Eamcet 2013 Engineering Solutions Engineering Key with Solutions

March 31, 2018 | Author: bankjobscoaching | Category: Lens (Optics), Force, Temperature, Circle, Torque


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EngineeringEAMCET-2013 Date: 10.05.13 SRI CHAITANYA EDUCATIONAL INSTITUTIONS, A.P. HYDERABAD Guntur Kakinada Machilipatnam VIJAYAWADA Visakhapatnam Tirupathi Eluru Bhimavaram Rajahmundry Tenali Srikakulam Ongole Anantapuram Nellore Amalapuram Chittoor Kurnool CENTRAL OFFICE- MADHAPUR EAMCET -2013 (CODE-B) 05-13 DATE : 10- MATHS 1. If the equation ax2 + 2hxy +by 2 ++2 gx + 2 fy + c = 0 represents a pair of straight lines, then the square of the distance of their point of intersection from the origin is c (a + b)- af 2 - bg 2 1) ab - h2 c (a + b)+ f 2 + g 2 2) ab - h2 3) c (a + b)- f 2 - g 2 ab - h2 4) c (a + b)- f 2 - g 2 (ab - h2 ) 2 ANS : 3 2. The equation x2 - 5xy + py 2 + 3x - 8 y + 2 = 0 represents a pair of straight lines. If q is the angle between them, then sin q = 1) 1 50 2) 1 7 3) 1 5 4) 1 10 ANS : 1 3. The equation of the pair of lines passing through the origin whose sum and product of slopes are respectively the arithmetic mean and geometric mean of 4 and 9 is 1) 12x2 - 13xy + 2 y 2 = 0 3) 12x2 - 15xy + 2 y 2 = 0 2) 12 x2 + 13xy + 2 y2 = 0 4) 12 x2 + 15xy - 2 y 2 = 0 ANS : 1 4. If the points (1, 2) and (3, 4) lie on the same side of the straight line 3x - 5 y + a = 0 then a lies in the set 1) [7, 11] 2) R - [7, 11] 3) [7, ) 4) ( , 11] ANS : 2 Sri Chaitanya Page 1 Hyderabad Engineering EAMCET-2013 Date: 10.05.13 5. If 2 x + 3 y = 5 is the perpendicular bisector of the line segment joining the points A 1, 1 and B, then B = 3 1) 21 49 , 13 39 2) 17 31 , 13 39 3) 7 49 , 13 39 4) 21 31 , 13 39 ANS : 1 6. If p and q are the perpendicular distances from the origin to the straight lines x sec q - y cos ec q = a and x cos q + y sin q = a cos2q , then 1) 4 p2 + q2 = a2 2) p2 + q2 = a2 3) p2 + 2q 2 = a2 4) 4 p2 + q2 = 2a2 ANS : 1 7. The origin is translated to (1, 2). The point (7, 5) in the old system undergoes the following transformations successively. i) Moves to the new point under the given translation of origin ii) Translated through 2 units along the negative direction of the new X-axis iii) Rotated through an angle direction. The final position of the point (7, 5) is 1) 9 - 1 , 2 2 p about the origin of new system in the clockwise 4 2) 7 1 , 2 2 3) 7 - 1 , 2 2 4) 5 - 1 , 2 2 ANS : 3 8. If X is a Poisson variate and P(X = 1)= 2P(X = 2) then P (X = 3)= 1) e- 1 6 e- 2 2 e- 1 2 e- 1 3 1 to each n, then m 2) 3) 4) ANS : 1 9. The random variable takes the values 1, 2, 3, the variance of X is 1) , m. If P (X = n)= (m + 1)(2m + 1) 6 2) m2 - 1 12 3) m+ 1 2 4) m2 + 1 12 ANS : 2 Sri Chaitanya Page 2 Hyderabad Engineering EAMCET-2013 Date: 10.05.13 10. A bag contains 2n + 1coins. It is known that n of these coins have a head on both sides, whereas the remaining n + 1 coins are fair. A coin is picked up at random from the bag and tossed. If the probability that the toss results in a head is 1) 10 2) 11 3) 12 31 , then n = 42 4) 13 ANS : 1 11. Two fair dice are rolled. The probability of the sum of digits on their faces to be greater than or equal to 10 is 1) 1 5 2) 1 4 3) 1 8 4) 1 6 ANS : 4 12. Two numbers are chosen at random from {1, 2, 3, 4, 5, 6, 7, 8} at a time. The probability that smaller of the two numbers is less than 4 is 1) 13. 7 14 r 2) 8 14 3) 9 14 4) u r 10 14 ANS : 3 r If a and b are two non-zero perpendicular vectors, then a vector y satisfying equations a y 1) a ca r2 r r r r u r r u r c (c scalar) and a y r b is ( (a b)) 2) a ca r2 ( (a b)) r r r r r r 3) r 1 2 a r (ca (a b)) r r r r r 4) r 1 2 a (ca (a b)) r r r r r r ANS : 3 14. A unit vector coplanar with i + j + 3k and i + 3 j + k and perpendicular to i + j + k is 1) 1 (j + k) 2 2) 1 r r r i- j + k 3 ( ) r 3) 1 r r j- k 2 ( ) r 4) r r r 1 r r r i+ j- k 3 ( ) ANS : 3 15. The shortest distance between the lines r = 3i + 5 j + 7k + l i + 2 j + k and r r r r r r r r = - i - j + k + m 7i - 6 j + k is r r ( ) ( ) 1) 16. 