Page 1 KINEMATICS- SET-1 1. From a town, cars start at regular intervals of 30 s and run towards another town with constant speed of 60 km/h. At some point of time, all of the cars simultaneously have to reduce their speed to 40 km/h due to bad weather conditions. What will become the time interval between arrivals of the cars at the second town during the bad weather? (a) 20 s (b) 30 s (c) 40 s (d) 45 s 2. Sam used to walk to school every morning, and it takes him 20 minutes. Once on his way he realized that he had forgotten his homework, notebook at home. He knew that if he continued walking to school at the same speed, he would be there 8 minutes before the bell, so he went back home for the notebook and arrived the school 10 minutes late. If he had walked all the way his usual speed, what fraction of the way to school had he covered at that moment when he turned back? (a) 8/20 (b) 9/20 (c) 10/20 (d) 12/20 3. A car moving at 160 km/h when passes the mark-A, driver applies brake and reduces its speed uniformly to 40 km/h at mark-C. The marks are spaced at equal distances along the road as shown below. Mark -A Mark -B Mark -C At which part of the track the car has instantaneous speed of 100 km/h? Neglect the size of the car. (a) At mark-B (b) Between mark-A and mark-B (c) between mark-B and mark-C (d) insufficient information to decide 4. Two particles A and B starts from the same point and move in the positive x-direction. Their velocity-time relationships are shown in the following figures. What is the maximum separation between them during the time interval shown? Particle A 1.00 m/s 2.00 m/s 1.00 s 2.00 s Particle B 1.00 m/s 2.00 m/s 1.00 s 2.00 s (a) 1.00 m (b) 1.25 m (c) 1.50 m (d) 2.00 m 5. A material particle is chasing the other one and both of them are moving on the same straight line. Their motion after they pass a particular point is recorded and the data obtained is shown by velocity-time graphs of the particles. How long after the start will the chase end? Velocity (m/s) Time (s) 3 4 (a) 4.0 s (b) 6.0 s (c) 12 s (d) insufficient information 6. Two cars A and B simultaneously start a race. Velocity of the car A varies with time according to the graph shown. It acquires a speed of 50 m/s few seconds before t = 100 s and then moves with this constant speed. Car B runs together with A to a place where both have velocity of 20 m/s, after this place car B moves with zero acceleration for one second and then follows velocity-time relationship identical to that of A with a delay of one second. In this way car B acquires the constant velocity one second after A acquires it. How much more distance ?s car A covers in the first 100 s? 50 0 0 100 ts () v m s ( / ) (a) ?s = 30 m (b) ?s < 30 m (c) ?s = 20 m (d) insufficient information 7. Two motorboats, which can move with velocities 4.0 m/s and 6.0 m/s relative to water are going up- stream. When the faster one overtakes the slower one, a buoy is dropped from the slower one. After lapse of some time both the boats turn back Page 2 KINEMATICS- SET-1 1. From a town, cars start at regular intervals of 30 s and run towards another town with constant speed of 60 km/h. At some point of time, all of the cars simultaneously have to reduce their speed to 40 km/h due to bad weather conditions. What will become the time interval between arrivals of the cars at the second town during the bad weather? (a) 20 s (b) 30 s (c) 40 s (d) 45 s 2. Sam used to walk to school every morning, and it takes him 20 minutes. Once on his way he realized that he had forgotten his homework, notebook at home. He knew that if he continued walking to school at the same speed, he would be there 8 minutes before the bell, so he went back home for the notebook and arrived the school 10 minutes late. If he had walked all the way his usual speed, what fraction of the way to school had he covered at that moment when he turned back? (a) 8/20 (b) 9/20 (c) 10/20 (d) 12/20 3. A car moving at 160 km/h when passes the mark-A, driver applies brake and reduces its speed uniformly to 40 km/h at mark-C. The marks are spaced at equal distances along the road as shown below. Mark -A Mark -B Mark -C At which part of the track the car has instantaneous speed of 100 km/h? Neglect the size of the car. (a) At mark-B (b) Between mark-A and mark-B (c) between mark-B and mark-C (d) insufficient information to decide 4. Two particles A and B starts from the same point and move in the positive x-direction. Their velocity-time relationships are shown in the following figures. What is the maximum separation between them during the time interval shown? Particle A 1.00 m/s 2.00 m/s 1.00 s 2.00 s Particle B 1.00 m/s 2.00 m/s 1.00 s 2.00 s (a) 1.00 m (b) 1.25 m (c) 1.50 m (d) 2.00 m 5. A material particle is chasing the other one and