APRJC model paper

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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 APRJC Model Paper APRJC MODEL PAPER APRJC Hall Ticket Number: Signature: Total marks: 150 Duration: 150 minutes ____________________________________________________________________________________ SECTION-I (MATHEMATICS) 1) Current flows from A to B when the truth value of 1. p (q r) is true 2. p (q r) is true 3. p (q r) is true 4. p (q r) is true 2) 11.3+ 13.5+ 15.7 + 1(2n-1)(2n+1) = 1. 12n+1 2. n2n-1 3. n2n+1 4. 12n-1 zeamail2@gmail.com APRJC Model Paper APRJC MODEL PAPER 3) If ox = b = cz = Jw and 1x + 1 = 1w + 1z, then 1. oc = bJ 2. ob = cJ 3. o +b = c + J 4. o +c = b + J 4) Perimeter of an equilateral triangle is a cm. Then area of the triangle is 1. 34 o2 2. 336o2 3. 32 o2 4. 318o2 5) Marks obtained by 50 students in a 50 marks exam are given below. Find the median of the data. Marks 1-10 11-20 21-30 31-40 41-50 No. of students 3 12 16 14 5 1. 26.25 2. 26.75 3. 25.25 4. 25.75 zeamail2@gmail.com APRJC Model Paper APRJC MODEL PAPER 6) AB and AC are secants of the circle with centre O as shown in figure. Find x in the figure. 1. 5 2. 12 3. 10 4. 6 7) If o = xcos0 + ysin0, b = xsin0 ycos0, then 1. o2 + b2 = x2 +y2 2. o2 b2 = x2 y2 3. o2 + b2 = 2(x2 + y2) 4. o2 b2 = 2(x2 y2) 8) The length of a side of a regular polygon of 24 sides inscribed in a circle of radius 1m is _____m. 1. 2sin15 2. 2sin7.5 3. sin15 4. sin7.5 zeamail2@gmail.com APRJC Model Paper APRJC MODEL PAPER 9) If scc0 = k, then match the following. Column-I Column-II i. sin0 ii. ton0 iii. cos0 a. 1k b. k2 1 c. k2-1k 1. i o, ii b, iii c 2. i c, ii b, iii o 3. i b, ii c, iii o 4. i o, ii c, iii b 10) Equation of the line through a given point (y1, x1) and having a slope m is 1. y y1 = m(x x1) 2. y x1 = m(x y1) 3. y + y1 = m(x + x1) 4. y + x1 = m(x +y1) 11) The statement (p (q) p) is 1. A contradiction 2. A tautology 3. Both contradiction and tautology 4. None 12) Let R R be defined by (x) = 3x 4. Then -1(2012) = 1. 671 2. 672 3. 673 4. 674 zeamail2@gmail.com APRJC Model Paper APRJC MODEL PAPER 13) Which of the following is not a factor of the polynomial x4 +5x3 + 5x2 5x 6? 1. x + 1 2. x + 2 3. x 1 4. x 3 14) Which of the following is a convex region? 1. 2. 3. 4. 15) Number of solution(s) of the inequality |2 x3| 0 1. Zero 2. 1 3. 6 4. Infinite zeamail2@gmail.com APRJC Model Paper APRJC MODEL PAPER 16) Let Sn = 1 + 2 + 3 ++n. Then limn Snn2 = 1. 2. 3. 1 4. None 17) ABC is right angled at C. If p is the length of the perpendicular from C to AB and AB = c, BC = o, CA = b, then p= 1. ucb 2. o +c 3. ubc 4. o +b 18) If ABC ~ PR and A = 32, then B + R = 1. 138 2. 48 3. 148 4. 58 zeamail2@gmail.com APRJC Model Paper APRJC MODEL PAPER 19) AM and BN are tangents of the circle of diameter 6 cm with centre O as shown in figure. If the points M, O, N are collinear and AM=4cm, then OB=? 1. 4 cm 2. 5 cm 3. 6 cm 4. None 20) If (0,0), (1,0), (0,1) are the midpoints of the sides of ABC, then the area of ABC is 1. 1 sq. units 2. 2 sq. units 3. sq. units 4. 4 sq. units 21) For which of the following sets, area of the triangle formed by the line ox by + c = 0 with the coordinate axes is 2 sq. units? 1. o = 2, b = 2, c = 4 2. o = 2, b = 2, c = 2 3. o = 2, b = 1, c = 2 4. o = 4, b = 2, c = 4 zeamail2@gmail.com APRJC Model Paper APRJC MODEL PAPER 22) 4(sin430 + cos460) 3(cos245 sin290) (sin240 + sin250) = 1. 0 2. 1 3. 2 4. 3 23) A ladder 14m long is placed against a vertical wall, so that it makes an angle 60 with the ground. At what height above the ground does the ladder touch the wall? (Take 2 = 1.414, 3 = 1.732) 1. 11.124 m 2. 12.124 m 3. 8.898 m 4. 