16 5 5 r r 0, c 2) r r r 0, a b 26 5 5 r r r 0, b c r 0 r r a c 3) 36 5 5 4) 46 5 5 ANS : r4 r r 0, b r 1) b a 2) a 3) 0 r 4) i + j + k r r r ANS : 3 Sri Chaitanya Page 3 Hyderabad Engineering EAMCET-2013 Date: 10.05.13 17. r r r r r r r P, Q, R and S are four points with the position vectors 3i - 4 j + 5k , 4k , - 4i + 5 j + k r r r and - 3i + 4 j + 3k respectively. Then the line PQ meets the line RS at the point. r r r r r r r r r r r r 1) 3i + 4 j + 3k 2) - 3i + 4 j + 3k 3) - i + 4 j + k 4) i + j + k r r r r r r r r r ANS : 2 18. The points whose position vectors are 2i + 3 j + 4k , 3i + 4 j + 2k and 4i + 2 j + 3k are the vertices of 1) an isosceles triangle 3) equilateral triangle 2) right angled triangle 4) right angled isosceles triangle ANS : 3 19. A person observes the top of a tower from a point A on the ground. The elevation of the tower from this point is 60o . He moves 60 m in the direction perpendicular to the line joining A and base of the tower. The angle of elevation of the tower from this point is 45o . Then the height of the tower (in meters) is 1) 60 3 2 2) 60 2 3) 60 3 4) 60 2 3 ANS : 1 20. If, in D ABC , 1) 300 1 1 3 , = then the angle C = a+ c b+ c a+ b+ c 2) 450 3) 600 4) 900 ANS : 3 21. In any triangle ABC, rr 1 2 + r2r 3+ r 3r 1= 1) D2 r2 2) D r 3) 2D r 4) D 2 ANS : 1 22. tan h- 1 1 + cot h- 1 (2) = 2 1) 1 log 3 2 5 13 3 5 2) 1 log 6 2 3) 1 log12 2 4) log3 ANS : 4 23. cos- 1 cos- 1 cos- 1 x x 1) 3 65 2) - 36 65 3) - 33 65 4) 1 ANS : 3 Sri Chaitanya Page 4 Hyderabad Engineering EAMCET-2013 Date: 10.05.13 24. The set of solutions of the system of equations : x + y = x, y are real, is 1) (x, y): cos x- y 1 = 2 2 1 2 2p 3 and cos x + cos y = , where 3 2 2) (x, y ): sin 4) empty set x- y 1 = 2 2 3) (x, y): cos (x - y) = ANS : 4 25. If tan (p cos q)= cot (p sin q) then a value of cos q 1) 1 2 2 p among the following is 4 2) 1 2 3) 1 2 4) 1 4 ANS : 1 26. sin q + cos q = p , sin3 q + cos3 q = q p(p2 3) 1) q 2) 2q 3) q 4) 2q ANS : 4 27. The period of f ( x) = cos 1) 2p 2) 4p x x is + sin 3 2 3) 8p 4) 12p ANS : 4 28. (1+ i)x - i (1+ 2i) y + i 2+ i 2- i 1 7 7 , 3 15 (x, y) 3) 7 - 7 , 5 15 1) 7 - 7 , 3 15 1/ n 2) 4) 7 7 , 5 15 ANS : 1 29. If f ( x) = ( p - xn ) , p > 0 and n is a positive integer, then f ( f (x)) = 1) x 2) x n 3) p1/ n 4) p - xn ANS : 1 30. {x 1) ( R log (1.6) 1- x2 (0.625) 6(1+ x) R } 3) (1, 7) 4) (- 1, 7) , 1) (7, ) 2) (- 1, 5) ANS : 4 Sri Chaitanya Page 5 Hyderabad Engineering EAMCET-2013 Date: 10.05.13 31. If I is the identity matrix of order 2 and A = induction gives 1) An = nA - (n - 1)I 3) An = 2n A - (n + 1)I 1 1 , then for n 1 , mathematical 0 1 2) An = nA + (n - 1)I 4) An = 2n- 1 A - (n - 1)I ANS : 1 32. n Cr- 1 330, nCr 462, nCr+ 1 462 r 1) 3 2) 4 3) 5 4) 6 ANS : 3 33. 10 men and 6 women are to be seated in a row so that no two women sit together. The number of ways they can be seated is : 1) 11! 10! 2) 11! 6! 5! 3) 10! 9! 5! 4) 11! 10! 5! ANS : 4 34. If tn denotes the number of triangles formed with n points in a plane no three of which are collinear and if tn+ 1 - tn = 36 , then n = 1) 7 2) 8 3) 9 4) 10 ANS : 3 10 35. The term independent of x (x 1) 105 2) 210 0, x 1) in the expansion of (x + 1) (x 2/3 - x 1/ 3 + 1) - (x - 1) (x - x ) is 3) 315 4) 420 ANS : 2 36. If x is small so that x 2 and higher powers can be neglected, then the approximate - 1 - 2 (1- 2 x) (1- 3x) is value for - 3 (1- 4 x) 1) 1- 2 x 2) 1- 3x 3) 1- 4 x 4) 1- 5x ANS : 3 37. If 1) 1 Ax + B Cx + D = 2 + 2 , then C + D = 2 x + x + 1 x + x+ 1 x - x+ 1 4 1 2) 1 3) 2 Page 6 4) 0 Hyderabad Sri Chaitanya Engineering EAMCET-2013 Date: 10.05.13 ANS : 4 38. 1 1 1 1 + + + + ........ 2.3 4.5 6.7 8.9 e 2 1) log 2) log e 2 3) log (2e) 4) e - 1 ANS : 2 39. If the harmonic mean between the roots (5 + 2 )x2 - bx + (8 + 2 5 ) = 0 is 4, then the value of b 1) 2 2) 3 3) 4 5 4) 4 + 5 ANS : 4 40. The set of solutions satisfying both x2 1) (- 4, 1) 2) ( 4, 5x 6 0 and x2 + 3x - 4 < 0 is 3) ( 2, 1) 3] [ 2, 1) 3) ( 4, 4) [ 4, 3] [ 2, 1] ANS : 2 41. If the roots of x3 - 42 x2 + 336 x - 512 = 0 , are in increasing geometric progression, then its common ratio is 1) 2 2) 3 3) 4 4) 6 ANS : 3 42. If a and b are the roots of the equation x2 - 2 x + 4 = 0 , then a 9 + b 9 = 1) - 28 2) 29 3) - 210 4) 210 ANS : 3 43. If A = 1) 64 - 8 5 2 4 satisfies the equation x2 + 4 x - p = 0 , then p = 2) 42 3) 36 4) 24 ANS : 2 x 2 x 3 x 6 x 5 x 9 44. x 4 x 8 x 11 x 15 1) 3x2 4 x 5 2) x3 8x 2 3) 0 4) 2 ANS : 4 45. The system of equations 3x 2 y z 6,3x 4 y 3z 14, 6 x 10 y 8z a, has infinite number of solutions, if a = 1) 8 Sri Chaitanya 2)12 3) 24 Page 7 4) 36 Hyderabad Engineering EAMCET-2013 Date: 10.05.13 ANS : 4 46. The number of real values of t such that the system of homogeneous equations tx (t 1) y (t 1) z (t 1) x ty (t 2) z (t 1) x (t 2) y tz 0 0 0 has non-trivial solutions, is 1) 3 2) 2 3) 1 4) 4 ANS : 3 47. 