IIT-JEE AIPMT AIEEE OLYMPIADS KVPY NTSE STaRT-01 CLASS-XII (SC.-MATHS) Time : 90 min. Maximum Marks : 00 GENERAL INSTRUCTIONS 1. he question paper contains 50 questions, 15 questions from Physics (1-15), 10 questions from Chemistry (16-5), 15 Questions from Mathematics (6-40) and 10 questions from Mental Ability (41-50).. The OMR sheet given in the examination hall is the Answer Sheet. 3. Blank papers, clip boards, log tables, slide rule, calculators, mobile or any other electronic gadgets in any form is not allowed. 4. Do not forget to mention your roll number neatly and clearly in the blank space provided in the answer sheet. 5. Each Question carries 4 marks. 1' mark will be deduct for each wrong answer. So attempt each question carefully. 6. No rough sheets will be provided by the invigilators. All the rough work is to be done in the blank space provided in the question paper. 7. In case of any dispute, the answer filled in the OMR sheet available with the institute shall be final. Name : Roll No. : Resonance Eduventures Pvt. Ltd. Corporate Office: J-, Jawahar Nagar Main, Kota (Rajasthan) - 34005, INDIA Tel.: +91-0744-301, 319, 437144 Fax: 0-39167, 0744-47144 Toll Free: 1800 00 44 Website : www.resonance.ac.in E-mail : contact@resonance.ac.in
PAGE # 1 1. At t = 0 a particle at (1, 0, 0) moves towards (4, 4, 1) with a constant velocity of magnitude of 65m/s. The position of the particle is measured in metre and time in second. The position of the particle at t = s is: 13 î 10 ĵ 40kˆ m 40 î 31ĵ 10kˆ m 16 î 0 ĵ 60kˆ m 31 î 40 ĵ 10kˆ m. What is the angle between î ĵ kˆ & î : 6 4 3 none 3. A particle is moving in a circle : The resultant force on the particle must be towards the centre. The resultant force may be towards the centre. The direction of the angular acceleration and the angular velocity must be same. The cross product of the tangential acceleration and the angular velocity will be zero. 4. A parallel beam of particles of mass m moving with velocity v impinges on a wall at an angle to its normal. The number of particles per unit volume in the beam is n. If the collision of particles with the wall is elastic, then the pressure exerted by this beam on the wall is : mn v cos mn v cos mn v cos mn v cos 5. A box 'A' is lying on the horizontal floor of the compartment of a train running along horizontal rails from left to right. At time 't', it decelerates. Then the reaction R by the floor on the box is given best by : 6. A force F 6 i 8j 10 k N produces acceleration 1 m/s in a body. The mass of the body is (in kg) : 6 i 8j 10 k 10 100 10 7. A ring rolls without sliding on a horizontal surface with a velocity of 10 m/s. It ascends a smooth continuous track as shown in the figure. The height upto which it will ascend is : 10m 5m 0m 5/m
PAGE # 8. The equation of motion of a particle having mass 1 g is d x dt + x = 0, where x is displacement (in m) from mean position. The frequency of oscillation is (in Hz) : 1 5 10 1 5 10 9. A body of mass kg is moving under the influence of a central force whose potential energy is given by U (r) = r 3 J. If the body is moving in a circular orbit having radius 5m, its energy will be : 65 J 50 J 500 J 15 J 10. Work done by all the forces on a system of particles is equal to : Change in kinetic energy of the system Change in potential energy of the system Change in total energy of the system Change in kinetic energy only if the forces acting are conservative. 11. A block of mass 10 kg is suspended through two light spring balances as shown in figure. Both the spring balances will read 10 kg. Both the spring balances will read 5 kg. The upper spring balance will read 10 kg and the lower spring balance will read zero. The individual readings of spring balances may be anything but their sum will be 10 kg. 1. Consider the situation as shown in the figure. The wall is smooth but the surface of A and B in contact are rough. The friction on B due to A in equilibrium state of the system : is upward is downward is zero the system cannot remain in equilibrium. 13. Two semi circular rings of uniform linear mass densities and of radius R each are joined to form a complete ring. The distance of the center of mass of complete ring from its geometrical centre is : 3R 8 R 3 3R 4 none of these
PAGE # 3 14. A tube in vertical plane is shown in figure. It is filled with a liquid of density and its end B is closedthen the force exerted by the fluid on the tube at end B will be : [Neglect atmospheric pressure and assume the radius of the tube to be negligible in comparison to ] 0 g A 0 g A 0 Cannot be determined 15. An electromagnetic wave travelling through a transparent medium is given by y 14 E x (y,t) Eox sin 3 10 t 7 in S unit then the refractive index of medium is : 5 10 1. 1.50 1.33 16. Which of the following has maximum ionization potential : Be K Na Mg 17. If E is heat of reaction for combustion of ethanol (liquid) at constant volume at 98 K, then heat of reaction at constant pressure, H will be : H = E RT H = E + RT H = E + RT H = E RT 18. Which of the following are isostructural : XeF, F NH 3, BF 3 CO 3, SO 3 PCl 5, C 5 19. 5 mole of SO and 5 moles of O are allowed to react to form SO 3 in a closed vessel. At the equilibrium stage 60% of SO is used up. The total number of moles of SO, O and SO 3 in the vessel now is : 8 6.5 9.5 8.5 0. In which of the following minerals aluminium is not present : Cryolite Mica Fledspar fluorspar 1. In a closed insulated container, a liquid is stirred with a paddle to increase the temperature. Which of the following is true? E 0, W 0, q = 0 E = 0, W 0, q 0 E 0, W = 0, q 0 E = q = 0, W 0. The correct IUPAC name of the following compound is : Methyl 4-chloro--ethyl-5, 5-dimethylcyclohexanol 1, 1-Dimethyl--methoxy-3-ethyl-5-chlorocyclohexane 5-Chloro-3-ethyl--methoxy-1, 1-dimethylcyclohexane 1-Chloro-5-ethyl-4-methoxy-3, 3-dimethylcyclohexanol
