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This is a model paper of APRJC exam conducted in Andhra Pradesh. This exam is of 10th class level.

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<p> zeamail2@gmail.com Page 1 APRJC MODEL PAPER APRJC Hall Ticket Number: Signature: Total marks: 150 Duration: 150 minutes ____________________________________________________________________________________ SECTION-I (MATHEMATICS) 1) The contrapositive of the statement In a ABC, if AB=AC then B = C" is 1. In a ABC, if B = C then AB = AC 2. In a ABC, if ABAC then B C 3. In a ABC, if B C then BC AB 4. In a ABC, if B C then AB AC 2) Which of the following is a symmetric matrix? 1. _1 2 42 3 74 7 5 _ 2. _1 2 42 3 74 7 5 _ 3. _1 2 33 2 14 7 5_ 4. _1 2 42 3 74 7 5_ zeamail2@gmail.com Page 2 APRJC MODEL PAPER 3) A and B are sets in the universal set . Which of the following is false? 1. A| B| = B A 2. A B = A = onJ B = 3. A B = B| A onJ A| B 4. A p = A 4) Let : R R defined by (x) = _x +1 i x 13 x i 0 x 13 +x i x 0 . Then f is ___________. 1. Only one-one function 2. Only onto function 3. A bijection 4. Neither one-one nor onto 5) The relation between x and y such that the point (x, y) is equidistant from the points (3, 6) and ( 3, 4) is _____ 1. x 3y + 5 = 0 2. x + 3y + 5 = 0 3. 3x y + 5 = 0 4. 3x + y 5 = 0 6) The quotient and remainder when x4 4x3 +4x2 2 is divided by x 3 respectively are 1. x3 + x + 3 onJ 6 2. x3 x + 3 onJ 6 3. x3 x2 + x + 3 onJ 7 4. x3 x2 x + 3 onJ 7 zeamail2@gmail.com Page 3 APRJC MODEL PAPER 7) If A = ji 00 i[ and i2 = 1, then A2012 = 1. ji 00 i[ 2. j2012i 00 2012i[ 3. j1 00 1[ 4. j2012 00 2012[ 8) At how many points the line 2x + y = 15 meets the curve y = x2? 1. 0 2. 2 3. 4 4. Infinite 9) 1 +3 + 5 + 7 ++(2n + 1) = 1. (n +1)2 2. n2 3. n2 +1 4. n2 1 10) The product (x y) [o b [xy is 1. (2ox2 +xy + 2by2) 2. (ox2 +xy + by2) 3. (ox2 +2xy + by2) 4. (ox2 xy + by2) zeamail2@gmail.com Page 4 APRJC MODEL PAPER 11) Middle term in the expansion of (x + x)8 is 1. 8C6 2. 8C6 x 3. 8C4 x 4. 8C4 12) If angles A, B, C are in Arithmetic progression in the ABC, then cos B = 1. 1/2 2. 3/2 3. 1 4. None 13) Maximum value of = x + 4y subject to the constraints 8x +5y 40, 4x +3y 12, x 0, y 0 occurs at the point: 1. (8,0) 2. (0,8) 3. (4,8) 4. (8,4) 14) If lmn = 1, then 11+I+m-1 + 11+m+n-1 +11+n+I-1 = 1. 0 2. 1 3. 2 4. None zeamail2@gmail.com Page 5 APRJC MODEL PAPER 15) limx 2j 1x-2 2x(x-1)(x-2)[ = 1. 2/3 2. 3/2 3. 4/3 4. 16) If the mth, nth, pth terms of a G.P form three consecutive terms of a geometric sequence, then m, n and p form three consecutive terms of ______________. 1. A geometric sequence 2. A harmonic sequence 3. An arithmetic sequence 4. None 17) In an equilateral triangle ABC, side BC is trisected at D, then A2AB2 =___________ 1. 9/7 2. 8/7 3. 7/9 4. 7/8 18) The points A(-4,-1), B(-2,-4), C(4,0) and D(2,3) are the vertices of 1. Parallelogram 2. Rectangle 3. Rhombus 4. Square zeamail2@gmail.com Page 6 APRJC MODEL PAPER 19) The value of for which cos 01-sIn0 + cos 01+sIn0 = 4 and (0 0 90) is______ 1. 30 2. 45 3. 60 4. 75 20) The point R(4,24) divides the line segment P(2,27), Q(10,15) in the ratio: 1. 4:1 2. 3:2 3. 2:3 4. 1:3 21) If (x) = (o xn)1/n where o > 0, and n is a positive integer, then (o)x = 1. o 2. x 3. 1/x 4. 1 22) What is the shape of box used in flow-charts for giving input? 1. Rhombus 2. Parallelogram 3. Rectangle 4. Oval 23) If = {(1,2), (2,3), (3,4), (4,1)}, then o = 1. {(3,1), (4,2), (3,1), (2,2)} 2. {(1,3), (2,2), (4,2), (3,4)} 3. {(1,3), (2,4), (3,1), (4,2)} 4. {(1,3), (4,4), (2,3), (3,4)} zeamail2@gmail.com Page 7 APRJC MODEL PAPER 24) If B = j1 21 3[, then B +B-1 = (wcrc I = j1 00 1[ ) 1. 