both of them are moving on the same straight line. Their motion after they pass a particular point is recorded and the data obtained is shown by velocity-time graphs of the particles. How long after the start will the chase end? Velocity (m/s) Time (s) 3 4 (a) 4.0 s (b) 6.0 s (c) 12 s (d) insufficient information 6. Two cars A and B simultaneously start a race. Velocity of the car A varies with time according to the graph shown. It acquires a speed of 50 m/s few seconds before t = 100 s and then moves with this constant speed. Car B runs together with A to a place where both have velocity of 20 m/s, after this place car B moves with zero acceleration for one second and then follows velocity-time relationship identical to that of A with a delay of one second. In this way car B acquires the constant velocity one second after A acquires it. How much more distance ?s car A covers in the first 100 s? 50 0 0 100 ts () v m s ( / ) (a) ?s = 30 m (b) ?s < 30 m (c) ?s = 20 m (d) insufficient information 7. Two motorboats, which can move with velocities 4.0 m/s and 6.0 m/s relative to water are going up- stream. When the faster one overtakes the slower one, a buoy is dropped from the slower one. After lapse of some time both the boats turn back KINEMATICS- SET-1 simultaneously and move at the same speeds relative to the water as before. Their engines are switched off when they reach the buoy again. If the maximum separation between the boats is 200 m after the buoy is dropped and water flow velocity is 1.5 m/s, find the distance between the two places where the boats meet the buoy. (a) 75 m (b) 150 m (c) 300 m (d) 350 m 8. Two students start running on a circular track from the same place at the same time and in two minutes one of them completes three and other four revolutions. Due to thick vegetation in circular area, each of the boys can see only one third of the track at a time. How long during their run they will remain visible to each other? (a) 20 s (b) 40 s (c) 80 s (d) 160 s 9. Three ants A, B and C initially rest on the vertices of an equilateral triangle on a large horizonal tabletop. The ants A and B can crawl with constant velocities A v ? and B v ? in any direction. Which of the following inequalities the speed of the third ant C must satisfy to preserve equilateral shape of the triangle? (a) v C < 0.5 (v A + v B ) (b) v C = 0.5 (v A + v B ) (c) v C < v A + v B (d) v C = v A + v B 10. A body experiences a drag force proportional to its speed, when it moves in constant water. A student drops several identical stones one by one from different heights into a deep lake and for each stone, he prepares graphs between v in water and time t. Having studied all of them, he finds that they can be divided into the following three categories. v v 0 t v v 0 t v v 0 t Which of the following explanations appear reasonable? (a) the first graph shows what happens when the ball is dropped from a small height, and the second shows what happens when it is dropped from a large height. (b) The first graph shows what happens when the ball is dropped from a large height, and the second shows what happens when it is dropped from a small height. (c) The third graph tells the possibility only when the stone is dropped from such a height that it acquires the speed v 0 at the instant it enters the water. (d) The third graph is not possible. 11. On a road going out of a city, the last traffic light glows green for 1.0 min and red for 2.0 min. After the traffic light, the road is straight and vehicles run at their constant speeds. This mode of operation of traffic lights causes the vehicles come out off the city in groups i.e., when traffic light is green a group of vehicles comes out and then next group during the next green signal and so on. Speeds of vehicles in a group lie in the range from 60 to 80 km/h. Some distance away from the traffic light, the groups will become indistinguishable. Assume that the vehicles acquires their constant speed in negligible time and mark the correct statement or statements. (a) at distance 4.0 km from the traffic light, the groups become indistinguishable. (b) at distance 8.0 km from the traffic light, the group become indistinguishable. (c) wider is the range of speed; longer is the distance where groups become indistinguishable. (d) larger is the number of fast moving vehicles, shorter is the distance where groups become indistinguishable. Page 3 KINEMATICS- SET-1 1. From a town, cars start at regular intervals of 30 s and run towards another town with constant speed of 60 km/h. At some point of time, all of the cars simultaneously have to reduce their speed to 40 km/h due to bad weather conditions. What will become the time interval between arrivals of the cars at the second town during the bad weather? (a) 