PAGE # 4 3. The correct stability order of the given resonating structures is : O CH CH CH CH C H ( I) III > II > IV > I I > II > III > IV I > III > II > IV IV > III > II > I 4. Hg, 353K The product of following reaction is H C C H + CH 3 COOH Acetone Acetaldehyde Vinyl ethanoate Ethyl ethanoate 5. The correct boiling point order of following compounds is : 6. The locus of centres of family of circles passing through the origin and cutting the circle x + y 4x + 6y 13 = 0 orthogonally is : 4x + 6y + 13 = 0 4x 6y + 13 = 0 4x + 6y 13 = 0 4x 6y 13 = 0 7. If a variable line passing through a fixed point (a, b) intersects the co-ordinate axes at A & B, then locus of the point of intersection of the lines through A and B and parallel to the co-ordinate axes is: x a + y b = 1 a x + b y = 1 a y + b x = 1 x b + y a = 1 8. Let x 3y = 0 be a given line and P (sin, 0) and Q (0, cos) be two points. Then P and Q lies on the same side of the given line if lies in the : Ist quadrant IVth quadrant IIIrd quadrant none of these 9. In a ABC if a = 7, b = 8, c = 9, then the length of the line joining B to the middle point of AC is : 6 7 8 9
PAGE # 5 30. A bag contains 9 cards numbered as 1,,...9. Cards are drawn one by one without replacement till an odd number comes. Probablity that it comes in 3rd draw is 1/7 3/8 5/4 1/ 31. The number of ways in which the digits of the number 1545375 can be arranged such that no two 5 s come together is 9! 3!! 7! 3!! 7 C 3 x6!! 3!! 7! 3. Mirror image of (1, 4) in the tangent at (0, 0) on the circle x + y x + y = 0 is (4, 1) (1, ), 1 1, 33. If sinx = cos x, then cos x (1 + cos x) equals 0 1 none of these 34. a 1, a, a 3... are in an A.P. If a 1 + a 5 + a 10 + a 15 + a 0 + a 4 = 5, then sum of its first 4 terms is 800 900 700 1000 35. If < a n > and <b n > be two sequence given by x y b n a n = n x + n y and b n = x y b n n x y n 1, n W, then the value of a 1 a a 3...a n is x y b 36. The solution set of x 4 + (x + ) + x 3x = 0 is x (, ] [ 1, ) x {, } x { } x {, 1, } n n x y b 37. Set of all real values of p such that both the roots of the equation (p 5)x px + (p 4) = 0 are positive, one is less than and other is lying between & 3, is 49, 4 4 49 (5, ) (, 4), 4 4, 49 4 1 38. If sin 1 x + cot 1 =, then x is equal to x 5 1 5 1 5 1 none of these
PAGE # 6 39. If function f(x) = 1 (3x 1) 4 5 4x 4 x x x 4 4 x, then the function f(x) is continuous at x = & x = 4 continuous at x =, discontinuous at x = 4 continuous at x = 4, discontinuous at x = discontinuous at x = & x = 4 40. The curve y e xy + x = 0 has a horizontal tangent at the point (1, 1) (0, 1) (1, 0) no point Directions : (41 to 43) Find the missing term : 41. 1, 3, 7, 5, 103,? 56 (B*) 51 515 509 4. ABCA, BCDB, CDEC, DEFD,? EFHE FEGF EFGF (D*) EFGE 43. 1 7 6 3 3? 5 4 8 35 74 104 1 3 4 Directions : (44 to 45) Assume the following : A @ B means A is greater than B ; A B means A is either greater than or equal to B ; A $ B means A is equal to B ; A B means A is smaller than B ; A # B means A is either smaller than or equal to B ; In each question, two statements followed by two conclusions I and II are given. Assuming the statement to be true, state which of the conclusions I and II is / are definitely true? Give answer if only conclusion I is true; if only conclusion II is true; if either I or II is true; and if both I and II are true.
PAGE # 7 44. Statements : P # Q, M N $ P Conclusions : I. M @ P II. N # Q 45. Statements : L M, R T $ L Conclusions :I. T M II. R @ L 46. How many squares does the figure have? 10 (B*) 11 1 14 47. Introducing a girl, Vipin said, "Her mother is the only daughter of my mother in law. "How is Vipin related to the girl? Uncle (B*) Father Brother Husband 48. Ram is to the South-East of Mukesh, Shyam is to the East of Mukesh and North-East of Ram. If Suresh is to the North of Ram and North-West of Shyam, in which direction of Mukesh is Suresh located? North-West South-West (C*) North-East South-East Directions : (49 to 50) Fill the blanks in the following questions from the choice given below. Which are based on pyramids. a b c d e f g h i j k l m n o p q r s t u v w x y z 49. elu : adi : :? : abe fmv dgl hmt (D*) inu 50. flt : klm : : iow :? hnv mno (C*) nop gmu ANSWER 1.. 3. 4. 5. 6. 7. 8. 9. 10. 11. 1. 13. 14. 15. 16. 17. 18. 19. 0. Space For Rough 1. Work. 3. 4. 5. 6. 7. 8. 9. 30. 31. 3. 33. 34. 35. 36. 37. 38. 39. 40. 41. 4. 43. 44. 45. 46. 47. 48. 49. 50.