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05/10/2024, 08:47 PRACTICE TEST-1 Bheeram Sreedhar Reddy International School KADAPA, AP Date : 05/10/2024...
05/10/2024, 08:47 PRACTICE TEST-1 Bheeram Sreedhar Reddy International School KADAPA, AP Date : 05/10/2024 PRACTICE TEST-1 Time : 1 Hours 0 Minutes Marks : 120 5. A particle is moving with velocity v = k(yi + Physics xj), where k is a constant. The general 1. A stone is dropped from a height h, equation for its path is simultaneously, another stone is thrown up from the ground which reaches a height 4 h. A) y = x2 + constant B) y2 = x + constant The two stones cross each other after time C) xy = constant D) y2 = x2 + constant ho at ar A) B) C) D) al 6. A ball is dropped from the roof of a tower of Sc ern dh 2. A steam boat goes across a lake and comes height h. The total distance covered by it in ol ion back (a) On a quite day when the water is the last second of its motion is equal to the still and (b) On a rough day when there is distance covered by it in first three seconds. nt Sree uniform air current so as to help the journey The value of h in meters is (g = 10 m/s2) onward and to impede the journey back. If A) 125 B) 200 C) 100 D) 80 the speed of the launch on both days was same, in which case it will complete the 7. A particle moves along a straight line such journey in lesser time that its displacement s at any time t is given dd am A) Case (a) B) Case (b) C) Same in both by s = t3 - 6t2 + 3t + 4 metre. The velocity, when the acceleration is zero, is D) Nothing can be predicted A) −12 ms−1 B) 3 ms−1 C) −9 ms−1 D) 42 ms−1 Re eer yI 3. A 2m wide truck is moving with a uniform 8. A stone is allowed to fall from the top of a speed v0 = 8 m/s along a straight horizontal tower and cover half the height of the tower in the last second of its journey. The time Bh road. A pedestrian stars to cross the road with a uniform speed v when the truck is 4 m taken by the stone to reach the foot of the away from him. The minimum value of v so tower is that he can cross the road safely is A) B) 4 s C) D) 9. The coordinates of a moving particle at any time t are given by x = αt3 and y = βt3. The speed of the particle at time t is given by A) 2.62 m/s B) 4.6 m/s C) 3.57 m/s A) B) D) 1.414 m/s C) D) 4. A particle moves along x-axis as x = 4(t - 2) 10. The vectors + a(t - 2)2. Which of the following is true? A) The initial velocity of particle is 4 and form a triangle, B) The acceleration of particle is 2a then the triangle is A) right angled triangle B) lateral triangle C) The particle is at origin at t = 0 C) isolated triangle D) None of these D) None of these https://sreedharreddy.etutor.co/paper-view-190 1/5 05/10/2024, 08:47 PRACTICE TEST-1 11. 16. A car travels 6 km towards north at an angle If , then the value of of 45° to the east and then travels distance of 4 km towards north at an angle of 135° to is the east. How far is the point from the starting point. What angle does the straight A) (A2 + B2 + AB)1/2 line joining its initial and final position makes B) with the east C) (A + B) D) A) km and tan−1 (5) 12. A particle is moving along a circular path of B) 10 km and tan−1 radius 6 m with a uniform speed 8 ms−1. The average acceleration when the particle C) km and tan−1 (5) completes one half of the revolution is D) km and tan−1 A) B) C) 17. Balls 'A' and 'B' are thrown from two points D) None of these lying on the same horizontal plane separated ho at ar by a distance 120 m. Which of the following al 13. A balloon rises from rest with a constant statements is correct. acceleration g/8. A stone is released from it Sc ern dh ol ion when it has risen to height h. The time taken by the stone to reach the ground is nt Sree A) B) C) D) 14. Two boys are standing at the ends A and B of a ground where AB = 'a'. The boy at B starts running in a direction perpendicular to A) The two balls can never meet. dd am AB with a velocity v1. The boy at A also B) The balls can meet if the Bell 'B' is thrown is later. starts running simultaneously with velocity ν in straight line and catches the B in time t, C) Two balls meet at a height of 45 m. Re eer then t is: yI D) Two balls meet at a height of 90 m. Bh 18. A parachutist after bailing out falls 50 m with out friction. When he opens the parachute he decelerates at 2 ms−2. He reaches the ground with a speed of 3 ms−1. At with height did he ball out A) 91 m B) 182 m C) 293 m D) 111 m B) C) 19. A man is walking on a horizontal road A) D) towards east with a speed of 1 km/hr. He has to hold the umbrella vertically up to protect 15. Two blocks A and B each of mass "m" are himself from the rain. When he stops placed on a smooth horizontal surface. Two walking, rain appears to fall at a speed of 2 horizontal force 'F' and '2F' are applied on km/hr making an angle 'α' with the vertical. the blocks "A" and "B" respectively. The Then 'α' is block "A" does not slide on block "B". The normal reaction acting between the two blocks is A) F B) F/2 C) D) 3F https://sreedharreddy.etutor.co/paper-view-190 2/5 05/10/2024, 08:47 PRACTICE TEST-1 A) tan−1(2) with vertical towards east B) tan−1(2) with vertical towards west C) 60° with vertical towards east B) D) 30° with vertical towards west 20. A particle is projected with velocity u at an angle of 45° with the horizontal on an inclined plane inclined at an angle α (α < 45°) as show in Figure. If particle hits the inclined plane horizontally, then C) ho at ar al Sc ern dh ol ion A) B) C) nt Sree D) 21. A particle of mass m is projected at an angle α to the horizontal with an initial velocity u. D) The work done by gravity during the time it dd am reaches its highest point is A) u2 sin2α B) C) Re eer D) yI 23. A wooden block of mass M rests on a 22. A projectile is fire with some velocity making horizontal surface. A bullet of mass m certain angle with the horizontal. Which of moving in the horizontal direction strikes and Bh the following graphs is the best gets embedded in it. The combined system representation for the kinetic energy of a covers a distance x on the surface. If the projectile (KE) versus its horizontal coefficient of friction between wood and the displacement (x)? surface is μ, the speed of the bullet at the time of striking the block is (where m is mass of the bullet) A) B) C) A) D) https://sreedharreddy.etutor.co/paper-view-190 3/5 05/10/2024, 08:47 PRACTICE TEST-1 24. A 1200 kg car is coasting down a 30° hill as shown in figure. At a time when the car’s speed is 12 m/s, the driver applies the brakes. What constant force F (parallel to the road) must result, if the car is to stop after travelling 100 m? B) A) 6.7 kN B) 6.7 N C) 100 N D) 20 N 25. A mass of 0.5 kg moving with