1 i 1 i 4 1 i 1 i 4 1) 0 2) 1 3) 2 4) 4 ANS : 3 48. If a complex number z satisfies z 2 1 1) the real axis z 2 1, then z lies on : 2) the imaginary axis 3) y=x 4) a circle ANS : 2 49. The solution of the differential equation 1) y sin 2x ex c 3) y ex cos 2x c dy 2 y tan 2 x e x sec 2 x is : dx 2) y cos 2 x e x c 4) y cos 2 x ex c ANS : 2 50. An integrating factor of the equation (1 y x2 y)dx ( x x3 )dy 0 is 1) e x 2) x 2 3) 1 x 4) x ANS : 4 51. The approximate value of into two equal parts is 1) 1 11 log 3 5 dx 2 3x 1 3 1,3 2) 107 110 3) 29 110 4) 119 440 ANS : 3 52. The area (in square units) bounded by the curves x 2 y 2 and x 1 3 y 2 is Sri Chaitanya Page 8 Hyderabad Engineering EAMCET-2013 Date: 10.05.13 1) 2 3 2) 1 3) 4 3 4) 5 3 ANS : 3 b 53. If dx 1 x2 0 1 dx , then b = 1 x2 b 1 3 1) tan 2) 3 2 3) 2 4) 1 ANS : 4 54. dx x(log x - 2)(log x - 3) I c I log x 3 log x 2 1) 1 log x 3 log x log x 2 2) log 3) log log x 2 log x 3 4) log (log x 3)(log x 2) ANS : 2 55. x sin x dx 1 cos x x tan x 2 p log sec x 2 c p 1) -4 2) 4 3) 2 4) -2 ANS : 1 56. ex 2 sin 2 x dx 1 cos 2 x 1) ex cot x c 2) 2ex sec2 x c 3) ex cos2 x c 4) ex tan x c ANS : 4 57. u log( x3 y3 z 3 3xyz) ( x y z)(ux u y uz ) 1) 0 2) x y z 3) 2 4) 3 ANS : 4 58. The focal length of a mirror is given by 2 f 1 1 . In finding the values of u and v, v u in f is 1) p 1 2 u 1 v 2) p 1 u 1 v 3) p 1 2 u 1 v 4) p 1 u 1 v ANS : 2 59. If the curves x2 1) p q 2 Sri Chaitanya py 2 1 and qx 2 y 2 1 are orthogonal to each other, then 2) 1 p 1 q 2 3) Page 9 1 p 1 q 2 4) 1 p 1 q 2 Hyderabad Engineering EAMCET-2013 Date: 10.05.13 ANS : 4 1 60. The relation between pressure p and volume v is given by pv 4 Constant. If the percentage decrease in volume is 1) 1 8 1 , then the percentage increase in pressure is 2 2) 1 16 3) 1 8 4) 1 2 ANS : 3 61. cos 1 y b 2log x ,x 0 2 x2 d2y dx 2 x dy = dx 1) 4y 2) -4y 3) 0 4) -8y ANS : 2 62. d ( x 1)( x 2 1)( x 4 1)( x8 1) dx (15x p 16 xq 1)( x 1) 2 ( p, q) 1) (12,11) 2) (15,14) 3) (16,14) 4) (16,15) ANS : 4 63. 1) y x x2 x x y y2 y 2 dy dx 2) x2 x y2 y 3) 1 4) 2 ANS : 3 64. f ( x) 1 1 1 x ; g ( x) 1 1 1 f ( x) g ' (2) 1) 1 5 2) 1 25 3) 5 4) 1 16 ANS : 2 65. tan 3 x sin 3 x x 0 x5 5 1) 2 lim 2) 3 2 3) 3 5 4) 2 5 ANS : 2 66. Let f be a non-zero real valued continuous function satisfying f ( x y) all x, y R.If f (2) 9, then f (6) 1) 32 Sri Chaitanya f ( x). f ( y) for 2) 36 3) 34 Page 10 4) 33 Hyderabad Engineering EAMCET-2013 Date: 10.05.13 ANS : 2 67. A variable plane passes through a fixed point (1,2,3). Then the foot of the perpendicular form the origin to the plane lies on 1) a circle 2) a sphere 3) an ellipse 4) a parabola ANS : 2 68. A plane passing through (-1,2,3) and whose normal makes equal angles with the coordinate axes is 1) x y z 4 0 2) x y z 4 0 3) x y z 4 0 4) x y z 0 ANS : 3 69. The direction ratios of two lines AB,AC are 1, 1, 1 and 2, 1,1. The direction ratios of the normal to the plane ABC are 1) 2,3, 1 2) 2, 2,1 3) 3,2, 1 4) 1, 2,3 ANS : 1 70. D(2,1,0), E (2,0,0), F (0,1,0) are mid-points of the sides BC, CA, AB OF ABC respectively Then, the centroid of ABC is 1) 1 1 1 , , 3 3 3 2) 4 2 , ,0 3 3 3) 1 1 1 , , 3 3 3 4) 2 1 1 , , 3 3 3 ANS : 2 71. The perpendicular distance from the point (1, ) to the line joining (1,00 ) and (1, ), (in 2 polar coordinates ) is 1) 2 2) 3 3) 1 4) 2 ANS : 4 72. If x 9 is a chord of contact of the hyperbola x2 y 2 9, then the equation of the tangent at one of the points of contact is 1) x + 3 y + 2 = 0 2) 3x - 2 2 y - 3 = 0 3) 3x - 2 y + 6 = 0 4) x - 3 y + 2 = 0 ANS : 2 73. x2 y 2 If the foci of the ellipse 25 16 x2 1 and the hyperbola 4 y2 b2 1 coincide, then b2 1) 4 2) 5 3) 8 4) 9 ANS : 2 Sri Chaitanya Page 11 Hyderabad Engineering EAMCET-2013 Date: 10.05.13 74. The midpoint of a chord of the ellipse x2 4 y 2 2 x 20 y 0 is (2, -4). The equation of the chord is 1) x 6 y 26 2) x 6 y 26 3) 6 x y 26 4) 6x y 26 ANS : 1 75. A circle of radius 4, drawn on a chord of the parabola y 2 8x as diameter, touches the axis of the parabola, Then, the slope of the chord is 1) 1 2 2) 3 4 3) 1 4) 2 ANS : 3 76. If the circle x2 y2 4x 6 y c 0 bisects the circumference of the circle x2 y2 6 x 4 y 12 0, then c 1) 16 2) 24 3) -42 4) -62 ANS : 4 77. (a,0) and (b,0) are centres of two circles belonging to a co-axial system of which y-axis is the rad circle is 1) (r 2 b2 a 2 )1/2 