20 s (b) 30 s (c) 40 s (d) 45 s 2. Sam used to walk to school every morning, and it takes him 20 minutes. Once on his way he realized that he had forgotten his homework, notebook at home. He knew that if he continued walking to school at the same speed, he would be there 8 minutes before the bell, so he went back home for the notebook and arrived the school 10 minutes late. If he had walked all the way his usual speed, what fraction of the way to school had he covered at that moment when he turned back? (a) 8/20 (b) 9/20 (c) 10/20 (d) 12/20 3. A car moving at 160 km/h when passes the mark-A, driver applies brake and reduces its speed uniformly to 40 km/h at mark-C. The marks are spaced at equal distances along the road as shown below. Mark -A Mark -B Mark -C At which part of the track the car has instantaneous speed of 100 km/h? Neglect the size of the car. (a) At mark-B (b) Between mark-A and mark-B (c) between mark-B and mark-C (d) insufficient information to decide 4. Two particles A and B starts from the same point and move in the positive x-direction. Their velocity-time relationships are shown in the following figures. What is the maximum separation between them during the time interval shown? Particle A 1.00 m/s 2.00 m/s 1.00 s 2.00 s Particle B 1.00 m/s 2.00 m/s 1.00 s 2.00 s (a) 1.00 m (b) 1.25 m (c) 1.50 m (d) 2.00 m 5. A material particle is chasing the other one and both of them are moving on the same straight line. Their motion after they pass a particular point is recorded and the data obtained is shown by velocity-time graphs of the particles. How long after the start will the chase end? Velocity (m/s) Time (s) 3 4 (a) 4.0 s (b) 6.0 s (c) 12 s (d) insufficient information 6. Two cars A and B simultaneously start a race. Velocity of the car A varies with time according to the graph shown. It acquires a speed of 50 m/s few seconds before t = 100 s and then moves with this constant speed. Car B runs together with A to a place where both have velocity of 20 m/s, after this place car B moves with zero acceleration for one second and then follows velocity-time relationship identical to that of A with a delay of one second. In this way car B acquires the constant velocity one second after A acquires it. How much more distance ?s car A covers in the first 100 s? 50 0 0 100 ts () v m s ( / ) (a) ?s = 30 m (b) ?s < 30 m (c) ?s = 20 m (d) insufficient information 7. Two motorboats, which can move with velocities 4.0 m/s and 6.0 m/s relative to water are going up- stream. When the faster one overtakes the slower one, a buoy is dropped from the slower one. After lapse of some time both the boats turn back KINEMATICS- SET-1 simultaneously and move at the same speeds relative to the water as before. Their engines are switched off when they reach the buoy again. If the maximum separation between the boats is 200 m after the buoy is dropped and water flow velocity is 1.5 m/s, find the distance between the two places where the boats meet the buoy. (a) 75 m (b) 150 m (c) 300 m (d) 350 m 8. Two students start running on a circular track from the same place at the same time and in two minutes one of them completes three and other four revolutions. Due to thick vegetation in circular area, each of the boys can see only one third of the track at a time. How long during their run they will remain visible to each other? (a) 20 s (b) 40 s (c) 80 s (d) 160 s 9. Three ants A, B and C initially rest on the vertices of an equilateral triangle on a large horizonal tabletop. The ants A and B can crawl with constant velocities A v ? and B v ? in any direction. Which of the following inequalities the speed of the third ant C must satisfy to preserve equilateral shape of the triangle? (a) v C < 0.5 (v A + v B ) (b) v C = 0.5 (v A + v B ) (c) v C < v A + v B (d) v C = v A + v B 10. A body experiences a drag force proportional to its speed, when it moves in constant water. A student drops several identical stones one by one from different heights into a deep lake and for each stone, he prepares graphs between v in water and time t. Having studied all of them, he finds that they can be divided into the following three categories. v v 0 t v v 0 t v v 0 t Which of the following explanations appear reasonable? (a) the first graph shows what happens when the ball is dropped from a small height, and the second shows what happens when it is dropped from a large height. (b) The first graph shows what happens when the ball is dropped from a large height, and the second shows what happens when it is dropped from a small height. (c) The third graph tells the possibility only when the stone is dropped from such a height that it acquires the speed v 0 at the instant it enters the water. (d) The third graph is not possible. 