when masses 1kg and 2kg are suspended respectively from its free end. Then the value of L is equal to: 17. The Young s modulus of a steel wire of length 6 m and crosssectional area 3 mm2, is 2 1111 N / m 2 . The wire is suspended from its support on a given planet. A block of mass 4 kg is attached to the free end of the wire. The acceleration due to gravity on the planet [29 June, 2022 (Shift-I)] L + L2 L1 L2 (b) 1 2 (c) 2L1 L2 (d) 3L1 2L2 (a) is 1 of its value on the earth. The elongation of wire is (Take g on 4 the earth = 10 m/s2) [1 Feb, 2023 (Shift-II)] (a) 1 cm (b) 1 mm (c) 0.1 mm (d) 0.1 cm 26. A wire of length L and radius r is clamped rigidly at one end. When the other end of the wire is pulled by a force F, its length increases by 5cm. Another wire of the same material of length 4L and radius 4r pulled by a force 4F under same conditions. The increase in length of this wire is ______ cm. [25 July, 2022 (Shift-I)] 18. A steel rod has a radius of 20 mm and a length of 20m. A force of 62.8 kN stretches it along its length. Young s modulus of steel is 2.0 1011 N/m2. The longitudinal strain produced in the wire is ____ 10 5 [06 April, 2023 (Shift-I)] 27. A uniform heavy rod of mass 20 kg, cross sectional area 0.4 m2 and length 20 m is hanging from a fixed support. Neglecting the lateral contraction, the elongation in the rod due to its own weight is x 10 9 m. The value of x is __________: (Given. Young s modulus Y = 2 1011 Nm 2 and g = 10 ms 2) [26 July, 2022 (Shift-II)] 19. A metal block of mass m is suspended from a rigid support through a metal wire of diameter 14 mm. The tensile stress developed in the wire under equilibrium state is 7 105 Nm 2. The value of mass m is __________ kg. 22 (Take, g = 9.8 ms 2 and = ) [6 April, 2023 (Shift-II)] 7 28. The area of cross section of the rope used to lift a load by a crane is 2.5 10 4 m2. The maximum lifting capacity of the crane is 10 metric tons. To increase the lifting capacity of the crane to 25 metric tons, the required area of cross section of the rope should be: (take g = 10 ms 2) [26 July, 2022 (Shift-II)] (a) 6.25 10 4 m2 (b) 10 10 4 m2 (c) 1 10 4 m2 (d) 1.67 10 4 m2 20. Two wires each of radius 0.2 cm and negligible mass, one made of steel and other made of brass are loaded as shown in the figure. The elongation of the steel wire is ___ 10 6 m. [Young s modulus for steel = 2 1011 Nm 2 and g = 10 ms 2] [10 April, 2023 (Shift-I)] 29. In an experiment to determine the Young s modulus, steel wires of five different lengths (1, 2, 3, 4, and 5m) but of same cross section (2 mm2) were taken and curves between extension and load were obtained. The slope (extension / load) of the curves were plotted with the wire length and the following graph is obtained. If the Young s modulus of given steel wires is x 1011 Nm 2, then the value of x is _________. [27 July, 2022 (Shift-II)] 1.6m steel 2 kg 1m brass 1.14 kg Extension 10 5 Nm 2 Load 21. Young s moduli of the material of wires A and B are in the ratio of 1 : 4, while its area of cross sections are in the ratio of 1 : 3. If the same amount of load is applied to both the wires, the amount of elongation produced in the wires A and B will be in the ratio of [Assume length of wires A and B are same] 1 2 3 4 5 Wire length (m) [10 April, 2023 (Shift-II)] (a) 36 : 1 (b) 12 : 1 (c) 1 : 36 (d) 1 : 12 30. The force required to stretch a wire of cross-section 1 cm2 to double its length will be: (Given Young s modulus of the wire = 2 1011 N/m2) [28 July, 2022 (Shift-I)] (a) 1 107 N (b) 1.5 107 N (c) 2 107 N (d) 2.5 107N 22. The length of wire becomes l1 and l2 when 100 N and 120 N tensions are applied respectively. If 10 l 2 = 11 l 1 , the 1 natural length of wire will be l1 . Here the value of x x is _______. [11 April, 2023 (Shift-I)] 31. A string of area of cross section 4 mm2 and length 0.5 m is connected with a rigid body of mass 2 kg. The body is rotated in a vertical circular path of radius 0.5 m. The body acquires a speed of 5 m/s at the bottom of the circular path. Strain produced in the string when the body is at bottom of the circle is ______ 10 5. 23. A wire of length L and radius r is clamped rigidly at one end. When the other end of the wire is pulled by a force f, its length increases by . Another wire of same material of length 2L and radius 2r is pulled by a force 2f Then the increase in its length will be : [15 April, 2023 (Shift-I)] (a) 2 (b) 1.25 1.0 0.75 0.5 0.25 (c) 4 (d) /2 12 (use Young s modulus 1011N /m2 and g = 10 m/s2) [28 July, 2022 (Shift-II)] 32. If the length of a wire is made double and radius is halved of its respective values. Then, the Young s modulus of the material of wire will: [29 July, 2022 (Shift-I)] (A) remain same (B) become 8 times its initial value 1 th (C) become of its initial value 4 40. Wires W1 and W2 are made of same material having the breaking stress of 1.25 109 N /m2 . W1 and W2 have cross-sectional area of 8 10 7 m2 and 4 10 7 m2, respectively. Masses of 20 kg and 10 kg hang from them as shown in the figure. The maximum mass that can be placed in the pan without breaking the wires is ____ kg. (Use g = 10 m/s2) [27 Aug, 2021 (Shift-II)] W1 (D) become 4 times its initial value (a) 2 10 9 m (b) 5 10 10 m 8 (c) 4 10 m (d) 5 10 8 m 20kg W2 10kg 33. If Y, K and are the value of Young s moduls, bulk modulus of rigidity of any material respectively. Choose the correct relation for these parameters [24 Feb, 2021 (Shift-I)] 9K (a) Y = (b) K = Y N/m 2 N/m 2 2 + 3K 9 3Y (c) = 3YK N/m 2 9K + Y pan 41. A uniform heavy rod of weight 10 kg ms 2, cross-sectional area 100 cm2 and length 20 cm is hanging from a fixed support. Young modulus of the material of the rod is 2 1011 Nm 2. Neglecting the lateral contraction, find the elongation of rod due to its own weight: [31 Aug, 2021 (Shift-I)] (d) Y = 9 K N/m 2 3K 34. A uniform metallic wire is elongated by 0.04 m when subjected to a linear force F. The elongation, if its length and diameter is doubled and subjected to the same force will be __________ cm. 42. Four identical hollow cylindrical columns of mild steel support a big structure of mass 50 103 kg, The inner and outer radii of each column are 50 cm and 100 cm respectively. Assuming uniform local distribution, calculate the compression strain of each column. [31 Aug, 2021 (Shift-II)] [Use Y = 2.0 1011 Pa, g = 9.8 m/s2] (a) 3.60 10 8 (b) 2.60 10 7 3 (c) 1.87 10 (d) 7.07 10 4 [24 Feb, 2021 (Shift-II)] 35. The length of metallic wire is 1 when tension in it is T1. It is 2 when the tension is T2. The original length of the wire will be: [26 Feb, 2021 (Shift-II)] T + T T (a) 2 1 1 2 (b) 1 1 T2 2 T1 + T2 T2 T1 (c) T2 1 T1 2 (d) 1 + 2 T2 T1 2 36. Two separate wires A and B are stretched by 2 mm and 4 mm respectively, when they are subjected to a force of 2N. Assume that both the wires are made up of same material and the radius of wire B is 4 times that of the radius of wire A. The length of the wires A and