2) (r 2 b2 a2 )1/2 3) (r 2 b2 a2 )1/3 4) (r 2 b2 a 2 )1/3 ANS : 2 78. If the length of the tangent from (h, k) to the circle x2 y 2 16 is twice the length of the tangent from the same point to the circle x2 y 2 2x 2 y 0, then 1) h2 k 2 4h 4k 16 0 3) 3h2 3k 2 8h 8k 16 0 2) h2 k 2 3h 3k 0 4) 3h2 3k 2 4h 4k 16 0 ANS : 3 Sri Chaitanya Page 12 Hyderabad Engineering EAMCET-2013 Date: 10.05.13 79. For the circle C with the equation x2 y 2 16 x 12 y 64 0 match the list-I with the list-II given below. List-I i) The equation of the polar of (-5,1) with respect to C ii) The equation of the tangent at (8, 0) to C iii) The equation of the normal at (2, 6) to C iv) The equation of the diameter of C through (8, 12) List-II a) y 0 b) y=6 c) x y 7 d) 13x 5 y 98 e) x 8 Correct match is i 1) 3) d c ii b d iii a a iv e b 2) 4) i d c ii a e iii b b iv e a ANS : 2 80. The circle 4 x2 4 y 2 12 x 12 y 9 0 1) touches both the axes 3) touches the y-axis only 2) touches the x-axis only 4) does not touch the axes ANS : 1 PHYSICS 81. A tension of 20N applied to a copper wire of cross sectional area 0.01cm2, Young s Modulus of copper is 1.1 1011 N / m2 and Poisson s ratio is 0.32. The decrease in cross sectional area of the wire is 1) 1.16 10- 6 cm2 2) 1.16 10- 5 m2 3) 1.16 10- 4 m2 4) 1.16 10- 3 cm2 ANS : 1 82. A capillary tube of radius r is immersed in water and water rises to a height of h . Mass of water in the capillary tube is 5 10- 3 kg . The same capillary tube is now immersed in a liquid whose surface tension is which rises into the capillary tube now is, (in kg) 1) 5 10- 3 Sri Chaitanya 2 times the surface tension of water. The angle of contact between the capillary tube and this liquid is 450. The mass of liquid 2) 2.5 10- 3 3) 5 2 10- 3 Page 13 4) 3.5 10- 3 Hyderabad Engineering EAMCET-2013 Date: 10.05.13 ANS : 1 83. The terminal velocity of a liquid drop of radius r falling through air is v. If two such drops are combined to form a bigger drop, the terminal velocity with which the bigger drop falls through air is (Ignore any buoyant force due to air) 1) 2v 2) 2 v 3) 3 4v 4) 3 2v ANS : 3 84. A glass flask of volume one litre is filled completely with mercury at 0 0C. The flask is now heated to 1000C. Coefficient of volume expansion of mercury is 1.82 10- 4 / 0 C and coefficient of linear expansion of glass is 0.1 10- 4 / 0 C . During this process, amount of mercury which overflows is 1) 21.2 cc 2) 15.2 cc 3) 2.12 cc 4) 18.2 cc ANS : 2 85. On a temperature scale Y, water freezes at -1600 Y and boils at -500 Y. On this Y scale, a temperature of 340 K is 1) - 106.30 Y 2) - 96.30 Y 3) - 86.30 Y 4) - 76.30 Y ANS : 3 86. Three moles of an ideal monoatomic gas undergoes a cyclic process as shown in the figure. The temperature of the gas in different states marked as 1,2,3 and 4 are 400 K, 700 K, 2500 K and 1100 K respectively. The work done by the gas during the process 12-3-4-1 is (Universal gas constant R) 1) 1650 R 2) 550 R 3) 1100 R 4) 2200 R ANS : 1 87. Efficiency of a heat engine whose sink is at a temperature of 300 K is 40%. To increase the efficiency to 60%, keeping the sink temperature constant, the source temperature must be increased by Sri Chaitanya Page 14 Hyderabad Engineering EAMCET-2013 Date: 10.05.13 1) 750 K 2) 500 K 3) 250 K 4) 1000 K ANS : 3 88. Two bodies A and B of equal surface area have thermal emissivities of 0.01 and 0.81 respectively. The two bodies are radiating energy at the same rate. Maximum energy is radiated from the two bodies A and B at wavelengths l A and l B respectively. Difference in these two wavelengths is 1mm . If the temperature of the body A is 5802 K, then value of l B is 1) 1 mm 2 2) 1mm 3) 2 mm 4) 3 mm 2 ANS : 4 89. An air column in a tube 32 cm long, closed at one end, is in resonance with a tuning fork. The air column in another tube, open at both ends, of length 66 cm is in resonance with another tuning fork. When these two tuning forks are sounded together, they produce 8 beats per second. Then the frequencies of the two tuning forks are, (Consider fundamental frequencies only) 1) 250 Hz, 258 Hz 2) 240 Hz, 248 Hz 3) 264 Hz, 256 Hz 4) 280 Hz, 272 Hz ANS : 3 90. A source of sound of frequency 640 Hz is moving at a velocity of 100 m/s along a road, 3 and is it an instant 30 m away from a point A on the road (as shown in figure). A person standing at O, 40 m away from the road hears sound of apparent frequency v1. The value of