a speed of 1.5 ho at ar m/s on a horizontal smooth surface, collides al with a nearly weightless spring of force Sc ern dh constant k = 50 N/m. The maximum ol ion compression of the spring would be C) nt Sree A) 0.15 m B) 0.12 m C) 1.5 m D) 0.5 m dd am 26. The correct graph representing the variation of total energy (Et), kinetic energy (Ek) and potential energy (U) of a satellite with its Re eer yI distance from the centre of Earth is Bh D) A) https://sreedharreddy.etutor.co/paper-view-190 4/5 05/10/2024, 08:47 PRACTICE TEST-1 27. A block of mass m is slowly pulled up on 28. Work done in time t on a body of mass m inclined plane of height h and inclination θ which is accelerated from rest to a speed v with the top of a string parallel to the incline. in time t1 as a function of time t is given by Which of the following statement is correct for the block when it moves up from the A) B) C) bottom to the top of the incline? D) 29. A bomb of mass 16 kg at rest explodes into two pieces of masses 4 kg and 12 kg. The velocity of the 12 kg mass is 4ms−1. The kinetic energy of the other mass is A) 144 J B) 288 J C) 192 J D) 96 J 30. A particle is moving with kinetic energy E, straight up an inclined plane with angle α, ho at ar A) Work done by the normal reaction force is zero. the co-efficient of friction being µ. The work done against friction, up to when the particle al B) Work done by the string on block is mgh. Sc ern dh comes to rest, is ol ion C) Work done by the gravity is mgh. A) B) C) nt Sree D) Work done by the block is −mgh/2. D) dd am Re eer yI Bh https://sreedharreddy.etutor.co/paper-view-190 5/5 SECTION NAME Date : 05/10/2024 PRACTICE TEST-1 Time : 1 Hours 0 Minutes Marks : 120 : ANSWER KEY : 1) A 2) A 3) C 4) B 5) D 6) A 7) C 8) D 9) B 10) A 11) A 12) C 13) B 14) D 15) D 16) C 17) C 18) C 19) D 20) C 21) D 22) D 23) C 24) A 25) A 26) C 27) A 28) D 29) B 30) A Bheeram Sreedhar Reddy International School https://sreedharreddy.etutor.co/paper-view-key-190 1/1 05/10/2024, 08:58 PRACTICE TEST-2 Bheeram Sreedhar Reddy International School KADAPA, AP Date : 05/10/2024 PRACTICE TEST-2 Time : 1 Hours 0 Minutes Marks : 120 4. Two blocks A and B of mass m and 2m Physics respectively are held at rest such that the 1. A horizontal force of 10 N is necessary to spring is in natural length. What is the just hold a block stationary against a wall. acceleration of both the blocks just after The coefficient of friction between the block release? and the wall is 0.2. The weight of the block is ho at ar al Sc ern dh ol ion nt Sree A) 20 N B) 50 N C) 100 N D) 2 N dd am 2. A block of mass m is attached to a massless A) g ↓, g ↓ B) C) 0, 0 D) g ↓, 0 spring of spring constant K. This system is accelerated upward with acceleration a. The 5. Two blocks A and B of masses 2m and m, Re eer elongation in spring will be respectively, are connected by a massless yI and inextensible string. The whole system is A) B) C) D) suspended by a massless spring as shown Bh 3. A bullet of mass 20 g traveling horizontally in the figure. The magnitudes of acceleration with a speed of 500 m/s passes through a of A and B, immediately after the string is wooden block of mass 8.0 kg initially at rest cut, are respectively on a level surface. The bullet emerges with a speed of 100 m/s and the block slides 20 cm on the surface before coming to rest. The coefficient of friction between the block and the surface is (g = 10 ms–2) A) g, g/2 B) g/2, g C) g, g D) g/2, g/2 A) 0.4 B) 0.25 C) 0.2 D) 0.16 https://sreedharreddy.etutor.co/paper-view-191 1/6 05/10/2024, 08:58 PRACTICE TEST-2 6. The acceleration of block B in the figure will be D) 8. A body of weight 50 N placed on a horizontal surface is just moved by a force of 28.2 N. The frictional force and the normal reaction are A) B) C) ho at ar al D) Sc ern dh 7. A particle of mass m is at rest at the origin at ol ion time t = 0. It is subjected to a force F(t) = A) 10 N, 15 N B) 20 N, 30 N C) 2 N, 3 N e−bt nt Sree F0 in the x direction. Its speed v(t) is D) 5 N, 6 N depicted by which of the following curves ? 9. From a canon mounted on a wagon at height H from ground, a shell is fired horizontally with a velocity v0 with respect to canon. The dd am canon and wagon has combined mass M A) and can move freely on the horizontal surface. The horizontal distance between Re eer shell and canon when the shell touches the yI ground is Bh B) A) B) C) D) C) https://sreedharreddy.etutor.co/paper-view-191 2/6 05/10/2024, 08:58 PRACTICE TEST-2 10. In the shown system, m1 > m2. Thread QR is 11. A metal sphere is hung by a string fixed to a holding the system. If this thread is cut, then well. The force acting on the sphere is just after cutting. shown in Figure. Which of the following statement is incorrect? ho at ar al Sc ern dh A) B) T2 = R2 + W2 ol ion C) T = R + W nt Sree D) R = W tan θ 12. Blocks A and C start from rest and move to the right with acceleration aA = 12t ms−2 and dd am A) aC = 3 ms−2. Here t is in seconds. The time Acceleration of mass m1 is zero and that of m2 is when block B again comes to rest is Re eer directed upward yI B) Acceleration of mass m2 is zero and that of m2 is Bh directed downward C) Acceleration of both the blocks will be same D) Acceleration of system is given by kg, A) 2 s B) 1 s C) 3/2 s D) 1/2 s where k is a spring factor 13. The block of mass M moving on the frictionless horizontal surface collides with the spring of spring constant K and compresses it by length L. The maximum momentum of the block after collision is A) Zero https://sreedharreddy.etutor.co/paper-view-191 3/6 05/10/2024, 08:58 PRACTICE TEST-2 C) 17. The value of frictional force and acceleration B) D) of block of mass 10 kg in the Figure are 14. A rough vertical board has an acceleration 'a' so that a 2 kg block pressing against it does not fall. The coefficient of friction between the block and the board should be A) 10 N, 1 m/s2 B) 20 N, 2 m/s2 C) 20 N, 0 m/s2 D) 10 N, 0 m/s2 18. What is the maximum value of the force F such that the block shown in the ho at ar A) > g/a B) < g/a C) = g/a D) > a/g arrangement, does not move? al 15. Consider the system shown in Figure. The Sc ern dh wall is smooth, but the surface of blocks A ol ion and B in contact are rough. The friction on B due to A in equilibrium is nt Sree A) 20 N B) 10 N C) 12 N D) 15 N 19. A particle is moving along the circular path dd am with a speed v and tangential acceleration is g at an instant. If the radius of the circular path be r, then the net acceleration of the particle at that instant is Re eer yI A) Upward B) Downward C) Zero A) B) C) D) The system cannot remain in equilibrium Bh 16. A small body of mass m slides down from D) the top of a