B are in the ratio of a : b. Then a/b can be expressed as 1/x where x is ______. [18 March, 2021 (Shift-I)] 37. The value of tension in a long thin metal wire has been changed from T1 to T2. The lengths of the metal wire at two different values of tension T1 and T2 are 1 and 2 respectively. The actual length of the metal wire is: [20 July, 2021 (Shift-I)] (a) T1 2 T2 1 (b) T1 T2 (c) T T 1 + 2 (d) 1 1 2 2 T1 T2 2 43. Speed of a transverse wave on a straight wire (mass 6.0 g, length 60 cm and area of cross- section 1.0 mm2) is 90 ms 1. If the young s modulus of wire is 16 1011 Nm 2, the extension of wire over its natural length is: [7 Jan, 2020 (Shift-I)] (a) 0.03 mm (b) 0.01 mm (c) 0.02 mm (d) 0.04 mm 44. A rod of length L at room temperature and uniform area of cross section A, is made of a metal having coefficient of linear expansion / C. It is observed that an external compressive force F, is applied on each of its ends, prevents any change in the length of the rod, when it temperature rises by T K. Young s modulus, Y, for this metal is: [9 Jan, 2019 (Shift-I)] T1T 2 1 2 38. The length of a metal wire is l1, when the tension in it is T1 and is l2 when the tension is T2. The natural length of the wire is: [20 July, 2021 (Shift-II)] (a) (c) (b) 1 2 F (b) F A DT A ( DT 273) (c) F (d) 2F 2A DT A DT 45. A load of mass M kg is suspended from a steel wire of length 2 m and radius 1.0 mm in Searle s apparatus experiment. The increase in length produced in the wire is 4.0 mm. Now the load is fully immersed in a liquid of relative density 2. The relative density of the material of load is 8. The new value of increase in length of the steel wire is: [12 Jan, 2019 (Shift-II)] (a) 3.0 mm (b) 4.0 mm (c) 5.0 mm (d) zero 1 + 2 2 1T2 2T1 (d) 1T2 + 2T1 T2 T1 T2 + T1 39. Two wires of same length and radius are joined end to end and loaded. The Young s modulii of the materials of the two wires are Y1 and Y2. The combination behaves as a single wire then its Young s modulus is: [25 July, 2021 (Shift-I)] (a) Y = (a) 46. A steel wire having a radius of 2.0 mm, carrying a load of 4 kg, is hanging from a ceiling. Given that g = 3.1 ms 2, what will be the tensile stress that would be developed in the wire? (a) (b) (c) (d) 2Y1Y2 Y1Y2 (b) Y= 3( Y 2(Y1 + Y2 ) 1 + Y2 ) (c) Y = Y1Y2 (d) Y = 2Y1Y2 Y1 + Y2 Y1 + Y2 13 [8 April, 2019 (Shift-I)] 4.8 106 Nm 2 5.2 106 Nm 2 6.2 106 Nm 2 3.1 106 Nm 2 47. Young s moduli of two wires A and B in the ratio 7 : 4. Wire A is 2 m long and has radius R. Wire B is 1.5 m long and has radius 2 mm. If the two wires stretch by the same length for a given load, then the value of R is close to [8 April, 2019 (Shift-II)] (a) 1.9 mm (b) 1.7 mm (c) 1.5 mm (d) 1.3 mm T2 Bulk Modulus, Shear Modulus, Elasticity Potential Energy 53. Match List-I with List-II: List-I 48. A boy s catapult is made of rubber cord which is 42 cm long, with 6 mm diameter of cross-section and of negligible mass. The boy keeps a stone weighing 0.02 kg on it and stretches the cord by 20 cm by applying a constant force. When released, the stone flies off with a velocity of 20 ms 1. Neglect the change in the area of cross-section of the cord while stretched. The Young s modulus of rubber is closest to: [8 April, 2019 (Shift-I)] (a) 104 Nm 2 (b) 108 Nm 2 (c) 106 Nm 2 (d) 103 Nm 2 49. In an experiment, brass and steel wires of length 1 m each with areas of cross section 1 mm2 are used. The wires are connected in series and one end of the combined wire is