CPT Solved Scanner (English) : Appendix 71

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1 CPT Solved Scanner (English) : Appendix 71 Paper-4: Quantitative Aptitude Chapter-1: Ratio and Proportion, Indices and Logarithm [1] (b) The integral part of a logarithms is called Characteristic and the decimal part of a logarithm is called mantissa. [2] (b) [3] (d) Given x 3y and y z and x : y 3 : 1 and y : z 2 : : : 2 x : y : z 6 : 2 : 3 [4] (c) If log 4 (x 2 + x) - log 4 (x + 1) 2 log 4 2 log 4 2 log 4 x 2 x 4 2 x 16

2 72 CPT Solved Scanner (English) : Appendix [5] (b) 1 Chapter-2: Equations [6] (c) HFTS/TRIAL x + y 1 (1) (E 1 ) x y 1 (2) (E 2 ) Solving these equation we get x 0, y 1 Solution of E 1 (2, 1) is satisfied and solution of E 2 ( 2, 1) is also satisfied. So, option (c) is correct. [7] (a) The mid point of line segment joining the points (-3, -4) and (-5, 6) (-4, 1) Slope (m) 4/5, Points are (-4, 1) The equation of the line passing through one points (x 1, y 1 ) is y - y 1 m(x - x 1 ) y - 1 (x + 4) 5(y - 1) 4x y - 5 4x x - 5y x - 5y [8] (d) Given Q.E x 2 - kx If α and β are the roots of Q.E

3 CPT Solved Scanner (English) : Appendix 73 α + β - b/a - k α + β k (1) α. β α. β α. β 8 (2) Given α - β 4 (3) Adding (1) & (3) α + β k α - β 4 2α k + 4 α in eg. (1) + β k β k - β β Putting the value of α and β in equation (2) 8 (k + 4) (k - 4) 8 4 k k 2 48 k + k + 4

4 74 CPT Solved Scanner (English) : Appendix [9] (a) If 2 x+y 2 2x-y 2 x+y 2 2x-y 2 3/2 2 x+y 2 3/2 and 2 2x y 2 3/2 we get x+y (1) and 2x y (2) Now Adding eq (1) & (2) x+y 2x y 3x 3 x 1 in eq (1) x+y 1+y y 1 Ans: x 1, y Chapter-3: Inequalities [10] (a) The common region required to satisfy above equations is depicted in option (A) as shown in its graph. Chapter-4: Simple and Compound Interest Including Annuity Applications [11] (b) Principal (P) 1000 R 11% T half yearly Future value A P

5 CPT Solved Scanner (English) : Appendix ( ) (1.11) [12] (c) For 2 years S.I. 600 and C.I. 660 S.I. 600 PR PR P (1) C.I. P (200 + R) R R 220 R 20% R 20% in equation (1) P 1500

6 76 CPT Solved Scanner (English) : Appendix Chapter-5: Basic Concepts of Permutations and Combinations [13] (b) Teachers (T) Students (S) 4 8 If taken at least two teacher. It may be following ways (i) 2T and 4S 4 C 2 8 C (ii) 3T and 3S 4 C 3 8 C (iii) 4T and 2S 4 C 4 8 C Total no of ways [14] (a) There are 10 students in the class No. of girls 3 No. of boys 7 B B B B B B B If any two girls never comes together No of ways 8 P 3. 7! [15] (c) The maximum number of points of intersection of n circle n P 2 10 P Chapter-6: Sequence and Series Arithmetic and Geometric Progression [16] (d) Given Series log x + log + log +... n terms First term (a) log x Common difference (d) T 2 T 1 log log x log Sum of n term of A.P. S n [2a + (n 1)d] log

7 CPT Solved Scanner (English) : Appendix 77 [17] (c) Given G.P. series consist of 2n terms a 1 + a 2 + a 3 + a 4 + a 5 + a n term Here S 1 a 1 + a 3 + a n terms a + ar 2 + ar n terms a [1 + r 2 + r n terms] a, 1 S 1 a... (1) and S 2 a 2 + a 4 + a n terms ar + ar 3 + ar n terms ar [1 + r 2 + r n terms] ar... (2)

8 78 CPT Solved Scanner (English) : Appendix equation (2) / equation (1) r Common Ratio [18] (a) If,, are in arithmetic Progression then (b a) (b + a) (c b) (c + b) b 2 a 2 c 2 b 2 b 2 + b 2 c 2 + a 2 2b 2 c 2 + a 2 a 2, b 2, c 2 are in A.P. Chapter-7: Sets, Functions & Relations [19] (a) If A and C A {0, 1, 2, 3, 4, 5} B {x : x is one digit prime number} {2, 3, 5, 7}

9 CPT Solved Scanner (English) : Appendix 79 {1, 2, 3, 4} B C {2, 3} A (B C) {0, 1, 2, 3, 4, 5} {2, 3} {2, 3} [20] (d) Let A be the set of square of Natural No. A {1 2, 2 2,3 2, 4 2,... } A {1, 4, 9, 16,...} If x A, y A then xy A [21] (d) Given function f(x) 2 - [(x + 1)] Domain Real Number and f(x) 2 - [x + 1] y 2 - [x + 1] [x + 1] 2 - y ± (x + 1) 2 - y + ve sign taking - ve sign x y - (x + 1) 2 - y x 2 - y - 1 x y x 1 - y x y So Range [, 2] x y - 3 Domain Real No, Range (, 2) Chapter-8: Limits and Continuity Intuitive Approach [22] (d) For L H L x 2 h x 2, h 0 L H L similarly 1 R h L

