Centers at Malleshwaram Rajajinagar Yelahanka Mathikere

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1 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 : 6 : 2 (d) 6 : 2 : 3 x = 3y and y = 2/3 of z, z = 3y/2 x : y : z = 3y : y : 3/2y = 6 : 2 : 3 2. If log 4 (x 2 +x) log 4 (x+1) = 2 then the value of x is: (a) 2 (b) 3 (c) 16 (d) 8 Log 4 (x 2 +x) log 4 (x+1) = 2 Log 4 [(x 2 +x)/(x+1)]= 2 x 2 + x = 4 2 x+ 1 using Log m - Log n = Log m/n using Log a m = y, means a y = m x 2 + x = 16(x+1) Now try substituting all options, we get x = If 2 x+y = 2 2x-y = 8 then the respective values of x and y are : (a) 1, 1/2 (b) ½, 1 (c) ½, ½ (d) None of these This can be solved by substituting all options with value of x and value of y. Let's try with option (a) x = 1, y = 1/2 2 x+y = 8, 2 1+1/2 = (2 3 ) 1/2, = 2 1.5, LHS = RHS 4. The value of (a) 0 (b) 1 (c) 5 (d) 60

2 5. The integral part of a logarithm is called, and the decimal part of a logarithm is called (a) Mantissa, Characteristic (b) Characteristic, Mantissa (c) Whole, Decimal (d) None of these In logarithm, first value before decimal is called as characteristic and value after decimal is called as mantissa. Example if Log = , 2 is called as characteristic and is called as mantissa 6. (a) (b) (c) (d) None of these When problem related to series are given, instead of simplifying we can solve as below Substitute n = 1 in all options, we should get the first term. In this case, if we substitute n = 1, we should get log x Try option (a), substitute n = 1, = = = 7. The value of (a) 0 (b) 1 (c) -1 (d) In algebra problems, instead of simplifying, we can solve by assuming numerical value. Assume x = 0, y = 1 and z = 2 8. Let E1, E2 are two linear equations in two variables x and y. (0, 1) is a solution for both the equations E1 & E2. (2, -1) is a solution of equation E1 only and (-2, -1) is a solution of equation E2 only then E1, E2 are : (a) x = 0, y = 1 (b) 2x y = -1, 4x + y = 1 (c) x + y = 1, x y = -1 (d) x + 2y = 2, x + y = 1 This problem also can be solved by substation method. It is given (2, -1) is a solution of equation E1 only. Substitute x = 2 and y = -1 in all options in first equation

3 (a) x = 0 and y = 1, not a correct option (b) Using x = 2 and y = -1 in 2x y = -1, 2(2) (-1) = -1, 5=-1, not a correct option (c) Using x = 2 and y = -1 in x+y = -1, 2-1 = 1 is correct option 9. If difference between the roots of the equation x 2 -kx +8 =0 is 4 then the value of K is: (a) 0 (b) ± 4 (c) ± 8 (d) ± 4 3 x 2 -kx +8 =0, general form of quadratic equation, ax 2 +bx+c=0, on comparison, a = 1, b= -k and c = 8. Product of roots = c/a = 8/1 = 8. Sum of products = -b/a = -(-k)/1 = k Let two roots be m and n. (m-n) 2 = (m+n) 2-4mn 4 2 = k 2 4*8,16 = k 2 32, K 2 = 48, K = ± If a line passes through the midpoint of the line segment joining the points (-3,-4) & (-5,6) and its slope is 4/5 then the equation of the line is: (a) 4x - 5y + 21 = 0 (b) 4x 5y + 11 = 0 (c) 5x 4y + 21 = 0 (d) 5x + 4y + 11 = 0 Mid-point =[ (-3) + (-5), -4+6 ] = (-4,1) 2 2 Straight line form of equation, ax-by+c=0, where x = -4, y = 1 and Slope = 4/5, a=4, b= 5, on substitution we get 4(-4)-5(1) + c = 0, c = = 21, Equation is 4x-5y+21 = If an amount is kept at Simple Interest, it earns Rs.600 in first 2 years but when kept at Compound Interest it earns at interest of Rs.660 for the same period; then the rate of interest and principle amount respectively are: (a) 20%; Rs.1200 (b) 10%; Rs.1200 (c) 20%; Rs.1500 (d) 10%; Rs.1500 Given simple interest for 2 years is Rs 600. Try all options (a) SI = 1200*20%*2 = 480 (b) SI = 1200*10%*2 = 240 (c) SI = 1500*20%*2 = 600 (d) SI = 1500*10%*2 = 300 Hence, correct option is (c) 12. Mr. X bought an electronic item for Rs What would be the future value of the item after two years, if the value is compounded semi-annually at the rate of 22% per annum? (a) Rs (b) Rs (c) Rs (d) Rs