connected to a rigid support and other end is subjected to elongation. The stress required to produce a net elongation of 0.2 mm is: [10 April, 2019 (Shift-II)] (Given, the Young s Modulus for steel and brass are respectively, 120 109 N/m2 and 60 109 N/m2 ) (a) 0.2 106 N/m2 (b) 4.0 106 N/m2 (c) 1.8 106 N/m2 (d) 1.2 106 N/m2 A force that restores an elastic body of unit area to its original state (I) Bulk modulus (B) Two equal and opposite forces parallel to opposite faces (II) Young s modulus (C) Forces perpendicular everywhere to the surface per unit area same everywhere (III) Stress (D) Two equal and opposite forces perpendicular to opposite faces (IV) Shear modulus Choose the correct answer from the options given below: [05 April, 2024 (Shift-II)] (A)-(II), (B)-(IV), (C)-(I), (D)-(III) (A)-(IV), (B)-(II), (C)-(III), (D)-(I) (A)-(III), (B)-(IV), (C)-(I), (D)-(II) (A)-(III), (B)-(I), (C)-(II), (D)-(IV) 54. Choose the correct relationship between Poisson ratio ( ). bulk modulus (K) and modulus of rigidity ( ) of a given solid object: [30 Jan, 2023 (Shift-I)] (a) 1.16 mm (b) 0.90 mm (c) 1.36 mm (d) 1.00 mm 51. A uniform cylindrical rod of length L and radius r, is made from a material whose Young s modulus of Elasticity equals Y. When this rod is heated by temperature T and simultaneously subjected to a net longitudinal compressional force F, its length remains unchanged. The coefficient of volume expansion, of the material of the rod, is (nearly) equals to: [12 April, 2019 (Shift-II)] (a) 9F/( r2YT) (b) F/(3 r2YT) (c) 3F/( r2YT) (d) 6F/( r2YT) (a) = 3 K 2 6 K + 2 (b) = 6 K + 2 3K 2 (c) = 3 K + 2 6 K 2 (d) = 6 K + 2 3 K 2 55. A certain pressure P is applied to 1 litre of water and 2 litre of a liquid separately. Water gets compressed to 0.01% whereas the liquid gets compressed to 0.03%. The ratio of Bulk modulus of water to that of the liquid is 3 . The value of x is_______. x [01 Feb 2023 (Shift-I)] 56. An aluminium rod with Young s modulus Y = 7.0 1010 N/m2 undergoes elastic strain of 0.04%. The energy per unit volume stored in the rod in SI unit is: [8 April, 2023 (Shift-I)] (a) 5600 52. A block of weight 100 N is suspended by copper and steel wires of same cross sectional area 0.5 cm2 and, length 3 m and 1 m, respectively. Their other ends are fixed on a ceiling as shown in figure. The angles subtended by copper and steel wires with ceiling are 30 and 60 , respectively. If elongation in copper wire is ( lC) and elongation in steel wire is ( lS), then the ratio D C D S is ____________. [Young s modulus for copper and steel are 1 (b) 8400 (c) 2800 (d) 11200 57. The elastic potential energy stored in a steel wire of length 20 m stretched through 2 cm is 80 J. The cross sectional area of the wire is ________ mm2. [13 April, 2023 (Shift-I)] (Given, y = 2.0 1011 Nm 2) [JEE Adv, 2019] 58. The bulk modulus of a liquid is 3 10 Nm 2. The pressure required to reduce the volume of liquid by 2% is: [24 June, 2022 (Shift-I)] 10 30 Copper wire 3m 60 Steel wire 1m (A) (a) (b) (c) (d) 50. The elastic limit of brass is 379 MPa. What should be the minimum diameter of a brass rod if it is to support a 400 N load without exceeding its elastic limit? [10 April, 2019 (Shift-II)] 1011 N/m2 and 2 1011 N/m2 respectively] List-II Block 14 (a) 3 108 Nm 2 (b) 9 108 Nm 2 (c) 6 108 Nm 2 (d) 12 108 Nm 2 59. The elastic behaviour of material for linear stress and linear strain, is shown in the figure. The energy density for a linear strain of 5 10 4 is _________kJ/m3. Assume that material is elastic upto the linear strain of 5 10 4. [26 June, 2022 (Shift-I)] 4 10 3 10 Strain 2 10 62. An object is located at 2 km beneath the surface of the water. If DV the fractional compression is 1.36%, the ratio of hydraulic V stress to the corresponding hydraulic strain will be [Given: density of water is 1000kgm 3 and g = 9.8 ms 2.] 