9.898 m 24) Let A = [o bc J and it is a non-singular matrix. Then A +(oJ bc)A-1 = 1. (o J)I 2. (o + J)I 3. (b c)I 4. (b + c)I zeamail2@gmail.com APRJC Model Paper APRJC MODEL PAPER 25) To solve any problem using computer, what is the sequence of steps to be followed? i. Make a careful and systematic analysis of the problem ii. Write an algorithm for the given problem iii. Draw a flow chart for the algorithm iv. Write a program for the algorithm and feed it into the computer 1. iii ii i: i 2. iii i: ii i 3. i ii iii i: 4. i ii i: iii 26) Following flow chart computes: 1. 1+2+3++100 2. 1+2+3++99 3. 1+2+3++101 4. None zeamail2@gmail.com APRJC Model Paper APRJC MODEL PAPER 27) x5 + 5x3 + 10x + 10x + 5x3 + 1xS is the binomial expansion of 1. (x 1x)5 2. (x + 1x)10 3. (x 1x)10 4. (x + 1x)5 28) limxk(x2012-k2012x2011-k2011) = 1. 20112012k 2. 20112012 1k 3. 20122011k 4. 20122011 1k 29) The root of the equation _x +_x +x +x + = x is 1. 1 2. 2 3. 3 4. 4 zeamail2@gmail.com APRJC Model Paper APRJC MODEL PAPER 30) From the adjacent figure, if C = A, 6CE = CA, EF B, then CPPB = 1. 2 2. 3. 2/3 4. 3/2 31) If sin0 = 1 sin20, then 1 +cos20 + cos40 = 1. 1 2. 2 3. 3 4. 0 zeamail2@gmail.com APRJC Model Paper APRJC MODEL PAPER 32) In the given figure, the radius of inner circle is a, then the radius of each of outer circles is _________________________ 1. (2 1)o 2. (2 + 1)o 3. u2 4. 2o 33) The areas of two similar triangles are 16 sq. cm and 9 sq. cm respectively. If the length of one side of second triangle is 3 cm, then the length of the corresponding side of the first triangle is___ 1. 163 cm 2. 94 cm 3. 4 cm 4. 92 cm 34) If the three points (p,2011), (2011,2012), (2012,2013) lie on a line L, then the slope of line L and value of p respectively are 1. 1, 2010 2. -1, 2011 3. 1, 2011 4. -1, 2010 zeamail2@gmail.com APRJC Model Paper APRJC MODEL PAPER 35) Which of the following is not a pair of perpendicular lines? 1. 4x y + 27 = 0, 2x +8y + 12 2. x = 0, y +2 = 0 3. x y = 2011, x + y = 2012 4. y = 0, y = x +2 36) If [ coso sinosino coso = A, then A-1 is 1. [ coso sinosino coso 2. [coso cososino sino 3. [coso sinosino coso 4. [sino sinocoso coso 37) If scc0 ton0 = 1p, then cos0 = 1. 2pp2+1 2. p2+12p 3. p2+1p2-1 4. p2-1p2+1 38) The range of the data 20,18,37,42,3,15,15,26,12 1. 15 2. 22 3. 39 4. 42 zeamail2@gmail.com APRJC Model Paper APRJC MODEL PAPER 39) The matrix form of the following network: 1. _ A B CA 0 1 1B 2 0 1C 1 2 0_ 2. _ A B CA 0 1 1B 1 0 2C 1 2 0_ 3. _ A B CA 1 1 0B 1 0 2C 2 1 0_ 4. _ A B CA 1 1 1B 2 0 1C 2 1 0_ zeamail2@gmail.com APRJC Model Paper APRJC MODEL PAPER 40) If A = j1 o0 1[, then A2012 = 1. j2012 o0 2012[ 2. j1 2012o0 1 [ 3. j1 o20120 1 [ 4. j1 2012o0 2012 [ 41) The maximum and minimum values of 7cosx 24sinx +5 over R respectively are 1. 30,-30 2. 20,-20 3. 30,-20 4. 20,-30 42) Let Sn = 1 + 1n + 1n2 + 1n3 + wcrc 1n &lt; 1. Then S3 S4 = 1. S2 2. S22 3. 2S2 4. 2S22 43) The charges of boring a well are `.100 for first metre and increase by `.1 for every subsequent metre. The total cost for boring 30 meters. 1. `.3435 2. `.2435 3. `.3345 4. `.2345 zeamail2@gmail.com APRJC Model Paper APRJC MODEL PAPER 44) If scc0 +ton0 = 2012, then scc0 ton0 = 1. 2011 2. 2012 3. 12011 4. 12012 45) The following Venn diagram represents doctors, fathers and men, then _________represents doctors. 1. Circle (i) 2. Square (ii) 3. Rectangle (iii) 4. None 46) If the harmonic mean of a and b is un+1+bn+1un+bn, then value of n is_____ 1. -1 2. 1 3. 0 4. - zeamail2@gmail.com APRJC Model Paper APRJC MODEL PAPER 47) sn40-cos40sn20-cos20 ton20 +scc20 = 1. 0 2. 1 3. 2 4. -1 48) If sin0 = 1517 and 0 0 90, then the value of 15cot0+17sn08tun0+16scc0 =_______ 1. 22/49 2. 23/49 3. 22/47 4. 23/47 49) Mean of a unimodal grouped data is 12.7. Then (3 Median Mode) = 1. 24.4 2. 25.4 3. 12.7 4. 14.4 50) If [o b] j1 20 0[ = [2 5], then a=_____ 1. 2 2. 5/2 3. 3 4. None zeamail2@gmail.com APRJC Model Paper 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, then radius of the lead-shot is _____. 1. 7.98 cm 2. 