4 Given P = 1000, n = 4 half years, I =22% p.a or 11% for half years Future value = 1000*(1+0.11) 4 = The common region of x + y 6; x + y 3, is for shown by shaded region: (a) Y x+y=6 (b) x+y=6 0 x x+y=3 0 x+y=3 (c) SS x+y=6 0 x x+y=3 (d) None of these Points on the line represents equations, points above the line is greater than and points below the line is lesser than inequality. x+y < 6 represents area below the line. x+y >3 represents above the line. Represented by option (a) 14. There are 10 students in a class, including 3 girls. The number of ways arrange them in a row, when any two girls out of them never come together: (a) 8P3 x 7! (b) 3P3 x 7! (c) 8P3 x 10! (d) None of these When girls are not to be together make arrangements among remaining people with one gap between them. Boys can be arranged in 7! Ways. Between them there are places available to be filled by 3 girls which can be done in 8P3. Now, both boys and girls can be arranged in 8P3*7! ways 15. The maximum number of points of intersection of 10 circles will be: (a) 2 (b) 20 (c) 90 (d) 180 When two circles intersect, maximum number of intersection points are 2, when three circles intersect, number of intersection points can be maximum of 6. In general np2. For 10 circles, maximum number of intersection points = 10P2 = 10 * 9 = 90

5 16. are in AP, then a 2 +b 2 +c 2 are in (a) Arithmetic Progression (b) Geometric Progression (c) Both A.P & G.P (d) None of these are T1, T2 and T3. In AP T3-T2 = T2-T1,,,, a 2 +b 2 +c 2 are in AP 17. In how many ways can a selection of 6 out of 4 teachers and 8 students be done so as to include at least two teachers? (a) 220 (b) 672 (c) 896 (d) 968 Teachers Students Total Available 4 8 Combination1 4C2 = 6 8C4 = 70 70*6 = 420 Combination2 4C3 = 4 8C3 = 56 4*56 = 224 Combination3 4C4 = 1 8C2 = 28 1*28 = 28 Total ways If set A = {x: x/2 Z, 0 x 10}, B = {x : x is one digit prime number} and C = {x : x/3 N, x 12} then A (B C) : (a) ɸ (b) Set A (c) Set B (d) Set C Set A = { 0,2,4,6,8,10} [ because x/2 should belong to Z(integers i. no decimals) ] Set B = {1,3,5,7} because one digit prime number. Set C = { Any number < 12} A = { 0,2,4,6,8,10} B C={1,3,5,7} A (B C) = ɸ, because nothing is common 19. A Geometric Progression consists of 2n terms. If the sum of the terms occupying the odd places is S1 and that of the terms in even places is S2, the common ratio of the progression is: (a) n (b) 2S1 (c) S2/ S1 (d) S1/ S2 Let GP be 1,2,4,8,16,32 Sum of terms occupying odd places = = 21, Sum of terms in even places = = 42 Common Ratio in this example is 2 which is 42/21, hence, in general r = S2/S1

6 20. The domain D and range R of the function f(x) = 2 - x +1 is: (a) D = Real numbers, R = (2, ) (b) D = Integers, R = (0, 2) (c) D = Integers, R = (-, ) (d) D = Real numbers, R = (-, 2] In general Domain contain any number and integers are part of real numbers hence D = Real number, as x increases value of 2 (x+1) decreases tends to -. Maximum value will be 2 when x = Let A be the set of the squares of natural numbers and x A, y A then : (a) x + y A (b) x - y A (c) x/y A (d) xy A Set A = { Squares of natural numbers} = {1,4,9,16,25,36 } Test option (a) x+y, 1+ 4 = 5 doesn t belong to A. Option is incorrect (b) x-y, 1 4 = -3 doesn t belong to A. Option is incorrect (c) x/y, ¼ = 0.25 doesn t belong to A. Option is incorrect (d) x*y = 1*4 = 4 belong to A. Correct option 22. Let f(x) = x 2 if x 0 = αx + β, if x < 0 is continuous at x = 0. Then find value of α and β: (a) α = any real number, β = 0 (b) α = 0, β = 0 (c) β = any real number, α = 0 (d) None of these Continuous at x = 0, LHL = RHL, αx + β = x 2 at x = 0, α0 + β = 0, hence β = 0 and α = any real number 23. = (a) 0 (b) 1 (c) -1 (d) Does not exist Compute LHL and RHL LHL =, RHL =. Hence limits doesn t exist 24. If the Arithmetic Mean of two numbers is 30 and Geometric Mean is 24 then what will be those two numbers? (a) 36 and 24 (b) 30 and 30 (c) 48 and 12 (d) None of these