11. On a road going out of a city, the last traffic light glows green for 1.0 min and red for 2.0 min. After the traffic light, the road is straight and vehicles run at their constant speeds. This mode of operation of traffic lights causes the vehicles come out off the city in groups i.e., when traffic light is green a group of vehicles comes out and then next group during the next green signal and so on. Speeds of vehicles in a group lie in the range from 60 to 80 km/h. Some distance away from the traffic light, the groups will become indistinguishable. Assume that the vehicles acquires their constant speed in negligible time and mark the correct statement or statements. (a) at distance 4.0 km from the traffic light, the groups become indistinguishable. (b) at distance 8.0 km from the traffic light, the group become indistinguishable. (c) wider is the range of speed; longer is the distance where groups become indistinguishable. (d) larger is the number of fast moving vehicles, shorter is the distance where groups become indistinguishable. KINEMATICS- SET-1 12. A boy takes 60 minutes to swim across a river, if his goal is to minimize time and he takes 180 minutes, if his goal is to minimize to zero the distance that he is being carried downstream. In both these efforts, the boy swims with the same speed relative to river currents. Which of the following statements can be true? (a) the boy can swim in still water faster than the river current. (b) the boy cannot swim in still water faster than the river current. (c) if river width is 3v2 km, speed of the river flow is 4 km/h. (d) if he crosses 3v2 km wide river in 60v2 min, he will be carried v2 km downstream. 13. A wax bar B rests between a wedge A and a vertical wall as shown in the figure. The wedge starts moving towards the wall with a constant acceleration of 0.5 mm/s 2 , and at the same instant heat given to the wall starts melting 1.0 mm length of the wax bar per second. The bar always remains horizontal. Use satisfactorily approximate value sin 37° = 3/5. Heat 37° A B Which of the following descriptions suits the above physical situation? (a) the bar first moves downwards and then upwards (b) the bar stops momentarily after 2 seconds from the beginning. (c) modulus of displacement of the bar in the first four seconds is 1.5 mm (d) distance travelled by the bar in the first four seconds is 1.5 mm 14. A model rocket fired from the ground ascends with constant upward acceleration. After 1.0 s from firing a small bolt is dropped from the rocket and after 5.0 s from firing, its fuel is then finished. The bolt strikes the ground after 2.0 s from the instant it was dropped. Acceleration due to gravity is g = 10 m/s 2 . (a) acceleration of the rocket while running on its fuel is 8.0 m/s 2 . (b) rocket was at height 100 m above the ground when its fuel was finished. (c) maximum speed of the rocket during its flight is 40 m/s (d) total airtime of the rocket is 15 s 15. Area between velocity-time graph and the time axis equals to displacement. Use this fact to find expression for average velocity and suggest suitable match between the two rows. Row-I v 2 v 1 T (a) v 2 v 1 T/2 (b) T v 2 v 1 34 T/ (c) T v 2 v 1 T/4 (d) T Row-II (p) 12 av v v v ?? (q) 12 3 4 av vv v ? ? (r) 12 3 4 av vv v ? ? (s) 12 2 av vv v ? ? 16. Component of a vector along and perpendicular to the position vector are known as the radial component and transverse components respectively. A particle is projected horizontally from the top of a tower. Assume acceleration due to gravity g uniform and take the origin of the coordinate system at the point of projection. Column-I (p) radial component of velocity (q) transverse component of velocity (r) radial component of acceleration (s) transverse component of acceleration Column-II (a) always increases (b) always decreases (c) first increases then decreases (d) first decreases then increases For Problems (17-20) A stone is dropped from the top of a tower. Before it hits the ground another stone is dropped. Assuming the Page 4 KINEMATICS- SET-1 1. From a town, cars start at regular intervals of 30 s and run towards another town with constant speed of 60 km/h. At some point of time, all of the cars simultaneously have to reduce their speed to 40 km/h due to bad weather conditions. What will become the time interval between arrivals of the cars at the second town during the bad weather? (a) 20 s (b) 30 s (c) 40 s (d) 45 s 2. Sam used to walk to school every morning, and it takes him 20 minutes. Once on his way he realized that he had forgotten his homework, notebook at home. He knew that if he continued walking to school at the same speed, he would be there 8 minutes before the bell, so he went back home for the notebook and arrived the school 10 minutes late. If he had walked all the