3.99 cm 3. 0.798 cm 4. 0.399 cm 52) Match the following: Column-I Column-II i. Heliocentric theory ii. Geocentric theory iii. Acceleration due to gravity at a height h above the surface of earth iv. Acceleration due to gravity at a depth h below the surface of earth a. g(1 2hr ) b. Ptolemy c. Copernicus d. g(1 hr) (g = acceleration due to gravity at surface of earth, r = radius of earth) 1. i-c, ii-b, iii-a, iv-d 2. i-b, ii-c, iii-d, iv-a 3. i-b, ii-c, iii-a, iv-d 4. i-c, ii-b, iii-d, iv-a 53) A body is thrown vertically upwards with a velocity 20m/s. The body reached maximum height and came back to ground. The total distance covered and displacement of the body respectively are (Take g=10m/s2, neglect air resistance) 1. 20m, 0m 2. 40m, 0m 3. 20m, 20m 4. 40m, 40m zeamail2@gmail.com APRJC Model Paper APRJC MODEL PAPER 54) An object of mass 2 kg is moving along a circle of radius 6m with a constant speed of 12m/s. The magnitude of centripetal force acting on the object is 1. 24 N 2. 48 N 3. 12 N 4. 96 N 55) The radius of curvature of a road is 2m. It is to be banked so that no friction force is required for car travelling on the road at 2m/s. The angle of banking is _____ 1. tan-1(20) 2. cot-1(10) 3. cot-1(5) 4. None 56) If length of a simple pendulum is made 4 times the original length, then 1. Time period becomes doubled 2. Acceleration due to gravity becomes doubled 3. Both 1 and 2 occur 4. Time period doesnt change 57) The wavelength range of -rays is ______ 1. 0.u1 1uu 2. 0.uu1 1 3. 1u 1uu 4. 1m 100km zeamail2@gmail.com APRJC Model Paper APRJC MODEL PAPER 58) In a stationary wave of wavelength , the distance between a node and the successive antinode is equal to 1. /4 2. /2 3. 3/4 4. 59) In a resonating air-column experiment, a tuning fork of frequency 412 Hz is used. The first and second resonating lengths are found to be 20cm and 60cm respectively. The velocity of sound in air from this experiment is ________ 1. 329.6 cm/s 2. 329.6 m/s 3. 164.8 cm/s 4. 164.8 m/s 60) For diffraction to occur, the dimensions of the obstacle should be 1. Comparable to the wavelength of the incident light 2. Very lesser than wavelength of the incident light 3. Very larger than wavelength of the incident light 4. None 61) Match the following: Column-I (Physical quantity) Column-II (Units) i. Luminous flux ii. Solid angle iii. Luminous intensity iv. Electromotive force a. Steradian b. Candela c. Lumen d. Volt 1. i-a, ii-b, iii-c, iv-d 2. i-a, ii-c, iii-b, iv-d 3. i-c, ii-d, iii-a, iv-b 4. i-c, ii-a, iii-b, iv-d zeamail2@gmail.com APRJC Model Paper APRJC MODEL PAPER 62) LASER is an acronym for 1. Light Amplification by Saturated Emission of Radiation 2. Light Amplification by Simplified Emission of Radio waves 3. Light Amplification by Stimulated Emission of Radiation 4. Light Amplification by Saturated Emission of Radio waves 63) Magnetic field induction at point A on the axial line as shown is given by B=_________ (where M is Magnetic moment, 2l is length of the bar magnet and d is the distance as shown) 1. c4n Md3 N/A-m 2. c2n Md3 N/A-m 3. c4n M(d+I)3 N/A-m 4. c2n M(d+I)3 N/A-m 64) Which of the following is NOT a ferromagnetic substance? 1. Gadolinium 2. Dysprosium 3. Caesium 4. Nickel zeamail2@gmail.com APRJC Model Paper APRJC MODEL PAPER 65) Process of fixing messages to radio frequency carrier waves is called_______ 1. Modulation 2. Demodulation 3. Transmission 4. Detection 66) Which of the following is false statement? 1. A semiconductor is an insulator at 0K 2. Holes are majority charge carriers in p-type semiconductor 3. A p-n junction diode offers a high resistance under reverse bias condition 4. is a symbol of p-n-p transistor 67) In a nuclear reactor, which of the following is/are used to maintain a steady output of energy? 1. Moderator 2. Control rods 3. Fuel elements 4. None zeamail2@gmail.com...</p>