10 10 [17 March, 2021 (Shift-II)] 10 (a) 1.44 107 Nm 2 (b) 1.96 107 Nm 2 10 (c) 2.26 109 Nm 2 (d) 1.44 109 Nm 2 1 10 0 63. A stone of mass 20 g is projected from a rubber catapult of length 0.1 m and area of cross section 10 6 m2 stretched by an amount 0.04 m. The velocity of the projected stone is _______ m /s. (Young s modulus of rubber = 0.5 109 N/m2) [27 July, 2021 (Shift-I)] 20 40 60 80 Stress [N/m2] 60. A square aluminium (shear modulus is 25 109Nm 2) slab of side 60 cm and thickness 15 cm is subjected to a shearing force (on its narrow face) of 18.0 104 N. The lower edge is riveted to the floor. The displacement of the upper edge is _________ m. [27 July, 2022 (Shift-I)] 64. When a rubber ball is taken to a depth of __________m in deep sea, its volume decreases by 0.5%. (The bulk modulus of rubber = 9.8 108 Nm 2 and Density of sea water = 103 kgm 3, g = 9.8 m/s2) [31 Aug, 2021 (Shift-I)] 61. The normal density of a material its and its bulk modulus of elasticity is K. The magnitude of increase in density of material, when a pressure P is applied uniformly on all sides, will be : [26 Feb, 2021 (Shift-I)] 65. Tw o s t e e l w i r e s h a v i n g s a m e l e n g t h a r e s u s p e n d e d from a ceiling under the same load. If the ratio of their energy stored per unit volume is 1 : 4, the ratio of their diameters is: [9 Jan, 2020 (Shift-II)] (a) K P (a) 1 : 2 (b) 1: 2 (c) 2 : 1 (d) 2 :1 66. A cube of metal is subjected to a hydrostatic pressure of 4 GPa. The percentage change in the length of the side of the cube is close to (Given bulk modulus of metal, B = 8 1010 Pa) [4 Sep, 2020 (Shift-II)] (a) 0.6 (b) 20 (c) 1.67 (d) 5 (b) PK (c) K P (d) P K 15 Answer Key (Manthan) EXERCISE -1 1. 11. 21. 31. 41. (d) (b) (b) (c) (b) 2. 12. 22. 32. 42. (c) (b) (b) (c) (a) 3. 13. 23. 33. 43. (b) (a) (b) (c) (b) 4. 14. 24. 34. 44. (c) (c) (c) (d) (b) 5. 15. 25. 35. 45. (c) (d) (d) (a) (d) 6. 16. 26. 36. 46. (a) (b) (c) (a) (a) 7. 17. 27. 37. (c) (d) (c) (d) 8. 18. 28. 38. (a) (c) (d) (d) 9. 19. 29. 39. (c) (d) (d) (d) 3. 13. 23. 33. 43. (a) (a) (a) (a) (a) 4. 14. 24. 34. 44. (b) (c) (b) (a, b) (c) 5. (b) 15. (a) 25. (b) 35. (c) 45. (a) 6. 16. 26. 36. 46. (c) (a) (d) (b) (100) 7. (d) 17. (c) 27. (b) 37. (b) 47. (16) 8. 18. 28. 38. 48. (c) (a) (a) (b) (b) 9. 19. 29. 39. 49. (b) (d) (c) (b) (b) 10. 20. 30. 40. (b) (a) (d) (b) EXERCISE -2 1. 11. 21. 31. 41. (c) (d) (a) (b) (b) 2. 12. 22. 32. 42. (a) (b) (b) (d) (c) 10. 20. 30. 40. 50. (c) (d) (a) (d) (b) EXERCISE -3 (PYQ S) 1. 11. 21. 31. 41. 51. 61. (c) [20] (b) [30] (b) (c) (d) 2. 12. 22. 32. 42. 52. 62. (d) (d) [2] (a) (b) [2] (d) 3. 13. 23. 33. 43. 53. 63. [16] (c) (b) (b) (a) (c) [20] 4. 14. 24. 34. 44. 54. 64. (c) 5. [2] [5] 15. (d) [6] 25. (c) [2] 35. (c) (a) 45. (a) (a) 55. [1] [500] 65. (d) 6. 16. 26. 36. 46. 56. 66. 16 [12] (b) [5] [32] (d) (a) (c) 7. 17. 27. 37. 47. 57. [3] (c) [25] (a) (b) [40] 8. 18. 28. 38. 48. 58. [5] [25] (a) (c) (c) (c) 9. 19. 29. 39. 49. 59. [600] 10. [1] [11] 20. [20] [2] 30. (a) (d) 40. [40] (*) 50. (a) [25] 60. [3]

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