2I 2. 4I 3. 3I 4. None 25) If ABC is a cyclic quadrilateral, then the value of cos A +cos B + cos C +cos is______ 1. 0 2. 1 3. 2 4. -1 26) The line joining (1,0) and (2,3) makes an angle of _______ with X-axis. 1. 30 2. 45 3. 60 4. 75 27) The frequency polygon is one drawn using 1. Midpoints of classes and frequencies 2. Endpoints of classes and frequencies 3. Upper boundaries of classes less than cumulative frequencies 4. Lower boundaries of classes greater than cumulative frequencies zeamail2@gmail.com Page 8 APRJC MODEL PAPER 28) If A, BE, CF are the medians of ABC. Then AB2+BC2+AC2A2+BL2+CP2 = 1. 4/3 2. 3. 5/2 4. 2/5 29) The area of quadrilateral formed by the four points (1,0), (0,1), (-1,0) and (0,-1) taken in order is 1. 2 2. 22 3. 42 4. 1 30) The domain of (x) = cos-1(2 x) is 1. [-1,3] 2. [1,3] 3. [1,-3] 4. [-1,-3] 31) The minutes hand of a clock is 3 cm long. How far does its top move in 20 minutes? 1. 9 cm 2. 10 cm 3. 22 cm 4. 44/7 cm 32) The solution of the matrix equation j2 54 3[ jxy[ = [119 is 1. 3, 1 2. -3, -1 3. 3, -1 4. -3, 1 zeamail2@gmail.com Page 9 APRJC MODEL PAPER 33) TAR is a tangent to the circle at A. If BIA = 20 onJ BAI = 28, then AR = 1. 20 2. 48 3. 42 4. 132 34) If cos(A +B) = 12, sin(A B) = 12 , then A = 1. 15 2. 30 3. 45 4. 60 35) The ratio of the roots of the equation x2 px +q = 0 is 1:k then the value of k(k+1)2 is _____ 1. qp2 2. p2q 3. pq 4. qp zeamail2@gmail.com Page 10 APRJC MODEL PAPER 36) If o cos 0 b sin0 = c, then o sin0 +b cos 0 = 1. o2 +b2 +c2 2. o2 b2 c2 3. o2 b2 +c2 4. o2 +b2 c2 37) The mean of 10 observations is 16.3. By an error, on observation is registered as 32 instead of 23, then the correct mean is_______ 1. 15.6 2. 15.4 3. 15.7 4. 15.8 38) Which of the following is a tautology? 1. (~(p q)) ((~p) (~q)) 2. ((~p) q) ((~p) q) 3. ((~p) q) (p (~q)) 4. p (~p) 39) Marks scored by 100 students in a 25 marks unit test of mathematics are given below. Their median is ________ Marks 0-5 5-10 10-15 15-20 20-25 Students 10 18 42 23 7 1. 12 2. 12.6 3. 12.3 4. 12.7 zeamail2@gmail.com Page 11 APRJC MODEL PAPER 40) The equation satisfied by the graph in the adjacent figure is__ 1. 5x 3y 15 > 0 2. 3x + 5y 15 0 3. 3x + 5y 15 0 4. 5x + 3y 15 0 41) limn j12+1n3 + 22+2n3 + 32+3n3 ++ n2n3[ = 1. 1/6 2. 3. 1/3 4. 42) If y = 1 + o + o2 +o3 + and |o| < 0.5, then 11-u = 1. y2 +2 + 3y 2. y2 +3y 2 3. y2 2y +2 4. y2 2y 2 zeamail2@gmail.com Page 12 APRJC MODEL PAPER 43) If (b + c), (c + o), (o + b) are in H.P, then 1u2, 1b2, 1c2 are in: 1. A.P 2. H.P 3. G.P 4. A.G.P 44) In the given figure, the radius of the circle is 5cm. AB =8cm, C = 6cm. 0P makes right angle at P on AB. 0 makes right angle at Q on C. AB C then P = _____cm 1. 7 2. 6 3. 5 4. 4 zeamail2@gmail.com Page 13 APRJC MODEL PAPER 45) Match the following: Column-I (Generation of computers) Column-II (type of circuits) i. First generation ii. Second generation iii. Third generation iv. Fourth generation a. Electronic circuits b. Integrated circuits c. Vacuum tubes d. Transistors 1. i J, ii c, iii b, i: o 2. i c, ii J, iii b, i: o 3. i c, ii J, iii o, i: b 4. i c, ii b, iii J, i: o 46) Two boys are on opposite sides of a tower of 100 m height. They measure the angle of elevation of the top of the tower as 30 and 45 respectively. The distance through which the boys are separated is (Take 3 = 1.732, 2 = 1.414) 1. 273.2 m 2. 