v1 is (velocity of sound = 340 m/s) 1) 620 Hz 2) 680 Hz 3) 720 Hz 4) 840 Hz ANS : 2 Sri Chaitanya Page 15 Hyderabad Engineering EAMCET-2013 Date: 10.05.13 91. The two surfaces of a concave lens, made of glass of refractive index 1.5 have the same radii of curvature R. It is now immersed in a medium of refractive index 1.75, then the lens 1) becomes a convergent lens of focal length 3.5 R 2) becomes a convergent lens of focal length 3.0 R 3) changes as a divergent lens of focal length 3.5 R 4) changes as a divergent lens of focal length 3.0 R ANS : 1 92. A microscope consists of an objective of focal length 1.9 cm and eye piece of focal length 5 cm. The two lenses are kept at a distance of 10.5 cm. If the image is to be formed at the least distance of distinct vision, the distance at which the object is to be placed before the objective is (Least distance of distinct vision is 25 cm) 1) 6.2 cm 2) 2.7 cm 3) 21.0 cm 4) 4.17 cm ANS : 2 93. Fresnel diffraction is produced due to light rays falling on a small obstacle. The intensity of light at a point on a screen beyond an obstacle depends on 1) the focal length of lens used for observation 2) the number of half-period zones that superpose at the point 3) the square of the sum of the number of half period zones 4) the thickness of the obstacle ANS : 2 94. A short bar magnet having magnetic moment 4 Am2, placed in a vibrating magnetometer, vibrates with a time period of 8 seconds. Another short bar magnet having a magnetic moment 8 Am2 vibrates with a time period of 6 seconds. If the moment of inertia of the second magnet is 9 10- 2 kg m2 , the moment of inertia of the first magnet is (Assume that both magnets are kept in the same uniform magnetic induction field.) 1) 9 10- 2 kg m2 2) 8 10- 2 kg m2 3) 5.33 10- 2 kg m2 4) 12.2 10- 2 kg m2 ANS : 2 Sri Chaitanya Page 16 Hyderabad Engineering EAMCET-2013 Date: 10.05.13 95. Two short bar magnets have their magnetic moments 1.2 Am2 and 1.0 Am2. They are placed on a horizontal table parallel to each other at a distance of 20 cm between their centres, such that their north poles pointing towards geographic south. They have common magnetic equatorial line. Horizontal component of earth s field is 3.6 10- 5 T . Then, the resultant horizontal magnetic induction at mid point of the line joining their centers is m 0 = 10- 7 H / m 4p 1) 3.6 10- 5 T 2) 1.84 10- 4 T 3) 2.56 10- 4 T 4) 5.8 10- 5 T ANS : 3 96. A deflection magnetometer is adjusted and a magnet of magnetic moment M is placed on it in the usual manner and the observed deflection is q . The period of oscillation of the needle before settling to the deflection is T. When the magnet is removed, the period of oscillation of the needle is T0 before settling to 00 - 00 . If the earth s induced magnetic field is BH , the relation between T and T0 is 1) T2 = T02 cos q 2) T 2 = T02 cos q 3) T = T0 cos q 4) T = T0 cos q ANS : 1 97. Two metal plates each of area A form a parallel plate capacitor with air in between the plates. The distance between the plates is d . A metal plate of thickness d/2 and of same area A is inserted between the plates to form two capacitors of capacitances C1 and C2 as shown in the figure. If the effective capacitance of the two capacitors is C| and the capacitance of the capacitor initially is C, then C' is C 1) 4 2) 2 3) 6 4) 1 ANS : 2 Sri Chaitanya Page 17 Hyderabad Engineering EAMCET-2013 Date: 10.05.13 98. In the circuit shown in the figure, the current I is 1) 6 Amp 2) 2 Amp 3) 4 Amp 4) 7 Amp ANS : 3 99. In the meter bridge experiment, the length AB of the wire is 1m. The resistors X and Y have values 5 W and 2 W respectively. When a shunt resistance S is connected to X, the balancing point is found to be 0.625 m from A. Then, the resistance of the shunt is 1) 5W 2) 10W 3) 7.5W 4) 12.5W ANS : 2 100. If E,M,J and G respectively denote energy, mass, angular momentum and universal gravitational constant, the quantity, which has the same dimensions as the dimensions of EJ 2 M 5G 2 1) Time 2) Angle 3) Mass 4) Length ANS : 2 101. The work done in moving an object from origin to a point whose position vector is r = 3i + 2j - 5k by a force F = 2i - j - k is 1) 1 unit 2) 9 units 3) 13 units 4) 60 units ANS : 2 Sri Chaitanya Page 18 Hyderabad Engineering EAMCET-2013 Date: 10.05.13 102. A particle is projected from the ground with an initial speed of v at an angle of projection q . The average