10 80 CPT Solved Scanner (English) : Appendix [23] (c) if f(x) 1 Here L H L R H L so function does not exist. is a continuous function, then R.H.L L.H.L Now R.H.L α x + β Puting x 0 α. 0 + β β 0 β 0 So β 0, α is any real Number. Chapter-9: Basic Concepts of Differential and Integral Calculus [24] (c) dx let: t dx dt 3 t. 2dt dx 2dt 2 3 t dt 2

11 CPT Solved Scanner (English) : Appendix 81 [25] (b) Let: x 2 t 2xdx dt xdx + c + c [26] (a) If y y diff w r t. x

12 82 CPT Solved Scanner (English) : Appendix Chapter-10: Statistical Description of Data [27] (b) DATA collected on religion from the census reports are secondary data. Chapter-11: Measures of Central Tendency and Dispersion [28] (a) The S.D. of First n natural Number is S.D.

13 CPT Solved Scanner (English) : Appendix 83 [29] (a) Given No. of observation N 10 Mean 20 c.v. 80 c.v S.D. S.D. 16 Variance (S.D.) 2 (16) [30] (b) If same amount is added to or subtracted from all the values of an individual series then S.D and variance both shall be unchanged. [31] (c) Let two number be a & b A.M 30 a + b 60 (1) G.M 24 ab 576 (2) Solving (1) & (2) we get a 48 and b 12 Chapter-12: Correlation and Regression [32] (c) Given Regression Equations 5x y 22 (1) 64x 45y 24 (2) Multiply by 45 in equation (1) we get 225x 45y 990 (3) equation (3) equation (2) 225x 45y x 45y x 966 x 6

14 84 CPT Solved Scanner (English) : Appendix Puting x 6 in equation (1) 5 6 y y 22 y 8 x 6 y 8 [33] (b) If Coeff. of Correlation (r) 0.90 Coeff. of Determination r 2 (0.90) [34] (d) If r 1 or + 1 then two lines of Regression become Identical. [35] (c) If r 0.6 Then Coeff. of determination r 2 (0.6) Chapter-13: Probability and Expected Value by Mathematical Expectation [36] (b) In a game, cards are thoroughly shuffled and distributed equally among four players. Sample space n(s) 52 C 13 Event (A) a specific player gets all four king n(a) 4 C 4 48 C 9 Probability P(A) 4 48 C 4 C9 52 C13 [37] (c) Require Probability P(one Red from the I st bag and one Black ball from the II nd bag) + P(one Red ball from the II nd bag and one Black ball from the I st bag) P(R 1 B 2 ) + P(R 2 B 1 ) P(R 1 ). P(B 2 ) + P(R 2 ). P(B 1 )

15 CPT Solved Scanner (English) : Appendix [38] (a) If P(A), P(B) and P(A B) then P(A/B')? We know that P(A B) P(A) + P(B) P(A B) + P(A B) P(A B) + P(A/ ) [P(A/B') P(A/ )] [39] (d) If two dice are rolled then Sample space n(s) 36 Event A getting sum is either 3 nor 6' n(a) P(A) 0.80 [40] (a) If two dice are rolled Sample Space n(s) 36 Event A The total sum is divisible by 3 or 4' {(1, 2) (2, 1) (5, 1) (1, 5) (3, 3) (4, 2) (2, 4) (4, 5) (5, 4) (6, 3) (3, 6) (6, 6) (1, 3) (3, 1) (2, 2) (6, 2) (2, 6) (5, 3) (3, 5) (4, 4)}

16 86 CPT Solved Scanner (English) : Appendix n(a) 20 P(A) Chapter-14: Theoretical Distributions [41] (c) Normal curve is symmetrical. [42] (c) For P(m) P( 1) P( 2) m 2 [43] (c) Given data 8, 9, 11, 15, 18, 20 Total No. of data n(s) 6 P(x < 15) Chapter-15: Sampling Theory [44] (b) The measure of divergence is less as the size of sample approaches that of the population. [45] (a) A parameter is characteristic of population. [46] (b) A sample may be defined as a part of population so selected with a view to representing the population in all its characteristics. Chapter-16: Index Numbers [47] (a) Purchasing power of money is the Reciprocal of Price Index Number. [48] (b) P 0 Q , P n Q P 0 Q n 1344, P n Q n 1880 Laspeyre s Index Number 1.39

17 CPT Solved Scanner (English) : Appendix 87 [49] (a) Years Consumer Price index Salary , X x x 38,400 D.A 38,400-24,000 14,400 [50] (c) The suitable Index No. for the comparison of charges in price level of every year is Chain Base Index Number.

18 88 CPT Solved Scanner (English) : Appendix FOR NOTES

19 CPT Solved Scanner (English) : Appendix 89 FOR NOTES

20 90 CPT Solved Scanner (English) : Appendix FOR NOTES

21 CPT Solved Scanner (English) : Appendix 91 FOR NOTES

Centers at Malleshwaram Rajajinagar Yelahanka Mathikere

Centers at Malleshwaram Rajajinagar Yelahanka Mathikere 1. x, y, z together start a business. If x invests 3 times as much as y invests and y invests two third of what z invests, then the ratio of capitals of x, y, z is : (a) 3 : 9 : 2 (b) 6 : 3 : 2 (c) 3 :