hemisphere of radius r. The surface of block and hemisphere are 20. A car is travelling with linear velocity v on a frictionless. The height at which the body circular road of radius r. If it is increasing its lose contact with the surface of the sphere is speed at the rate of 'a' m/s2, then the resultant acceleration will be A) B) C) D) A) B) C) D) https://sreedharreddy.etutor.co/paper-view-191 4/6 05/10/2024, 08:58 PRACTICE TEST-2 21. A particle is moving on a circular path of 24. A uniform disc of radius R and mass M is radius r with uniform velocity v. The change free to rotate only about its axis. A string is in velocity when the particle moves from P to wrapped over its rim and a body of mass m Q is is tied to the end of the string as shown in the figure. The body is released from rest, then the acceleration of the body is ho at ar A) 2v cos 40° B) 2v sin 40° C) 2v sin 20° A) B) C) D) al Sc ern dh 25. Two blocks of masses 10 kg and 20 kg are D) 2v cos 20° ol ion connected by a massless string and are 22. Figure shows a block A of mass 6m having a placed on a smooth horizontal surface as nt Sree smooth semi-circular groove of radius a shown in the figure. If a force F = 600 N is placed on a smooth horizontal surface. A applied to 10 kg block, then the tension in block B of mass m is released from a the string is position in groove where its radius is horizontal. The speed of block A when block B reaches its bottom is dd am A) 100 N B) 200 N C) 300 N D) 400 N Re eer yI 26. A bead of mass m is sliding down the fixed inclined rod without friction. It is connected to a point P on the horizontal surface with a Bh light spring of spring constant K. The bead is A) D) Zero initially released from rest and the spring is B) C) initially unstressed and vertical. The bead 23. A piece of wire is bent in the shape of just stops at the bottom of the inclined rod. parabola y = kx2 (y-axis vertical) with a bead Find the angle which the inclined rod makes of mass m on it. The bead can slide on the with horizontal. wire without friction. It stays at the lowest point of the parabola when the wire is at rest. The wire is now accelerated parallel to the x- axis with a constant acceleration a. The distance of the new equilibrium position of the bead, where the bead can stay at rest with respect to the wire from the y-axis is A) B) C) D) A) B) C) D) https://sreedharreddy.etutor.co/paper-view-191 5/6 05/10/2024, 08:58 PRACTICE TEST-2 27. A string of length l fixed at one end carries a 29. A particle of mass "m" is initially situated at mass m at the other end. The string makes the point "p" inside a hemispherical surface rev/s around the axis through the fixed of radius "r" as shown in figure. A horizontal end as shown in figure. The tension in string acceleration of magnitude "a0" is suddenly is produced on the particle in the horizontal direction the time taken by the particle to touch the sphere again if gravitational acceleration is neglected is A) B) C) A) 16 ml B) 4 ml C) 8 ml D) 2 ml ho at ar 28. A stone of mass 1 kg tied to a light in D) al extensible string of length Sc ern dh is whirling in a circular path of radius L in a 30. A hemispherical bowl of radius R is rotating ol ion vertical plane. The ratio of the maximum about its own axis. A small ball kept in the tension in the string to the minimum tension bowl rotates with the bowl without slipping on nt Sree in the string is 4 and if g is taken to be 10 its surface. The surface of the bowl is smooth and the angle made by the radius m/s2. The speed of stone at the highest point through the ball with the vertical is "α". Find of the circular is the angular speed at which bowl is rotating A) 20 m/s B) C) dd am A) B) D) 10 m/s C) D) Re eer yI Bh https://sreedharreddy.etutor.co/paper-view-191 6/6 SECTION NAME Date : 05/10/2024 PRACTICE TEST-2 Time : 1 Hours 0 Minutes Marks : 120 : ANSWER KEY : 1) D 2) C 3) B 4) A 5) B 6) A 7) C 8) B 9) A 10) A 11) C 12) D 13) C 14) A 15) D 16) B 17) C 18) A 19) C 20) B 21) C 22) C 23) B 24) D 25) D 26) A 27) A 28) D 29) C 30) C Bheeram Sreedhar Reddy International School https://sreedharreddy.etutor.co/paper-view-key-191 1/1 05/10/2024, 09:08 PRACTICE TEST-3 Bheeram Sreedhar Reddy International School KADAPA, AP Date : 05/10/2024 PRACTICE TEST-3 Time : 1 Hours 0 Minutes Marks : 160 7. A drunkard walking in a narrow lane takes 5 Physics steps forward and 3 steps backward, 1. A particle moves along the sides AB, BC, CD followed again by 5 steps forward and steps of a square of side 25 m with a velocity of 15 backward, and so on. Each step is 1 m long ms−1. Its average velocity is_______ms-1 and requires 1 s. How long will it take for the drunkard to fall in a pit 13 m away from the ho at ar start is (in sec)___ al 8. An aeroplane flies around a square field Sc ern dh ABCD of each side 1000 km. Its speed along ol ion AB is 250 kmh−1, along BC 500 kmh−1, along CD 200 kmh−1, and along DA 100 nt Sree kmh−1. Its average speed (in kmh−1) over the entire trip is______. 9. A 2m car is moving with a speed of along a straight horizontal road. 2. A wind tunnel is to be used with a 20 cm high dd am A boy starts crossing the road with constant model car to approximately reproduce the speed when the car is 2m away from him. situation in which a 550 cm high car is moving at 15 m/s. then the wind speed in the The minimum speed(in ms−1) of the boy to Re eer tunnel is________Km/s. cross the car safely is_______. yI 3. A particle of mass 10 kg starts from point A, 10. Rain is falling vertically downwards with a with an initial velocity of 3 m/s towards velocity of 3 km/hr. A man walks in the rain with a velocity of 4 km/hr. The raindrops will Bh negative x-axis, it has been acted by a force of 10 N towards positive x-axis. then the fall on the man with a velocity(in Km/hr) _______. distance travelled by particle in 4 s 11. In the figure, pulleys are smooth and strings is_________m. are massless, m1 = 1kg, m2 = 1/3 kg. To 4. A pebble is thrown vertically upwards from a bridge with an initial velocity of 10 ms−1. It keep m3 at rest, mass m3 should be strikes water after 5 s. The height of the _________ kg bridge is (g = 10 m/s2)_________m. 5. Two trains along the same straight rails moving with constant speed 60 km/hr and 30 km/hr respectively towards each other. If at time t = 0, the distance between them is 90 km, the time when they collide is in hrs_____. 