velocity of the particle between its time of projection and time it reaches highest point of trajectory is 1) v 1 + 2cos2 q 2 2) v 1 + 2sin 2 q 2 3) v 1 + 3cos2 q 2 4) v cos q ANS : 3 103. Two wooden blocks of masses M and m are placed on a smooth horizontal surface as shown in figure. If a force P is applied to the system as shown in figure such that the mass m remains stationary with respect to block of mass M, then the magnitude of the force P is 1) ( M + m) g tan b 2) g tanb 3) mg cosb 4) ( M + m) g cos ec b ANS : 1 104. A ball at rest is dropped from a height of 12m. It looses 25% of its kinetic energy on striking the ground and bounces back to a height h . Then value of h is 1) 3 m 2) 6 m 3) 9 m 4) 12 m ANS : 3 105. Two bodies of mass 4kg and 5 kg are moving along east and north directions with velocities 5 m/s and 3m/s respectively. Magnitude of the velocity of centre of mass of the system is 1) 25 m/s 9 2) 9 m/s 25 3) 41 m/s 9 4) 16 m/s 9 ANS : 1 106. A mass of 2.9 kg is suspended from a string of length 50 cm and is at rest. Another body of mass 100 g, which is moving horizontally with a velocity of 150 m/s strikes and sticks to it. Subsequently when the string makes an angle of 600 with the vertical, the tension in the string is g = 10m / s 2 1) 140 N ( 2) 135 N ) 3) 125 N 4) 90 N ANS : 2 Sri Chaitanya Page 19 Hyderabad Engineering EAMCET-2013 Date: 10.05.13 107. The upper half of an inclined plane with an angle of inclination f , is smooth while the lower half is rough. A body starting from rest at the top of the inclined plane comes to rest at the bottom of the inclined plane. Then the coefficient of friction for the lower half is 1) 2 tan f 2) tan f 3) 2sin f 4) 2cos f ANS : 1 108. Moment of inertia of a body about an axis is 4 kgm2 . The body is initially at rest and a torque of 8 Nm starts acting on it along the same axis. Work done by the torque in 20 sec, in Jules, is 1) 40 2) 640 3) 2560 4) 3200 ANS : 4 109. A uniform circular disc of radius R, lying on a frictionless horizontal plane is rotating with an angular velocity w about its own axis. Another identical circular disc is gently placed on the top of the first disc coaxially. The loss in rotational kinetic energy due to friction between the two discs, as they acquire common angular velocity is (I is Moment of Inertia of the disc) 1) 1 2 Iw 8 2) 1 2 Iw 4 3) 1 2 Iw 2 4) Iw2 ANS : 2 110. The gravitational force acting on a particle, due to a solid sphere of uniform density and radius R, at a distance of 3R from the centre of the sphere is F1 . A spherical hole of radius (R/2) is now made in the sphere as shown in the figure. The sphere with hole now exerts a force F2 on the same particle. Ratio of F1 to F2 is 1) 50 41 2) 41 50 3) 41 25 4) 25 41 ANS : 1 Sri Chaitanya Page 20 Hyderabad Engineering EAMCET-2013 Date: 10.05.13 111. Two particles A and B of masses m and 2m are suspended from two massless springs of force constants K1 and K 2 . During their oscillation, if their maximum velocities are equal, then ratio of amplitudes of A and B is 1) K1 K2 2) K2 2K1 3) K2 K1 4) 2K1 K2 ANS : 2 112. Of the following, NAND gate is 1) 2) 3) 4) ANS : 4 113. The base current in a transistor circuit changes from 45 m A to 140 m A. Accordingly, the collector current changes form 0.2 mA to 4.00 mA. The gain in current is 1) 9.5 2) 1 3) 40 4) 20 ANS : 3 114. A U235 nuclear reactor generates energy at rate of 3.70 107 J / s . Each fission liberates 185 MeV useful energy. If the reactor has to operate for 144 104 seconds, then, the mass of the fuel needed is (Assume Avogadro s number = 6 1023 mol- 1 ,1eV 1.6 10- 19 J ) 1) 70.5 kg 2) 0.705 kg 3) 13.1 kg 4) 1.31 kg ANS : 2 115. The radius of 1) 3.6 10- 12 m 72 Te125 nucleus is 6 fermi. The radius of 13 A127 nucleus in meters is 72 Te125 2) 3.6 10- 15 m 3) 7.2 10- 8 m 4) 7.2 10- 15 m ANS : 2 116. The work function of a metal is 2 eV. If a radiation of wavelength 3000 A is incident on 0 it, the maximum kinetic energy of the emitted photoelectrons is (Planack s constant h 6.6 10- 34 JS; Velocity of light c 3 108 m / s; 1eV 1.6 10- 19 J ) 1) 4.4 10- 19 J 2) 5.6 10- 19 J 3) 3.4 10- 19 J 4) 2.5 10- 19 J ANS : 3 Sri Chaitanya Page 21 Hyderabad Engineering EAMCET-2013 Date: 10.05.13 117. Initially a photon of wavelength l 1 falls on photocathode and emits an electron of maximum energy E1 . If the wavelength of the incident photon is changed to l 2 , the maximum energy