# 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.

### Text of APRJC model paper

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 < 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

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