6. The ceiling of a long hall is 25 m high.the maximum horizontal distance in m that a ball thrown with a speed of 40 ms−1 can go without hitting the ceiling of the hall is _____. https://sreedharreddy.etutor.co/paper-view-192 1/4 05/10/2024, 09:08 PRACTICE TEST-3 12. A man is raising himself and the crate on 15. Two blocks of masses 4 kg and 2 kg are which he stands with an acceleration of 5 m connected by a heavy string of mass 3 kg s−2 by a massless rope−and−pulley and placed on rough horizontal plane. The 2 arrangement. Mass of the man is 100 kg and kg block is pulled with a constant force F as shown in Figure. The co-efficient of friction that of the crate is 50 kg. If g = 10 ms−2, then between the blocks and the ground is the tension(N) in the rope is_______ 0.5.The value of F (in N)so that tension in the string is constant throughout the motion of the blocks is__________. 16. A block of mass 2 kg is resting over another block of mass 6kg. 2 kg block is connected to one end of a string fixed to vertical wall as shown. If the co-efficient of friction between the blocks is 0.4, the force required to pull ho at ar out the 6 kg block with an acceleration of 1.5 al Sc ern dh m/s2 will be (g = 10 ms–2)_________N. ol ion nt Sree 13. A block of mass 1 kg is placed on a rough incline as shown. The co-efficient of friction between block and incline is 0.4. The acceleration (in ms–2) of block is (g = 10 ms– dd am 2, = 1.7) is_____. 17. As shown in the figure, two equal masses each of 2 kg are suspended from a spring balance. The reading of the spring Re eer yI balance(in Kg) will be______ Bh 14. In the arrangement shown in Figure, co- efficient of friction between the two blocks is. The force of friction acting 18. A particle moves in the x-y plane under the between the two blocks is(in N)__________ action of force such that the value of its linear momentum at time t is Px = 2cost and Py = 2sint. The angle θ between and at time t will be(in degrees)___________. 19. A wooden block of mass 0.9 kg is suspended from the ceiling of a room by a long thin wire. A bullet of mass 0.1 kg moving horizontally with a speed of 100 m/s strikes the block and gets embedded in it. The height(m) to which the block rises will be (g = 10 m/s2)_________. https://sreedharreddy.etutor.co/paper-view-192 2/4 05/10/2024, 09:08 PRACTICE TEST-3 20. A ball weighing 10 g hits a hard surface 26. A particle of mass 0.1 kg is subjected to a vertically with a speed of 5 m/s and force which varies with distance as shown in rebounds with the same speed. The ball figure. If it starts its journey from rest at x = remains in contact with the surface for 0.01 0, its velocity(in m/s) at x = 12 m is_____ s. The average force exerted by the surface on the ball is(in N)________. 21. A bullet weighing 50 gm leaves the gun with a velocity of 30 ms–1. If the recoil speed imparted to the gun is 1 ms–1, the mass of the gun is (in Kg)___________. 22. A particle moves in X-Y plane under the action of forces F such that the values of 27. A stone of mass 1 kg tied to a light linear momentum 'p' at any times is px = 2 inextensible string of length L = 10/3 m is whirled in a circular path of radius L in a cos t and py = 2 sin t. The angle between vertical plane. If the ratio of the maximum at the time t will be in tension in the string to the minimum tension ho at ar degrees________. is 4 and if g is taken to be 10 ms−2, the 23. A mass of 3 kg desending vertically al speed(in m/s) of the stone at the highest downward supports a mass of 2 kg by Sc ern dh point of the circle is____. means the end of 5s, the string breaks. ol ion 28. A 20 g bullet pierces through plate of mass ________(in m)is higher the 2 kg mass will m1 = 1 kg an then comes to rest inside a go further. nt Sree second plate of mass m2 = 2.98 kg. It is found that the two plates, initially at rest, now move with equal velocities. The percentage loss in the initial velocity of bullet when it is between m1 and m2 (neglect any loss of dd am material of the bodies, due to action of bullet) will be______. 29. A ball of mass 0.1 kg is suspended by a Re eer string. It is displaced through an angle of 60° yI 24. A block is moving on an inclined plane and left. When the ball passes through the making an angle 45° with the horizontal and mean position, the tension(in N) in the string the coefficient of friction is μ. The force Bh is____. required to just push it up the inclined plane 30. A vertical spring of force constant 100 N/m is is 3 times the force required to just prevent it attached with a hanging mass of 10 kg. Now from sliding down. If we define N = 10 μ, an external force is applied on the mass so then N is________. that the spring is stretched by additional 2 m. The work done(in J) by the force F is (g = 10 m/s2)_______. 25. A block of mass m moving at a speed v compresses a spring through a distance x before its speed is halved. The spring constant of the spring is. Find value of n _____ https://sreedharreddy.etutor.co/paper-view-192 3/4 05/10/2024, 09:08 PRACTICE TEST-3 31. A body of mass 2 kg slides down a curved 34. The relationship between force and position track which is quadrant of a circle of radius 1 is shown in Figure (in one-dimensional metre. All the surfaces are frictionless. If the case). The work done(in ergs) by the force in body starts from rest, its speed(in m/s) at the displacing a body from x = 1 cm to x = 5 cm bottom of the track is______. is_______. 35. A bob is suspended from a crane by a cable of length l = 5m. The crane and the bob are moving at a constant speed v0. The crane is ho at ar stopped by a bumper and the bob on the al 32. A particle is released from rest at origin. It cable swings out an angle of 60°. The initial Sc ern dh moves under the influence of potential field speed v0 is (g = 9.8m/s2)in m/s_____. ol ion U= x2 − 3x, where U is in Joule and x is in 36. Two bodies of masses 2 kg and 4 kg are metre. Kinetic energy at x = 2 m will be in moving with velocities 10 m/s and 2 m/s nt Sree Joules______. towards each other. The velocity(in m/s) of 33. A block of mass m = 0.1 kg is released from their centre of mass is___. a height of 4 m on a curved smooth surface. 