way his usual speed, what fraction of the way to school had he covered at that moment when he turned back? (a) 8/20 (b) 9/20 (c) 10/20 (d) 12/20 3. A car moving at 160 km/h when passes the mark-A, driver applies brake and reduces its speed uniformly to 40 km/h at mark-C. The marks are spaced at equal distances along the road as shown below. Mark -A Mark -B Mark -C At which part of the track the car has instantaneous speed of 100 km/h? Neglect the size of the car. (a) At mark-B (b) Between mark-A and mark-B (c) between mark-B and mark-C (d) insufficient information to decide 4. Two particles A and B starts from the same point and move in the positive x-direction. Their velocity-time relationships are shown in the following figures. What is the maximum separation between them during the time interval shown? Particle A 1.00 m/s 2.00 m/s 1.00 s 2.00 s Particle B 1.00 m/s 2.00 m/s 1.00 s 2.00 s (a) 1.00 m (b) 1.25 m (c) 1.50 m (d) 2.00 m 5. A material particle is chasing the other one and both of them are moving on the same straight line. Their motion after they pass a particular point is recorded and the data obtained is shown by velocity-time graphs of the particles. How long after the start will the chase end? Velocity (m/s) Time (s) 3 4 (a) 4.0 s (b) 6.0 s (c) 12 s (d) insufficient information 6. Two cars A and B simultaneously start a race. Velocity of the car A varies with time according to the graph shown. It acquires a speed of 50 m/s few seconds before t = 100 s and then moves with this constant speed. Car B runs together with A to a place where both have velocity of 20 m/s, after this place car B moves with zero acceleration for one second and then follows velocity-time relationship identical to that of A with a delay of one second. In this way car B acquires the constant velocity one second after A acquires it. How much more distance ?s car A covers in the first 100 s? 50 0 0 100 ts () v m s ( / ) (a) ?s = 30 m (b) ?s < 30 m (c) ?s = 20 m (d) insufficient information 7. Two motorboats, which can move with velocities 4.0 m/s and 6.0 m/s relative to water are going up- stream. When the faster one overtakes the slower one, a buoy is dropped from the slower one. After lapse of some time both the boats turn back KINEMATICS- SET-1 simultaneously and move at the same speeds relative to the water as before. Their engines are switched off when they reach the buoy again. If the maximum separation between the boats is 200 m after the buoy is dropped and water flow velocity is 1.5 m/s, find the distance between the two places where the boats meet the buoy. (a) 75 m (b) 150 m (c) 300 m (d) 350 m 8. Two students start running on a circular track from the same place at the same time and in two minutes one of them completes three and other four revolutions. Due to thick vegetation in circular area, each of the boys can see only one third of the track at a time. How long during their run they will remain visible to each other? (a) 20 s (b) 40 s (c) 80 s (d) 160 s 9. Three ants A, B and C initially rest on the vertices of an equilateral triangle on a large horizonal tabletop. The ants A and B can crawl with constant velocities A v ? and B v ? in any direction. Which of the following inequalities the speed of the third ant C must satisfy to preserve equilateral shape of the triangle? (a) v C < 0.5 (v A + v B ) (b) v C = 0.5 (v A + v B ) (c) v C < v A + v B (d) v C = v A + v B 10. A body experiences a drag force proportional to its speed, when it moves in constant water. A student drops several identical stones one by one from different heights into a deep lake and for each stone, he prepares graphs between v in water and time t. Having studied all of them, he finds that they can be divided into the following three categories. v v 0 t v v 0 t v v 0 t Which of the following explanations appear reasonable? (a) the first graph shows what happens when the ball is dropped from a small height, and the second shows what happens when it is dropped from a large height. (b) The first graph shows what happens when the ball is dropped from a large height, and the second shows what happens when it is dropped from a small height. (c) The third graph tells the possibility only when the stone is dropped from such a height that it acquires the speed v 0 at the instant it enters the water. (d) The third graph is not possible. 