346.4 m 3. 241.4 m 4. 282.8 m 47) The medians BE and CF of a ABC intersect at G. Area of GBC is S1 and area of quadrilateral AFGE is S2. Then S1S2 = 1. 1 2. 3. 2/3 4. 3/2 zeamail2@gmail.com Page 14 APRJC MODEL PAPER 48) Match the following: Column-I (polynomial) Column-II (non-factor) i. x3 2x2 x + 2 ii. x3 + x2 4x 4 iii. x3 + 2x2 x 2 iv. x3 x2 4x + 4 a. x + 1 b. x + 2 c. x 2 d. x 1 1. i o, ii b, iii c, i: J 2. i J, ii c, iii b, i: o 3. i b, ii J, iii c, i: o 4. i J, ii b, iii o, i: c 49) A, B, C are three sets of values of x: A: 2,3,7,1,3,2,3 B: 7,5,9,12,5,3,8 C: 4,4,11,7,2,3,4 Which of the following is correct? 1. Mean of A = Mode of C 2. Mean of C = Median of B 3. Median of B = Mode of A 4. Mean, Median and Mode of A are equal 50) The father of co-ordinate geometry is 1. George Counter 2. Gauss 3. Leibnitz 4. Rene Descartes zeamail2@gmail.com Page 15 APRJC MODEL PAPER SECTION-II (PHYSICAL SCIENCE) 51) While measuring the diameter of a lead-shot using a screw gauge, the reading on the pitch scale is found to be 7.5 mm and that on the head scale is 48. If the least count is 0.01 mm and zero error is +0.05 mm. then the diameter of the lead-shot is________ 1. 7.98 mm 2. 7.93 mm 3. 8.03 mm 4. None 52) Which of the following is false? (Take g=10 m/s2) 1. At the centre of Earth, acceleration due to gravity is zero 2. At the poles, acceleration due to gravity is maximum 3. The weight of 400 gm stone is 0.4 kgf. 4. The gravitational force of attraction between two bodies is directly proportional to the sum of their masses 53) The resistance of a brass wire of length 300 m and area of cross section 3.4 10-6m2 is 6 ohms. Then the specific resistance of material of wire is________ ohm-meter 1. 6.8 10-8 2. 6.8 10-9 3. 1.7 10-8 4. 1.7 10-9 54) The acceleration due to gravity on a planet whose mass and radius are half that of the earth is ____ m/s2 (Take acceleration due to gravity on earth = 9.8 m/s2) 1. 9.8 2. 4.9 3. 19.6 4. 2.45 zeamail2@gmail.com Page 16 APRJC MODEL PAPER 55) A stone is thrown vertically up with an initial velocity of 10m/s. The maximum height reached and the time of ascent respectively are (Take g=10m/s2) 1. 10m, 2 sec 2. 5m, 2 sec 3. 5m, 1 sec 4. 10m, 1 sec 56) Choose the incorrect statement. 1. If a car of mass 1200 kg takes a turn of a curved road of radius 180 m with a speed of 6 m/s, then the centripetal force acting on the car is 240 N 2. In a uniform circular motion, if the radius is doubled the centripetal force now required is half as great as before. 3. The angular velocity of a stone moving along a circular path and making 20 revolutions in 10 seconds is approximately 12.57 rad/s 4. The angular velocity of earth about its own axis is n86400 roJ/s 57) Which of the following is the Magic triangle of Ohms law? zeamail2@gmail.com Page 17 APRJC MODEL PAPER 58) A road is banked at an angle corresponding to the velocity (Vo). A car maintains a speed V on this curved road. If V < Vo, then the car 1. Slips towards the centre 2. Skids outside 3. Moves without any deviation 4. Moves back 59) The values of lengths of different pendulums and acceleration due to gravity at different planets are given below. Pendulums Planets L. l = 100 cm M. l = 90 cm N. l = 120 cm P. g = 9.8 m/s2 Q. g = 19.6 m/s2 R. g = 4.9 m/s2 Which of the following combinations will give more time period? 1. Pendulum L, planet P 2. Pendulum N, planet Q 3. Pendulum M, planet R 4. Pendulum N, planet R 60) Which of the following electromagnetic radiation is used in radiography? 