7 Problem can be solved by trying all options. Compute GM for all options., Hence option ( c ) is the correct answer. 25. Data collected on religion from the census reports are: (a) Primary data (b) Secondary data (c) Sample data (d) (a) or (b) Census report itself is a Primary Data. Any data taken from the Census Report (for example data on religion) is Secondary Data. 26. The SD of first n natural numbers is (a) (b) (c) n/2 (d) None of these This is direct formula derived from concepts of standard deviation 27. If same amount is added to or subtracted from all the value of the individual series then the standard deviation and variance both shall be: (a) Changed (b) Unchanged (c) Same (d) None of these When same amount is added or subtracted, it is called as change of origin. SD and Variance are independent of change of origin. Hence SD and variance remain unchanged 28. If r = 0.6 then the coefficient of non-determination is : (a) 0.4 (b) -0.6 (c) 0.36 (d) 0.64 Co-Efficient of non-determination = 1 r 2 = = = If mean and coefficient of variation of the marks of n students is 20 and 80 respectively. What will be variance? (a) 256 (b) 16 (c) 25 (d) None of these CV = SD/Mean *100, 80 = SD/20*100, SD = 20*80/100, SD = 16, Variance = If the coefficient of correlation between x and y variables is 0.90 then what will be the coefficient of determination: (a) 0.10 (b) 0.81 (c) 0.94 (d) None of these

8 Co-Efficient of determination = r 2 = = The two lines of regression become identical when: (a) r = 1 (b) r = -1 (c) r = 0 (d) (a) or (b) Regression lines become identical when correlation is perfect. Perfect correlation may be positive or negative. Hence it is either r = +1 or r = Two dice are tossed what is the probability that the total is divisible by 3 or 4. (a) 20/36 (b) 21/36 (c) 14/36 (d) None of these Total possible outcomes = 6*6 = 36, Total divisible by 3 or 4 means sum of total may b ={3,4,6,8,9,12}. Favourable outcomes are = {(1,2),(2,1),(1,3),(2,2),(3,1),(1,5)(2,4),(3,3),(4,2),(5,1),(2,6),(3,5),(4,4),(5,3),(6,2),(3,6),(4,5),(5,4),(6,3), (6,6)} =20. Probability = 20/ The regression are as follows Regression equation of X on Y : 6X-2Y=20 Regression equation of Y on X : 64X-45Y=24 What will be the mean of X and Y? (a) X = 8, Y= 6 (b) X = 6, Y = 6 (c) X = 6, Y = 8 (d) X = 8, Y = 8 Regression lines intersect at their means. Solve two simultaneous equations to find point of intersection. This can be solved by substituting values of x and y from options in the equations. Try option (a) x = 8, y = 6 in 6x 2y = 20, 6(8) 2(6) = =36 20 Try option (b) x = 6, y = 6 in 6x 2y = 20, 6(6) 2(6) = =24 20 Try option (c) x = 6, y = 8 in 6x 2y = 20, 6(6) 2(8) = = Correct option 34. If P(A) = 2/3, P(B) = 3/5, P(A U B) = 5/6 then P(A/B ) is: (a) 7/12 (b) 5/12 (c) 1/4 (d) ½ P(A/B`) = P(A B )/P(B`) P(B) = 3/5, P(B`) = 1-3/5 = 2/5 P(A B) = (2/3) + (3/5) (5/6) = (2*10) + (3*6) (5*5) / 30 =13/30 P(A B ) = P(A) P(A B) = 2/3 13/30 = / 30 = 7/30 P(A/B`) = (7/30)/(2/5) = 7*5/(30*2) = 7/12

9 35. If 2 dice are rolled simultaneously then the probability that their sum is neither 3 nor 6 is: (a) 0.5 (b) 0.75 (c) 0.25 (d) 0.80 Total possible outcomes = 6*6 = 36, Sum is 3 or 6, outcomes are {(1,2),(2,1), (1,5)(2,4),(3,3),(4,2),(5,1), } =7. Probability of either sum is 3 or 6 = 7/36. Probability of neither 3 nor 7 = 1-7/36 = 29/36 = In a game, cards are thoroughly shuffled and distributed equally among four players. What is the probability that a specific player gets all the four kings? (a) 52C4 x 48C13/52C11 (b) 4C4 x 48C9/52C13 (c) 13C9 x 39C9/52C13 (d) 4C4 x 39C9 52c13 52 cards when equally distributed, each will get 13 each, total possible events = 52C13 One getting all four kings can be in 4C4 ways remaining 9 can be anything in left over cards=52-4 = 48, favourable out comes = 4C4*48C9/53C For a Poisson variate X, P(X=1)=P(X=2). What is the mean of X? (a) 1 (b) 3/2 (c) 2 (d) 5/2 Probability mass function in Poisson distribution is P(x) = e -µ µ x /x!. If P(x = 1) = P(x=2), then e -µ µ 2 /2! = e -µ µ 1 /1!, µ = A bag contains 4 red and 5 black balls. Another bag contains 5 red, 3 black balls. If one ball is drawn at random from each bag. Then the probability that one red and one black ball drawn is. (a) 12/72 (b) 25/72 (c) 37/72 (d) 13/72 Possibilities, Red from 1 st bag and black from 2 nd bag or red from 2 nd bag and black from 1st bag = (4/9 * 3/8) + (5/8*5/9) = (12/72) + (25/72) = 37/ If Σ p0q0 = 1360, Σ pnq0 = 1900, Σ p0qn = 1344, Σ pnqn = 1880 then the Laspeyre s index number is: (a) 0.71 (b) 1.39 (c) 1.75 (d) None of these Laspeyre s Index number =