of the electron emitted becomes E 2 . Then value of hc (h = Planck s constant, c = Velocity of light )is 1) hc = ( 3) hc = ( E1 + E2 ) l 1l 2 l2- l1 E1 - E2 )( l 2 - l 1 ) l 1l 2 2) hc = 4) hc = E1 - E 2 ( l 1l 2 ) l2- l1 l2- l1 .E1 l 1l 2 E2 ANS : 2 118. The sensitivity of a galvanometer that measures current is decreased by 1 times by 40 using shunt resistance of 10W . Then, the value of the resistance of the galvanometer is 1) 400W 2) 410W 3) 30W 4) 390W ANS : 4 119. A series LCR circuit is connected across a source of alternating emf of changing frequency and resonates at frequency f 0 . Keeping capacitance constant, if the inductance (L) is increased by resonant frequency now is 1) 31/4 f0 2) 3 f0 3) 3 times and resistance is increased (R) by 1.4 times, the ( 3-1 ) 1/4 f0 4) 1 3 1/4 f0 ANS : 4 120. The ends of an element of zinc wire are kept at a small temperature difference D T and a small current (I) is passed through the wire. Then, the heat developed per unit time T and I 1) is proportional to D T 2) is proportional to I3 and D 3) is proportional to Thomson coefficient of the metal T only 4) is proportional to D ANS : 1 Sri Chaitanya Page 22 Hyderabad Engineering EAMCET-2013 Date: 10.05.13 CHEMISTRY 121. For which one of the following reactions, the entropy change is positive ? 1) H2 (g) 1 O2 2 (g) H 2O (l ) 2) Na+ Cl (g) (g) H 2O (l ) H 2O (g ) NaCl ( s) 3) NaCl (l ) NaCl ( s) 4) ANS : 4 122. Match the following List-I A) Solid dispersed in liquid B) Liquid dispersed in liquid C) Gas dispersed in liquid D) Liquid dispersed in solid A 1) 3) IV III B I I C II II D III IV 2) 4) List-II I) Emulsion II) Foam III) Gel IV) Sol V) Aerosol A III IV B I I C V V D II III ANS : 1 123. Observe the following statements : 1. Heavy water is harmful for the growth of animals 2. Heavy water reacts with Al4C3 and forms deuterated acetylene 3. BaCl2 .2 D2O is an example of interstitial deuterate The correct statements are : 1) 1 & 3 2) 1 & 2 3) 1,2 & 3 4) 2 & 3 ANS : 1 124. Na2CO3 and NaHCO3. 20 ml of X when titrated using methyl Orange indicator consumed 60 ml of 0.1 M HCl solution. In another experiment, 20 ml of X solution when titrated using phenolphthalein consumed 20 ml of 0.1 M HCl solution. The concentrations (in mol lit- 1 ) of Na2CO3 and NaHCO3 in X are respectively 1) 0.01, 0.02 2) 0.1, 0.1 3) 0.01, 0.01 4) 0.1, 0.01 ANS : 2 Sri Chaitanya Page 23 Hyderabad Engineering EAMCET-2013 Date: 10.05.13 125. Diborane reacts with HCl in the presence of AlCl3 and liberates : 1) H 2 2) Cl2 3) BCl3 4) Cl2 & BCl3 ANS : 1 126. How many corners of SiO4 unit are shared in the formation of three dimensional silicates ? 1) 3 2) 2 3) 4 4) 1 ANS : 3 127. Which one of the following is not correct ? 1) Pyrophosphoric acid is a tetrabasic acid 2) Pyrophosphoric acid contains P-O-P linkage 3) Pyrophosphoric acid contains two P-H bonds 4) Orthophosphoric acid can be prepared by dissolving P4O10 in water ANS : 3 128. Na2 S2O3 reacts with moist Cl2 to form Na2 SO4 , HCl and X. Which one of the following is X ? 1) H 2 S 2) SO2 3) SO3 4) S ANS : 4 129. The role of copper diaphragm in Whytlaw1) preventing the corrosion of electrolytic cell 3) as anode 2) preventing the mixing of H 2 and F2 4) as cathode ANS : 2 130. Liquid X is used in Bubble chamber to detect neutral mesons and gamma photons. Then, X = 1) He 2) Ne 3) Kr 4) Xe ANS : 4 131. A compound absorbs light in the wavelength region 490-500 nm. Its complementary Colour is : 1) Red 2) Blue 3) Orange 4) Blue-green ANS : 1 132. Which of the following is not added during the extraction of silver by cyanide process? 1) NaCN 2) Air 3) Zn Page 24 4) Na2 S2O3 Hyderabad ANS : 4 Sri Chaitanya Engineering EAMCET-2013 Date: 10.05.13 133. Cataract and skin cancer are caused by 1) Depletion of Nitric oxide 3) Increase in Methane 2) Depletion of Ozone layer 4) Depletion of Nitrous oxide ANS : 2 134. Which one of the following gives Prussion blue colour ? 1) Fe2 Fe (CN )6 2) Na4 Fe (CN )6 3) Fe3 Fe (CN )6 3 4) Fe4 Fe (CN )6 3 ANS : 4 135. C2 H 6 450 C C2 H 4 H 2 Above reaction is called as 1) Combustion 2) Rearrangement 3) Pyrolysis 4) Cleavage ANS : 3 136. Assertion (A) : - NH 2 group of aniline is ortho, para directing in electrophilic substitutions. Reason (R) : - NH 2 group stabilises the arenium ion formed by the ortho, para attack of the electrophile. The correct answer is 1) Both (A) and (R) are correct,(R) is the correct explanation of (A). 