37. A uniform metre scale balances at the 40 cm On the horizontal surface, path AB is friction mark when weight of 10 g and 20 g are μ = 0.1. If the impact of block with the vertical suspended from the 10 cm and 20 cm dd am wall at C be perfectly elastic, the total marks. The weight(in g) of the metre scale distance(in m) covered by the block on the is_____. horizontal surface before coming to rest will 38. Position of two particles are given by x1 = 2t Re eer be(take g = 10 m/s2)___. yI and x2 = 2 + 3t. The velocity of centre of mass at t = 2s is 2 m/s. Velocity(in m/s) of centre of mass at t = 4 s will be_________. Bh 39. A Non uniform rod of (AB) length 50 cm has a linear density λ = 4x + 5 where λ is in kg/m and "x" is in met. The distance of centre of mass of the bar from its midpoint is (in cm)_______ 40. In the figure shown ABC is a uniform wire. If centre of mass of wire lies vertically below point A, then is close to: https://sreedharreddy.etutor.co/paper-view-192 4/4 SECTION NAME Date : 05/10/2024 PRACTICE TEST-3 Time : 1 Hours 0 Minutes Marks : 160 : ANSWER KEY : 1) 5 2) 0.41 3) 5 4) 75 5) 1 6) 150 7) 37 8) 190.5 9) 5 10) 5 11) 1 12) 1125 13) 1.6 14) 8 15) 45 16) 17 17) 2 18) 90 19) 5 20) 10 21) 1.5 22) 90 23) 4.9 24) 5 25) 1 26) 40 27) 10 28) 25 29) 1.96 30) 200 31) 4.43 32) 2 33) 59 34) 20 35) 7 36) 2 37) 70 38) 2 39) 1.4 40) 1.37 Bheeram Sreedhar Reddy International School https://sreedharreddy.etutor.co/paper-view-key-192 1/1 CHEMISTRY HOLIDAYS ASSIGNMEMT CHEMICAL BONDING 1. The dipole moment of NH3 is: 1) Less than dipole moment of NC 3 2) Higher than dipole moment of NC 3 3) Equal to the dipole moment of NC 3 4) None of these 2. BeF2 has zero dipole moment whereas H2O has dipole moment because: 1) Water is linear 2) H2O is bent 3) F is more electronegative than O 4) Hydrogen bonding is present in H2O 3. Dipole moment is shown by: 1) 1, 4 – dichlorobenzene 2) Cis 1, 2 - dichloro ethene 3) Trans -1, 2 - dichloro ethane 4) Benzene 4. Which of the following species are polar: A) C 6H6 B) XeF2 C) SO2 D) SF4 E) SF6 Correct answer is: 1) B and D 2) A, B and E 3) A and E 4) C and D 5. The correct order of dipole moment is: 1) CH4 NF3 NH3 H2O 2) NF3 CH4 NH3 H2O 3) NH3 NF3 CH4 H2 O 4) H2O NH3 NF3 CH4 6. Glycerol is more viscous than glycol the reason is 1) Higher molecular wt 2) More covalent 3) More hydrogen bonding 4) Complex structure 7. Weakest hydrogen bond is: 1) O – H ----- N 2) S – H ----- S 3) F – H ----- F 4) N – H ----- N 8. Maximum no. of hydrogen bonds formed by a water molecule in ice is: 1) 4 2) 3 3) 2 4) 1 9. Acetic acid exists as dimer in benzene due to: 1) Condensation reaction 2) Hydrogen bonding 3) Presence of carboxyl group 4) None of the above 10. In which of the following molecule, the shown hydrogen bond is not possible: H O O H H C N H N H O H H H 1) 2) O O H Cl H O Cl Cl C H O 3)ON O 4) Cl H 11. Density of ice is less than that of water because of: 1) Presence hydrogen bonding 2) Crystal modification of ice 3) Open porous structure of ice due to hydrogen bonding 4) Different physical states of these 12. KF combines with HF to form KHF2. The compound contains the species: 1) K F and H 2) K F and HF 3) K and HF2 4) KHF and F2 13. The boiling point of p-nitro phenol is higher than that of o-nitro phenol because: 1) NO2 group at p-piston behaves in a different way from that at o-position 2) Intramolecular hydrogen bonding exists in p-nitro phenol 3) There is intermolecular hydrogen bonding in p-nitro phenol 4) p-nitro phenol has a higher molecular weight than o-nitro phenol 14. The correct order of volatility is: 1) NH3 H2 O 2) p-nitro phenol < o-nitro phenol 3) CH3OH CH3 O CH3 4) HF HC 15. o-nitro phenol can be easily steam distilled whereas p-nitro phenol cannot be. This is because of 1) Intermolecular hydrogen bonding in o-nitro phenol 2) Intramolecular hydrogen bonding in o-nitro phenol 3) Intramolecular hydrogen bonding in p-nitro phenol 4) Dipole moment of p-nitro phenol is large than that of o-nitro phenol 16. The ion that is isoelectronic with CO and having same bond order is: 1) CN 2) O2 3) O2 4) N2 17. Which of the following is paramagnetic: 1) O2 2) CN 3) CO 4) NO 18. The bond-orders of the given species are such that 1) O2 O2 O22 O2 2) O2 O2 O2 O22 3) O2 O22 O2 O2 4) O22 O2 O2 O2 19. The number of anti-bonding electron pairs in O22 molecular ion on the basis of molecular orbital theory is (at no. O = 8): 1) 2 2) 3 3) 4 4) 5 20. The correct order of the O – O bond length in O2 ,H2O2 and O3 is 1) O3 H2O2 O2 2) O2 H2 O2 O3 3) O2 O3 H2O2 4) H2O2 O3 O2 21. Bond length of C – O is minimum in 1) CO 2) CO2 3) CO32 4) HCOO 22. The molecule having one unpaired electron is 1) NO 2) CO 3) CN 4) O2 23. In a homonuclear molecule which of the following set of orbitals are degenerate? * 1) 2s and 1s 2) 2px and 2py 3) 2px and 2pz 4) 2pz and 2p x 24. Which compound has the weakest bond? 1) Diamond 2) Neon (solid) 3) KC 4) Water (ice) 25. The energy of 2s orbital is greater than 1s * orbital because 1) 2s orbital is bigger than 1s * orbital 2) 2s orbital is a bonding orbital whereas 1s * is an anti-bonding orbital 3) 2s orbital has a greater value of n than 1s * orbital 4) None 26. Valency expresses: 1) Total electrons in an atom 2) Atomicity of an element 3) Oxidation number of an element 4) Combining capacity of an element to form chemical bonds 27. Electrovalent bond is formed between: 1) Two electronegative atoms 2) Electropositive and electronegative atoms 3) Two electropositive atoms 4) Two similar metal atoms 28. The ionic bonds X Y are formed when: I) ionisation enthalpy of X is low II) Electron affinity of Y is high III) Lattice energy of XY is high IV) Lattice energy of XY is low 1) I and II 2) II and III 3) I, II and III 4) IV only 29. The melting point of RbBr is 682 C while that of NaF is 988 C. The principal reason for this fact is: 1) The molar mass of NaF is less than that of RbBr 2) The bond in RbBr has more covalent character than in NaF 3) The difference in the electronegativity between Rb and Br is smaller than the difference between Na and F 4) The lattice energy of RbBr is less than the lattice energy of NaF because the internuclear distance rc ra is greater for RbBr than for NaF 30. Four elements, P, Q, R and S have atomic numbers z 1,z,z 1 and z 2 respectively. If z is 17, then bond between which pair of elements will be most ionic? 1) S and Q 2) P and R 3) S and R 4) S and P 31. The electronic configurations of four elements are: A) 1s 2 ,2s 2 2p6 ,3s 2 3p4 B) 1s 2 ,2s2 2p6 ,3s2 3p5 C) 1s 2 ,2s2 sp6 ,3s1 D) 1s 2 ,2s 2 2p6 ,3s 2 The formulae of ionic compounds that could be formed between them are: 1) A 2C,DA,CB,D2B 2) C2 A,DA,CB,DB 3) AC,D2 A,C2B,DB 4) C2 A,DA,CB,DB2 32. The correct order of lattice energies of the following compounds is: 1) NaC MgC 2 MgO A 2O3 2) A 2O3 MgC 2 MgO NaC 3) A 2O3 MgO MgC 2 NaC 4) MgC 2 A 2O3 MgO NaC 33. Polarisation is the distortion of the shape of an anion by the cation. Which of the following statements is correct? 1) Maximum polarisation is done by a cation of high charge 2) A large cation is likely to bring large degree of polarization 3) A smaller anion is likely to undergo a high degree of polarization 4) Minimum polarisation is done by a cation of small size 34. Highest covalent character is found in which of the following? 1) CaF2 2) CaI2 3) CaC 2 4) CaBr2 35. According to Fajan rules, the covalent character is most favoured in: 1) Small cation, large anion 2) Small cation, small anion 3) Large cation, large anion 4) Large cation, small anion 36. Which one of the following has pyramidal structure? 