10 40. In the year 2010 the monthly salary was Rs.24,000. The consumer price index number was 140 in the year 2010 which rises to 224 in the year If he has to be rightly compensated what additional monthly salary to be paid to him: (a) Rs. 14,400 (b) Rs. 38,400 (c) Rs. 7,200 (d) None of these Year IN Salary ? *224/140 = Increase in salary should be = = Purchasing power of money is: (a) Reciprocal of price index number (c) Unequal to price index number (b) Equal to price index number (d) None of these Index number represents increase of prices. As price increases, value of money decreases. Hence purchasing power of money is reciprocal of price index number. 42. If a discrete random variable follows uniform distribution and assumes only the values 8,9,11,15,18,20. Then P(X 15) is : (a) 1/2 (b) 1/3 (c) 2/3 (d) 2/7 X can take values 8,9,11,15,18,20 implying 6 possibilities. X 15 may take values 8,9,11,15 that is 4 possibilities. Probability = 4/6 = 2/3 43. The normal curve is: (a) Positively skewed (b) Negatively skewed (c) Symmetrical (d) All these Normal curve is bell shaped with one peak at µ, where mean, mode and median coincide. Normal curve is divided into two equal parts by µ. Hence it is unskewed or symmetrical. 44. A sample may be defined as a part of population is selected with a view to representing in all its (a) Units (b) Characteristics (c) Costs (d) Errors Sample is a sub-set of population. Objective of sample is to form an opinion about population with lesser time, expense and at the same time more efficient. Hence. It is about representation of characteristics

11 45. A parameter is a characteristic of: (a) Population (b) Sample (c) Both a) & b) (d) None of the above A statistical measure like mean, SD computed for observations from population is called as parameter. 46. The measure of divergence is as a size of the sample approaches that of the population: (a) More (b) Less (c) Same (d) None of these When sample size is different from population size, difference between values of population and sample is called as divergence. As sample size increases, it considers more number of observations from the population and hence divergence will reduce. 47. If price are changing year by year, then what should be preferred: (a) Fixed base index number (c) Chain base index number (b) Fisher s ideal index number (d) Both (a) and (c) Price Index number represents change in prices in current year as compared to Base Year. Chain index number represents change in price in current year as compared to previous year. When prices are changing year by year, chain index number is preferred 48. then dy/dx = (a) (b) (c) (d) Problem can be solves by using chain rule. Differentiate using power rule then differentiation the variable inside using quotient rule 49. (a) (b) (c) (d) None of these Problem can be solves by using Partial integration. Then apply logarithm integration to obtain the solution

12 50. (a) (b) (c) (d) None of these Problem can be solved by using concept of integration by substitution and later apply concept of definite integral If you found this useful, let us know by sending a message to or an to info@samvitacademy.in If you are in Bangalore and would like to attend our classes for CPT or IPCC, let us know through phone or (details above) and we will ensure that you get the best from our amazingly young and brilliant faculty. We wish you the best! Our next CPT Batch starts in July and IPCC Batch starts in August in Malleshwaram and Rajajinagar Get to know our faculty Gaurav Rajaram - All India Rank Holder in CPT. Cleared CA in his first attempt. Teaches Accounting and Direct Taxes Chinmaya Hegde - All India Rank holder in ALL 3 levels of CA! Teaches Financial Management and Accounting Punarvas Jayakumar - The best teacher for Law in Bangalore and probably even the South of India. Cleared CA in his first shot although he was from a science background Kriti Goel - Amazing at Cost Accounting and Economics, she has been able to achieve tremendous results in her classes. She makes it fun and makes you love her subjects

Please read our disclaimer These questions have been compiled by Samvit Academy ('we') from Online Sources who have in turn compiled the same from students memory as well from our own discussions

13 Please read our disclaimer These questions have been compiled by Samvit Academy ('we') from Online Sources who have in turn compiled the same from students memory as well from our own discussions with students who have written the examination. We cannot give any assurance that the same/similar questions appeared in the examination as it is purely based on memory. Any conclusions that you draw from the above questions and solutions are solely at your risk and we are not responsible for the same.

CPT Solved Scanner (English) : Appendix 71

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