1. -rays 2. X-rays 3. Microwaves 4. Radio waves zeamail2@gmail.com Page 18 APRJC MODEL PAPER 61) In a resonating air column experiment with a closed-end tube, first resonance occurs when the length of air column is 10 cm. second resonance occurs at 1. 5 cm 2. 20 cm 3. 30 cm 4. 40 cm 62) A house is fitted with ten lamps of each 60 Watt. If each lamp burns for 5 hours a day on an average, the cost of consumption in a month of 30 days at 80 paise per unit is 1. `.36 2. `.72 3. `.18 4. `.54 63) Distance between a node and the next antinode in a stationary wave is 10 cm. Then the wavelength is 1. 5 cm 2. 40 cm 3. 20 cm 4. 10 cm 64) Which isotope is used to kill cancer cells? 1. Cobalt 2. Sodium 3. Iodine 4. Carbon 65) Newtons corpuscular theory explains the phenomenon of 1. Interference 2. Polarization 3. Diffraction 4. Refraction zeamail2@gmail.com Page 19 APRJC MODEL PAPER 66) A wire of length 10 cm carrying a current 2A is held perpendicular to a uniform magnetic field of induction 2 10-3 wb/m2. The force on the wire is 1. 4 10-3 N 2. 4 10-2 N 3. 4 10-4 N 4. 4 10-5 N 67) For destructive superposition of waves, the phase difference between the waves is 1. 2. /2 3. 2 4. 3/2 68) When the north pole of the magnet is towards the north of earth the null points are found 1. At the centre of the magnet 2. At the poles 3. On the axial line 4. On the equatorial line 69) Which of the following does not form n-type semiconductor? 1. Arsenic 2. Antimony 3. Phosphorus 4. Indium zeamail2@gmail.com Page 20 APRJC MODEL PAPER 70) Two magnetic poles one of which is 9 times as strong as other, exert a force of 81 dyne on one other, when placed 10 cm apart. The pole strengths in CGS units are 1. 30, 270 2. 60, 540 3. 20, 180 4. 10, 90 71) The magnetic moment of a bar magnet is 200 units. If the magnet is cut into two parts of equal size along axial line, then the magnetic moment of each part is _______units. 1. 200 2. 100 3. 50 4. 400 72) Current i in the circuit is 1. 1 A 2. 2 A 3. 3 A 4. 4 A zeamail2@gmail.com Page 21 APRJC MODEL PAPER 73) The pair of isotones among the following is 1. 3114Si, 3215P 2. 136 C, 137 N 3. 2110Nc, 2210Nc 4. 4019K, 4020Co 74) In BCD code, the first 4-bits are called ________ and the remaining 4-bits are called ________. 1. Numeric bits, Zone bits 2. Zone bits, Numeric bits 3. Arithmetic bits, Zone bits 4. Zone bits, Arithmetic bits 75) Match the following: Column-I Column-II i. Ruby laser ii. He-Ne laser iii. iv. A. p-n-p transistor B. n-p-n transistor C. 6328 D. 6943 1. i , ii C, iii A, i: B 2. i , ii C, iii B, i: A 3. i C, ii , iii A, i: B 4. i C, ii , iii B, i: A zeamail2@gmail.com Page 22 APRJC MODEL PAPER 76) The principal quantum number and azimuthal quantum number of last electron in the element with atomic number 24 are 1. 4,1 2. 4,0 3. 3,2 4. 3,1 77) Match the following: Column-I (Quantum numbers) Column-II i. n ii. l iii. m iv. s a. angular momentum of electrons b. energy of orbits c. shape of orbitals d. orientation of sub-shells 1. i o, ii b, iii c, i: J 2. i b, ii c, iii J, i: o 3. i b, ii c, iii o, i: J 4. i J, ii c, iii b, i: o 78) Shapes of CO2 and PCl3 respectively are 1. Angular, Linear 2. Angular, Pyramidal 3. Linear, Pyramidal 4. Linear, Bent 79) Chief component of cooking gas is 1. Butane 2. Ethane 3. Methane 4. Octane zeamail2@gmail.com Page 23 APRJC MODEL PAPER 80) The dative bond in NH4+ molecule is formed 1. By lone pair of electrons from hydrogen shared between nitrogen and proton 2. By lone pair of electrons from nitrogen shared...</p>