1) NH3 2) SiF4 3) H2O 4) BF3 37. If a molecule MX 3 has zero dipole moment, the sigma bonding orbitals used by M are: 1) Pure p 2) sp – hybrids 3) sp2 – hybrids 4) sp3 – hybrids 38. The ratio of and - bonds in tetracyano ethylene is: 1) 2 : 1 2) 1 : 1 3) 1 : 2 4) 1 : 3 39. In sp3 d3 hybridization, which d – orbitals are involved? 1) d x2 y 2 ,d z 2 ,d xy 2) d x2 y 2 ,d xy ,d yz 3) d z2 ,d yz ,d xy 4) d xy ,d yz ,d zx 40. Select the correct code for the following repulsive forces, according to VSEPR theory: I) Lone pair – lone pair > lone pair – bond pair II) Lone pair – bond pair > bond pair – bond pair III) Lone pair – lone pair > bond pair – bond pair IV) Lone pair – bond pair > lone pair – lone pair 1) I, II and III 2) II and IV 3) I, III and IV 4) I and IV 41. Dipole moment of AX 4 type molecule is zero. The geometry and shape of the molecule can be: 1) Tetrahedral 2) Square planar 3) Either tetrahedral or square planar 4) None of the above 42. Molecular orbital electronic configuration for ‘x’ anion is: 2 1 2* 2 2 2 * KK 2s 2s 2px 2py 2pz 2px 1) N2 2) O2 3) N22 4) O22 43. The correct stability order of the following resonance structure is: I) H2C N N II) H2 C N N III) H2 C N N IV) H2 C N N 1) I > II > IV > III 2) I > III > II > IV 3) I > II > III > IV 4) III > I > IV > II 44. The molecule which does not exhibit dipole moment is: 1) NH3 2) CHC 3 3) H2O 4) CC 4 45. The common features among the species CN , CO and NO are: 1) Bond order three and isoelectronic 2) Bond order three and weak field ligands 3) Bond order two and – acceptors 4) Isoelectronic and weak field ligands PERIODIC CLASSIFICATION 46. The electronic configuration of the element just above the element with atomic number 43 in the same group is 2 2 6 2 6 5 2 2 2 6 2 6 10 2 5 1) 1s 2s 2p 3s 3p 3d 4s 2) 1s 2s 2p 3s 3p 3d 4s 4p 2 2 6 2 6 6 1 2 2 6 2 6 10 1 6 3) 1s 2s 2p 3d 3p 3d 4s 4) 1s 2s 2p 3s 3p 3d 4s 4p 47. Assertion (A):Zn is not a transition element Reason (R): Elements with incompletely filled d-orbital are called Transition elements 1) Both (A) and (R) are true and (R) is the correct explanation of (A) 2) Both (A) and (R) are true and (R) is not the correct explanation of (A) 3) (A) is true but (R) is false 4) (A) is false but (R) is true 48. An isotope of copper on bombardment with a proton undergoes a nuclear reaction yielding element X as shown. 63 1 1 1 29 X 1 H 60 n 21 H X Which group in the periodic table does X belong to? 1) 6 2) 8 3) 10 4) 12 49. Which of the following can be explained using Lanthanide Contraction? 1) Zr and Hf has same radius 2) Zr and Zn have same oxidation state 3) Zr and Y have same radius 4) Zr and Nb have similar oxidation state 50. Lanthanide contraction is caused due to 1) The imperfect shielding on outer electrons by 4f-electrons from the nuclear charge 2) The appreciable shielding on outer electrons by 4f-electrons from the nuclear charge 3) The appreciable shielding on outer electrons by 5d-electrons from the nuclear charge 4) The same effective nuclear charge from Ce to Lu 51. If the density of Al is 2.7 g/cc and atomic weight is 26.98, calculate the radius of the Aluminium atom assuming it to be spherical 1) 2.582A 2) 1.356A 3) 1.583A 4) 3.158A 52. Bond distance of C-F in CF4 and Si-F in SiF4 are respectively 1.33A and 1.54A Bond length of C-Si bond is 1.87A. Calculate the covalent radius of F ignoring the electronegativity differences. 1.33 1.54 1.87 1) 0.64A 2) A 3 1.54 3) 0.5A 4) A 2 53. O2 and Si4 are isoelectronic species. If ionic radius of O2 is 1A , the ionic radius of Si 4 can be 1) 1.4A 2) 0.41A 3) 2.8A 4) 1.5A 54. Which of the following is the least soluble in water? 1) CaSO4 2) MgSO4 3) Na 2SO4 4) BaSO4 55. Formation of oxide or sulphide ion is endothermic because 1) More stability of the oxide or sulphide ion 2) More energy gain due to coupling 3) Electrostatic repulsion outweighs the energy gain due to coupling 4) Both A and B 56. Pair of ions with similar polarizing power 1) Li ,Mg 2 2) Li ,Na 3) Mg 2 ,Ca 2 4) Mg 2 ,K 57. The electronic configuration of the atom having maximum difference in first and second ionisation energies is 1) 1s2 2s2 2p1 2) 1s 2 2s2 2p6 3s1 3) 1s 2 2s2 2p3 4) 1s 2 2s2 2p6 3s2 58. The IP1,IP2 ,IP3 ,IP4 and IP5 of an element are 7.1, 14.3, 34.5, 46.8, 162.2 eV respectively. The element is likely to be 1) Na 2) Si 3) F 4) Ca 59. If the first 4 ionisation potentials (in eV) of an element are given as 6, 10, 16 and 45 respectively, the molecular weight of its oxide will be, if atomic weight of element is x 1) x + 48 2) 2x + 48 3) 3x + 48 4) x + 32 60. The amount of energy released when 10 6 atoms of Iodine in vapor state are 13 converted into iodide ion is 4.8 10 J. What is the Electron gain enthalpy of Iodine in kJ/mole? 1) 489 2) 289 3) 259 4) 389 61. Which of the following cannot be considered as a fixed quantity? 1) Electronegativity 2) First Ionisation Potential 3) Electron gain enthalpy 4) Second Ionisation potential 62. The correct order of acidic strengths for CO2 ,CuO,CaO,H2O is 1) CaO CuO H2O CO2 2) H2 O CuO CaO CO2 3) CaO H2O CuO CO2 4) H2O CO2 CaO CuO 63. Which of the following statements are wrong? I. Bi3 is more stable than Bi5 II. Mn shows + 8 oxidation state. III. The oxidation state of an element is always less than or equal to its group number IV. s-block elements show variable oxidation states 1) II and IV 2) II and III 3) I, II and III 4) II, III and IV 64. If an element X shows 2 oxidation states +2 and +3 and forms an oxide in such a way that the ratio of the element +2 and +3 state is 1 : 3 in the compound. The formula of this oxide is 1) X 4 O11 2) X 5O11 3) X 8 O11 4) X 9O11 65. Which of the following statement is wrong for the transition elements - 1) Transition elements are placed from 3rd to 6th period 2) Last electron enters in (n – 1)d orbital 3) Exhibits variable valency 4) General electronic configuration is n 1 d110 ns1,2 66. The electronic configuration of four elements are given below. Which element does not belong to the same block as others - 2 14 10 1) Xe 6s 4f 5d 2) Ar 4s2 3d5 3) Rn 7s2 5f 7 6d1 4) Kr 4d 6 5s2 67. An element ‘X’ on emitting - particles do not change its group number in the periodic table. The element is 1) Lanthanum 2) Cerium 3) Lawrencium 4) Radium 68. 