2) Both (A ) and (R) are correct, (R) is not the correct explanation of (A). 3) (A) is correct, but (R) is not correct 4) (A) is not correct, but (R) is correct ANS : 1 137. In which of the following properties, the two enantiomers of lactic acid differ from each other ? 1) Sign of specific rotation 3) Melting point 2) Density 4) Refractive index ANS : 1 138. Heating chloroform with aqueous sodium hydroxide solution forms : 1) Sodium acetate 3) Sodium formate 2) Sodium oxalate 4) Chloral ANS : 3 Sri Chaitanya Page 25 Hyderabad Engineering EAMCET-2013 Date: 10.05.13 139. The products formed in the reaction of phenol with Br2 dissolved in CS2 at 0°C are : 1) o-bromo. m-bromo and p-bromophenols 2) o- bromo and p- bromophenols 3) 2, 4, 6-tri bromo and 2, 3, 6-tri bromophenols 4) 2, 4-di bromo and 2, 6-di bromophenols ANS : 2 140. The structure of PCC is : 1) 3) 2) 4) ANS : 4 141. The pKa values of four carboxylic acids are given below. Identify the weakest carboxylic acid. 1) 4.89 2) 1.28 3) 4.76 4) 2.56 ANS : 1 142. Identify X and Y in the following reactions : ANS : 3 Sri Chaitanya Page 26 Hyderabad Engineering EAMCET-2013 Date: 10.05.13 143. Example of a biodegradable polymer pair is : 1) Nylon-6,6 and Terylene 3) Bakelite and PVC 2) PHBV and Dextron 4) PET and Polyethylene ANS : 2 144. The number of hydrogen bonds between Guanine & Cytosine; and between Adenine & Thymine in DNA is : 1) 1, 2 2) 3, 2 3) 3, 1 4) 2, 1 ANS : 2 145. Identify Phenacetin from the following : ANS : 4 146. The number of radial nodes of 3s and 2p orbitals respectively are : 1) 0, 2 2) 2, 0 3) 1, 2 4) 2, 1 ANS : 2 147. The basis of quantum mechanical model of an atom is : 1) angular momentum of electron 3) dual nature of electron 2) quantum numbers 4) black body radiation ANS : 3 148. The number of elements present in fourth period is : 1) 32 2) 8 3) 18 4) 2 ANS : 3 Sri Chaitanya Page 27 Hyderabad Engineering EAMCET-2013 Date: 10.05.13 149. Identify the correct set : Molecule 1) PCl5 2) Ni ( CN ) 4 3) SF6 4) IF3 2- hybridisation of central atom dsp3 sp 3 sp3 d 2 dsp3 shape square pyramidal tetrahedral octahedral pyramidal ANS : 3 150. Which one of the following statements is correct ? 1) Hybrid orbitals do not form s bonds 2) Lateral overlap of p-orbitals or p- and d-orbitals produces p - bonds 3) The strength of bonds follows the order :s 4) s-orbitals do not form s bonds p- p <s s- s <p p- p ANS : 2 151. Which one of the following is an example of disproportionation reaction ? 1) 3Cl2 ( g ) 6OH (aq) 2) Ag 2 (aq) Ag (s) 3) Zn(s) CuSO4 (aq) 4) 2KClO3 (s) ClO 3 (aq) 5Cl (aq) 3H 2O(1) 2 Ag (aq) Cu(s) ZnSO4 (aq) 2KCl (s) 3O2 ( g ) ANS : 1 152. At T(k), the ratio of Kinetic energies of 4 g of H 2 1) 1: 4 2) 4 :1 3) 2 :1 (g) and 8g of O2 is : (g) 4) 8 :1 ANS : 4 153. Which one of the following is an isotonic pair of solutions? 1) 0.15 M NaCl and 0.1 M Na2 SO4 2) 0.2 M Urea and 0.1 M Sugar 3) 0.1 M BaCl2 and 0.2 M Urea 4) 0.2 M MgSO4 and 0.1 M NH 4Cl ANS : 1 Sri Chaitanya Page 28 Hyderabad Engineering EAMCET-2013 Date: 10.05.13 154. The vapour pressure in mm of Hg, of an aqueous solution obtained by adding 18 g of glucose (C6 H12O6 ) to 180 g of water at 100o C is : 1) 7.60 2) 76.0 3) 759 4) 752.4 ANS : 4 155. During the electrolysis of copper sulphate aqueous solution using copper electrode, the reaction taking place at the cathode is : 1) Cu + Cu(2aq ) + 2) Cu(2aq 2e) 2e1 H2 2 (g) Cu(s) 1 O2 2 (g ) 2e- 3) H(+ eaq) 24) SO4( aq) SO3(g ) ANS : 2 156. The extent of charge of lead accumulator is determined by 1) amount of PbSO4 in the battery 2) amount of PbO2 in the battery 3) specific gravity of H 2 SO4 of the battery 4) amount of Pb in the battery ANS : 3 157. The number of octahedral and tetrahedral holes respectively present in a hexagonal close packed (hcp) crystal of X atoms are : 1) X, 2X 2) X, X 3) 2X, X 4) 2X, 2X ANS : 1 158. Which one of the following plots is correct for a first order reaction? ANS : 3 Sri Chaitanya Page 29 Hyderabad Engineering EAMCET-2013 Date: 10.05.13 159. The degree of ionization of 0.10 M lactic acid is 4.0% The value of K c is 1) 1.66 10- 5 2) 1.66 10- 4 3) 1.66 10- 3 4) 1.66 10- 2 ANS : 2 160. The pH of a buffer solution made by mixing 25 ml of 0.02 M NH 4OH and 25 ml of 0.2 M NH 4Cl at 25o C is : ( pKb of NH 4OH = 4.8 ) 1) 5.8 2) 8.2 3) 4.8 4) 3.8 ANS : 2 Sri Chaitanya Page 30 Hyderabad
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