11. On a road going out of a city, the last traffic light glows green for 1.0 min and red for 2.0 min. After the traffic light, the road is straight and vehicles run at their constant speeds. This mode of operation of traffic lights causes the vehicles come out off the city in groups i.e., when traffic light is green a group of vehicles comes out and then next group during the next green signal and so on. Speeds of vehicles in a group lie in the range from 60 to 80 km/h. Some distance away from the traffic light, the groups will become indistinguishable. Assume that the vehicles acquires their constant speed in negligible time and mark the correct statement or statements. (a) at distance 4.0 km from the traffic light, the groups become indistinguishable. (b) at distance 8.0 km from the traffic light, the group become indistinguishable. (c) wider is the range of speed; longer is the distance where groups become indistinguishable. (d) larger is the number of fast moving vehicles, shorter is the distance where groups become indistinguishable. KINEMATICS- SET-1 12. A boy takes 60 minutes to swim across a river, if his goal is to minimize time and he takes 180 minutes, if his goal is to minimize to zero the distance that he is being carried downstream. In both these efforts, the boy swims with the same speed relative to river currents. Which of the following statements can be true? (a) the boy can swim in still water faster than the river current. (b) the boy cannot swim in still water faster than the river current. (c) if river width is 3v2 km, speed of the river flow is 4 km/h. (d) if he crosses 3v2 km wide river in 60v2 min, he will be carried v2 km downstream. 13. A wax bar B rests between a wedge A and a vertical wall as shown in the figure. The wedge starts moving towards the wall with a constant acceleration of 0.5 mm/s 2 , and at the same instant heat given to the wall starts melting 1.0 mm length of the wax bar per second. The bar always remains horizontal. Use satisfactorily approximate value sin 37° = 3/5. Heat 37° A B Which of the following descriptions suits the above physical situation? (a) the bar first moves downwards and then upwards (b) the bar stops momentarily after 2 seconds from the beginning. (c) modulus of displacement of the bar in the first four seconds is 1.5 mm (d) distance travelled by the bar in the first four seconds is 1.5 mm 14. A model rocket fired from the ground ascends with constant upward acceleration. After 1.0 s from firing a small bolt is dropped from the rocket and after 5.0 s from firing, its fuel is then finished. The bolt strikes the ground after 2.0 s from the instant it was dropped. Acceleration due to gravity is g = 10 m/s 2 . (a) acceleration of the rocket while running on its fuel is 8.0 m/s 2 . (b) rocket was at height 100 m above the ground when its fuel was finished. (c) maximum speed of the rocket during its flight is 40 m/s (d) total airtime of the rocket is 15 s 15. Area between velocity-time graph and the time axis equals to displacement. Use this fact to find expression for average velocity and suggest suitable match between the two rows. Row-I v 2 v 1 T (a) v 2 v 1 T/2 (b) T v 2 v 1 34 T/ (c) T v 2 v 1 T/4 (d) T Row-II (p) 12 av v v v ?? (q) 12 3 4 av vv v ? ? (r) 12 3 4 av vv v ? ? (s) 12 2 av vv v ? ? 16. Component of a vector along and perpendicular to the position vector are known as the radial component and transverse components respectively. A particle is projected horizontally from the top of a tower. Assume acceleration due to gravity g uniform and take the origin of the coordinate system at the point of projection. Column-I (p) radial component of velocity (q) transverse component of velocity (r) radial component of acceleration (s) transverse component of acceleration Column-II (a) always increases (b) always decreases (c) first increases then decreases (d) first decreases then increases For Problems (17-20) A stone is dropped from the top of a tower. Before it hits the ground another stone is dropped. Assuming the KINEMATICS- SET-1 stones stick to the ground after hit, the separation (s) between them is plotted against time (t). Portion OA and BC of the graph are parabolic, while portion AB is a straight line. Acceleration due to gravity is 10 m/s 2 . s(m) 10 O 1 2 3 4 t(s) C B A 20 40 17. The second stone is dropped (a) 1s after the first (b) 1.5 s after the first (c) 2 s after the first (d) 3 s after the first 18. The height of the tower is (a) 25 m (b) 30 m (c) 40 m (d) 45 m 19. When the first stone hits the ground, the second stone was moving with (a) 10 m/s at 40 above the ground (b) 10 m/s at 25 above the ground (c) 20 m/s at 20 above the ground (d) 20 m/s at 25 above the ground 20. Which of the following equations can be used to represent the separation as function of time is (a) s = 5t 2 ; 0 = t = 1 (b) s = 10t; 1 = t = 3 (c) 45 â€“ 5(t-1) 2 ; 3 = t = 4 (d) all of the above ANSWERS 1.[d] 2.[b] 3.[c] 4.[b] 5.[b] 6.[a] 7.[c] 8.[b] 9.[d] 10.[b,c] 11.[b] 12.[a,c,d] 13.[a,b,d] 14.[a,b,c,d] 15. [p â€“ a,d] [q â€“ a,d] [r â€“ a,b] [s â€“ a,c] 16. [p â€“ a] [q â€“ a] [r â€“ a] [s â€“ b] 17.[a] 18.[d] 19.[d] 20.[d]Read More

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