3 students Ram, Shyam and Raj measured the radius of an element A. The values of their practical were not same (Ram = 110 nm, Shyam = 190 nm and Raj = 108 nm). Their teacher explained that their measurement were correct by saying that the recorded values are - 1) Metalic, vanderwall and covalent radii respectively 2) Covalent, Metallic and Vander wall radii respectively 3) Vander wall, Metallic and covalent radii respectively 4) None of the above 69. Element X, Y and Z have atomic numbers 19, 37 and 55 respectively. Which of the following statements is true - 1) Their ionisation potential would increase with the increasing atomic number 2) ‘Y’ would have an ionisation potential in between those of ‘X’ and ‘Z’ 3) ‘Z’ would have the highest ionisation potential 4) ‘Y’ would have the highest ionisation potential 70. Following graph shows variation of I.P. with atomic number in second period (Li – Ne). Value of I.P. of Na (11) will be - Ne Be N F (I.P.) C Li B 3 4 5 6 7 8 9 10 11 z 1) Above Ne 2) Below Ne but above O 3) Below Li 4) Between N and O 71. Which of the following has a sp-hybridised carbon atom? A) Cyclopropene B) Bicyclobutene C) Propadiene D) 1,3-butadiene 72. Which is the correct structure of 5, 6, 6-trimethyl-3-heptyne? A) B) C) D) 73. The compound having only primary hydrogen atoms is A) Butane B) Isobutene C) Cyclohexane D) 2,3-dimethylbut-2-ene 74. Which of the following can be correct description of C6H14 ? A) 2-methyl pentane : 2-tertiary, 2 secondary and 3 primary carbons. B) 2, 3-dimethyl butane : 3-tertiary, 4 primary carbons. C) 2,2-dimethyl butane : 1 quaternary, 1 secondary and 4 primary carbons. D) 2-ethyl-2-methyl propane : 1 quaternary, 1 secondary and 4 primary carbons. 75. What is correct in the IUPAC name of a compound 4,4-dichloro-1- bromocyclohexane? A) Locants positions are wrongly numbered. B) Locants name are written in correct order. C) Parent name is incorrect. D) There is only one carbon without any hydrogen on it. 76. Which is wrong about C4H6 ? A) It represents an alkyne B) It represents a diene C) It represents a bicyclo compound D) It represents a spiro alkane 77. Which of the following pair of compounds do not have the same empirical formula? A) Carboxylic acid-Acid anhydride B) Carboxylic acid-Ester C) Aldehyde-Ketone D) Alcohols-Ethers 78. Which of the following cannot be IUPAC name of compound C4H8O2 ? A) Butanoic acid B) Butanedial C) Ethylethanoate D) Methyl propanoate 79. Which of the following compounds has isopropyl group? A) 2,2,3,3-tetramethylpentane B) 2,2-dimethylpentane C) 2,2,3-trimethylpentane D) 2-methylpentane 80. Name of the compound given below is CH3 H3C CH3 CH3 A) 2,3-diethylheptane B) 3-methyl-4-ethyloctane C) 5-ethyl-6-methyloctane D) 4-ethyl-3-methyloctane O 81. What is the correct IUPAC name of O ? A) Dioxy butane B) 2, 6-dioxy butane C) 1, 2-dimethoxy ethane C) Dimethyl ethyl ether 82. The structure of 4-methylpent-2-en-1-ol is A) CH3 2 C CHCH2CH 2OH B) CH3 2 CHCH CHCH2OH C) CH3CH2CH CHCH2OH D) CH3CHOHCH C CH3 2 83. The IUPAC name of is H3C CH CH2 CH CH2Cl C2 H 5 OH A) 1-chloro-4-methylhexane-2-ol B) 1-chloro-4-methylhexan-2-al C) 1-chloro-4-ethylpenta-2-ol D) 1-chloro-2-hydroxy-4-methylhexane 84. The IUPAC name of the following compound is O C CH CH2 OH NH2 OH A) 3-amino-2hydroxy propanoic acid B) 2-amino-propan-3-o1-1-oic acid C) 2-amino-3-hydroxy propanoic acid D) Amino hydroxyl propanoic acid 85. An aldehyde has molecular formula C5 H10 O. Which cannot be an IUPAC name of this aldehyde? A) Pentanal B) 2-methyl butanal C) 3-methyl pentanal D) 2, 2-dimethyl propanal 86. Ethanoyl chloride is the IUPAC name of A) CH3CH2Cl B) CH3COCl C) CCl3CHO D) CH2ClCOOH 87. The IUPAC name of H5 C2 O C O H3 C CH CH3 A) Ethoxy methanone B) Ethyl-2-methyl propanoate C) Ethoxypropanone D) 2-methyl ethoxy propanone 88. The IUPAC name of the following compound is O H 5C2 O H3C O A) Propionic acetic anhydride B) Ethanoic propanoic anhydride C) Aceto ethanoate D) Ethanoic anhydride 89. The IUPAC name of compound is Cl O A) 2-ethyl-3-methyl butanoyl chloride B) 2,3-dimethyl pentanoyl chloride C) 3,4-dimethyl pentanoyl chloride D) 1-chloro-1-oxo-2,3-dimethyl pentane 90. Which of the following is an incorrect name according to IUPAC? A) 2-cyclopropyl butane B) 1-bromo-2, 2-dichloro cyclobutane C) Cyclohexyl cyclohexane D) 1-cyclobutyl cyclobutane 91. The IUPAC name of the following compound is HO A) 3,3-dimethyl-1-hydroxycyclohexane. B) 1,1-dimethyl-3-hydroxycyclohexane. C) 3,3-dimethylcyclohexanol. D) 1,1-dimethyl-3-cyclohexanol. 92. What is the correct IUPAC name of the following compound? CH3 A) 3, 5-diethenyl toluene B) 1, 3-diethenyl-5-methyl benzene C) 3-ethenyl-5-methyl styrene D) 1, 3, 5-triethenylmethyl benzene 93. Which is the correct structural formula of 4-hydroxy benzene-1, 3- dicarbonitrile? CN CN HO B) NC OH CN OH NC OH CN C) CN D) CN 94. The IUPAC name of the following compound is OH CN Br A) 4-bormo-3-cyanophenol B) 2-bromo-5-hydroxybenzonitrile C) 2-cyano-4-hydroxy bromobenzene D) 6-bromo-3-hydroxybenzonitrile 95. The IUPAC name of C 6 H 5 COCl is A) Benzoyl chloride B) Benzene chloroketone C) Benzene carbonylchloride D) Chlorophenyl ketone 96. Which of the following compounds has wrong IUPAC name? H3C CH CH2 CHO H3C CH CH CH3 A) CH3 B) OH CH3 3-methylbutanal 2-methylbutan-3-ol O CH3CH2CH2COOCH2CH3 H3 C CH C C 2H5 C) D) Ethylbutanoate CH3 2-methylpentan-3-one 97. Which of the following is the correct IUPAC name? A) 3-Ethyl-4, 4-dimethylheptane B) 4,4-Dimethyl-3-ethylheptane C ) 5-Ethyl-4, 4-dimethylheptane D) 4,4-Bis(methyl)-3-ethylheptane O O 98. The IUPAC name for CH3 C CH2 CH2 C OH is ________. A) 1-hydroxypentane-1,4-dione B) 1,4-dioxopentanol C) 1-carboxybutan-3-one D) 4-oxopentanoic acid Cl NO2 99. The IUPAC name for CH3 A) 1-Chloro-2-nitro-4-methylbenzene B) 1-Chloro-4-methyl-2-nitrobenzene C) 2-Chloro-1-nitro-5-methylbenzene D) m-Nitro-p-chlorotoluene 100. Assertion (A): All the carbon atoms in H2C C CH2 are sp2 hybridised Reason (R): In this molecule all the carbon atoms are attached to each other by double bonds. A) Both A and R are correct and R is the correct explanation of A. B) Both A and R are correct but R is not the correct explanation of A. C) Both A and R are not correct. D) A is not correct but R is correct. KEY 1) 2 2) 2 3) 2 4) 4 5) 1 6) 3 7) 2 8) 1 9) 2 10) 3 11) 3 12) 3 13) 3 14) 2 15) 2 16) 1 17) 1 18) 2 19) 3 20) 4 21) 1 22) 1 23) 2 24) 2 25) 3 26) 4 27) 2 28) 1 29) 4 30) 1 31) 4 32) 3 33) 1 34) 2 35) 1 36) 1 37) 3 38) 2 39) 4 40) 1 41) 1 42) 1 43) 2 44) 4 45) 1 46) 1 47) 1 48) 2 49) 1 50) 1 51) 3 52) 3 53) 2 54) 4 55) 3 56) 1 57) 2 58) 2 59) 2 60) 2 61) 1 62) 1 63) 1 64) 3 65) 1 66) 3 67) 3 68) 1 69) 2 70) 3 71. C 72. C 73. D 74. D 75. D 76. D 77. A 78. B 79. D 80. D 81. C 82. B 83. B 84.C 85. C 86. B 87. B 88. B 89. B 90. B 91.C 92. B 93. D 94. B 95. C 96. B 97. B 98.D 99. C 100. D EXERCISE (O-2) MULTIPLE OBJECTIVE TYPE : 1. If cosx = tanx, then which of the following is/are true ? 1 1 (A) + cos 4 x = 1 (B) + cos4 x = 2 sin x sin x (C) cos4x + cos2x = 1 (D) cos4x + cos2x = 2 1 1 2. If tan A = - and tan B = - , then A + B = 2 3 p 3p 5p 7p (A) (B) (C) (D) 4 4 4 4 3 3. If cos ( A - B ) = and tanA tanB = 2, then which of the following is/are correct ? 5 1 2 (A) cosA cosB = - (B) sin A sin B = 5 5 1 4 (C) cos ( A + B ) = - (D) sin A cos B = 5 5 1 t 4. If sin t + cos t = , then tan is equal to 5 2 1 1 (A) –1 (B) - (C) 2 (D) - 3 6 5. If tan2a + 2tana.tan2b = tan2b + 2tanb.tan2a, then (A) tan2a + 2tana.tan2b = 0 (B) tana + tanb = 0 (C) tan2b + 2tanb.tan2a = 1 (D) tana = tanb 6. If 3sinb = sin(2a + b), then tan(a + b) – 2 tan a is (A) independent of a (B) independent of b (C) dependent of both a and b (D) independent of a but dependent of b 7. If L = cos2 84º + cos2 36º + cos 36º cos 84º M = cot 73º cot 47º cot 13º N = 4 sin 156º sin 84º sin36º, then which of the following option(s) is(are) correct? p (A) L < 1 (B) M > tan 2 (C) N > sin (D) 0 < LMN 4 cos3x 1 p 8. If = for some angle x, 0 £ x £ , which of the following is/are true ? cos x 3 2 sin 3x 7 2 (A) = (B) cos2x = sin x 3 3 1 2 5 (C) tanx = (D) sin 2x = 5 6 9. If a + b + g = 2p, then a b g a b g (A) tan + tan + tan = tan tan tan 2 2 2 2 2 2 a b b g g a (B) tan tan + tan tan + tan tan = 1 2 2 2 2 2 2 a b g a b g (C) tan + tan + tan = - tan tan tan 2 2 2 2 2 2 a b b g g a (D) tan tan + tan tan + tan tan = 1 4 4 4 4 4 4 10. If x + y = z, then cos2x + cos2y + cos2z – 2 cos x cos y cos z is equal to (A) cos2z (B) sin2z (C) cos(x + y – z) (D) 1 11. If A,B,C are angles of a triangle ABC and tanA tanC = 3; tan B tanC = 6 then, which is (are) correct? p (A) A = (B) tanA tanB = 2 4 tan A (C) =3 (D) tanB = 2 tanA tan C 12. Which of the following is/are true ? æp ö æp ö cos 2q (A) sin ç + q ÷ sin ç - q ÷ = è4 ø è4 ø 2 (B) In a DABC, if tanA = 2, tanB = 3, then tanC = 1 (C) Minimum value of 4tan2q + cot2q is 4 (wherever defined) (D) Range of 3sin2q + 4sinqcosq + 5cos2q is éë 4 - 5, 4 + 5 ùû n 1 13. Let ƒn ( q ) = å n=0 4 n ( ) sin 4 2n q. Then which of the following alternative(s) is/are correct? æpö 1 æ pö 2+ 2 æ 3p ö (A) ƒ2 ç 4 ÷ = (B) ƒ3 ç ÷ = (C) ƒ4 ç 2 ÷ = 1 (D) ƒ5(p) = 0 è ø 2 è8ø 4 è ø cos x + cos 2 x + cos 3x + cos 4 x + cos 5x + cos 6x + cos 7 x 14. Let y = , then which of the following sin x + sin 2x + sin 3x + sin 4x + sin 5x + sin 6 x + sin 7 x hold good? (A) The value of y when x = p/8 is not defined. (B) The value of y when x = p/16 is 1. (C) The value of y when x = p/32 is 2 -1. (D) The value of y when x = p/48 is 2 + 3. Paragraph for Question Nos. 15 to 17 Consider the polynomial P(x) = (x – cos 36°)(x – cos 84°)(x – cos156°) 15. The coefficient of x2 is 1 5 -1 (A) 0 (B) 1 (C) – (D) 2 2 16. The coefficient of x is 3 3 3 (A) (B) – (C) – (D) zero 2 2 4 17. The absolute term in P(x) has the value equal to 5 -1 5 -1 5 +1 1 (A) (B) (C) (D) 4 16 16 16 Paragraph for Question 18 to 19 2p 4p Let a,b,c are respectively the sines and p,q,r are respectively the cosines of a, a + and a + , 3 3 then 18. The value of (a + b + c) + (ab + bc + ca) is 3 3 (A) 0 (B) (C) 1 (D) - 4 4 19. The value of (qc – rb) is- 3 3 (A) 0 (B) - (C) (D) depends on a 2 2 INTEGER TYPE 4 3sec B - 4cosecB 20. If acute angle A = 3B and sin A = then is 5 2 2p 4p 6p 7p l 21. If the value of cos + cos + cos + cos = -. Find the value of l. 7 7 7 7 2 np 2 sin 2 q 22. If cot(q – a), 3cotq, cot(q + a) are in AP (where, q ¹ , a ¹ kp, n, k Î I ), then is equal to 2 sin 2 a sin q sin 3q sin 9q æk ö 23. If k1 = tan27q – tanq and k 2 = + + then ç 1 ÷ is equal to cos3q cos 9q cos 27q è k2 ø 1 - 4 sin10° sin 70° 24. The value of the expression is 2 sin10° MATRIX MATCH TYPE 25. In the following matrix match Column-I has some quantities and Column-II has some comments or other quantities Match the each element in Column-I with corresponding element(s) in Column-II Column-I Column-II æ p p pö (A) The value of 4 ç 2 cos3 - cos2 - cos ÷ is (P) 4 è 7 7 7ø (B) If A + B + C = p and cosA = cosB. cosC then (Q) 8 tanB. tanC has the value equal to æ cos 20° + 8sin 70° sin 50° sin10° ö (C) 4ç ÷ is equal to (R) 2 è sin 2 80° ø (D) The maximum value of 12sinq – 9sin2q is (S) 1 (T) 6 EXERCISE (S-1) æ 7p ö æ pö æ 3p ö æ 7p ö æ pö æ 3p ö 1. If X = sin ç q + ÷ + sin ç q - ÷ + sin ç q + ÷ , Y = cos ç q + ÷ + cos ç q - ÷ + cos ç q + ÷ , è 12 ø è 12 ø è 12 ø è 12 ø è 12 ø è 12 ø X Y then prove that - = 2 tan 2q. Y X 2. Prove that : (a) tan 20°. tan 40°. tan 60°. tan 80° = 3 p 3p 5p 7p 3 (b) sin 4 + sin 4 + sin 4 + sin 4 = 16 16 16 16 2 (c) cos²a + cos² (a + b) - 2cos a cos b cos (a + b) = sin²b (d) (4 cos29° – 3) (4 cos227° – 3) = tan9°. m+n 3. If m tan(q – 30°) = n tan (q + 120°), show that cos2q =. 2(m - n) 4 5 p 4. If cos (a + b) = ; sin (a – b) = & a , b lie between 0 & , then find the value of 5 13 4 tan 2a. a+ b 5. If the value of the expression sin25°. sin35°.sin85° can be expressed as , where c a,b,c Î N and are in their lowest form, find the value of (a + b + c). 6. If a + b = g, prove that cos2a + cos2b + cos2g = 1 + 2 cos a cos b cos g. æ p öæ (2k - 1) p ö æ (2k + 1) p ö æ (4k - 1) p ö 7. Let P(k) = ç 1 + cos ÷ ç 1 + cos ÷ ç 1 + cos ÷ ç 1 + cos ÷ , then find the è 4k ø è 4k øè 4k øè 4k ø value of (a) P(5) and (b) P(6). 8. Calculate without using trigonometric tables : 2cos 40° - cos20° (a) 4cos20° - 3 cot 20° (b) sin 20° p 3p 5p 7p (c) cos 6 + cos6 + cos6 + cos6 (d) tan10° – tan50° + tan70° 16 16 16 16 9. Given that (1 + tan 1°) (1 + tan2°)....(1 + tan45°) = 2n, find n. 10. (a) If y = 10 cos2x – 6 sinx cosx + 2 sin2x, then find the greatest & least value of y. (b) If y = 1 + 2 sinx + 3 cos2x, find the maximum & minimum values of y " x Î R. (c) If y = 9 sec2x + 16 cosec2x, find the minimum value of y for all permissible value of x. æ pö (d) If a < 3 cos ç q + ÷ + 5 cosq + 3 < b, find a and b, where a is the minimum value & b is the è 3 ø maximum value. EXERCISE (O-2) [MULTIPLE OBJECTIVE TYPE] x x 1. The equation 2sin. cos2x + sin 2x = 2 sin. sin2x + cos2x has a root for which 2 2 1 1 (A) sin2x = 1 (B) sin2x = – 1 (C) cosx = (D) cos2x = – 2 2 2. sin2x - cos 2x = 2 - sin 2x if (A) x = np/2, n Î I (B) tan x = 3/2 (C) x = (2n + 1) p/2, n Î I (D) x=np+(-1)n sin-1(2/3), nÎI 3. 4 sin4x + cos4x = 1 if 1 æ 1ö (A) x = np (B) x = np ± cos–1 ç 5 ÷ 2 è ø np (C) x = (D) none of these, (n Î I) 2 4. Which of the following set of values of x satisfies the equation 2 2 x -3 sin x +1) 2( 2 sin + 2( 2- 2 sin x +3 sin x ) = 9 is p (A) x = xp, n Î I (B) x = 2np + ,nÎI 2 p p (C) x = np ± ,nÎI (D) x = np ± ,nÎI 6 3 5. 5 sin2 x + 3 sinx cosx + 6 cos2x = 5 if (A) tan x = - 1/ 3 (B) sin x = 0 (C) x = np + p/2, n Î I (D) x = np + p/6, n Î I kp 6. If sum of all the solution of the equation cot x + csc x + sec x = tan x in [0, 2p] is , then the 2 value of k is greater than (A) 1 (B) 2 (C) 3 (D) 4 7. The equation sin x + cos (k + x) + cos (k – x) = 2 has real solution(s), then s
