CA Business Mathematics Questions
Q1. The income of A and B are in the ratio 3:2 and their expenditure in the ratio 5:3. if each saves Rs. 1500, then B’s income is
a) Rs. 6000
b) Rs. 4500
c) Rs. 3000
d) Rs. 7500
Q2. The ratio between the speeds of two trains is 7:8. If the second train runs 400 Kms. in 5 hours, the speed of the first train is
a) 10 Km/hr
b) 50 Km/hr
c) 70 Km/hr
d) None of these
Q3. Rs 407 are to be divided among A, B and C so that their shares are in the ratio 1/4:1/5:1/6.
The shares of A, B, C are:
a) 165,132,110
b) 165,110,132
c) 132,110,165
d) 110,132,165
Q4. Two numbers are in the ratio 3 : 4; if 6 be added to each terms of the ratio, then the new ratio will be 4 : 5, then the numbers are
a) 14, 20
b) 17, 19
c) 18 and 24
d) None of these
Q5. A dealer mixes rice costing Rs 13.85 per kg with rice costing Rs 15.54 and sell the mixture at Rs 17.60 per kg. So, he earned a profit of 14.6% on his sale price. The proportion in which he
mixes the two qualities of rice is
a) 3:7
b) 5:7
c) 7:9
d) 9:11
Q6. For 3 months, the salary of a person are in the ratio 2:4:5. If the difference between the product of salaries of the 1st 2 months and last 2 months is Rs 48000000, then the salary of the person for the 2nd month will be
a) Rs 4000
b) Rs 6000
c) Rs 8000
d) Rs 12000
Q7. The area of a triangle with vertices (1,3), (5,6) and (-3,4) in terms of square units is
a) 5
b) 3
c) 8
d) 13
Q8. A man starts his job with a certain monthly salary and earns a fixed increment every Yr. if his salary was Rs 1500 after 4 Yr of service and Rs 1800 after 10 Yr of service, what was his starting salary and what is the annual increment in Rs?
a) Rs 1300, Rs 50
b) Rs 1100, Rs 50
c) Rs 1300, Rs 30
d) none
Q9. The centroid of the triangle ABC is at the point (2,3). A and B are the points (5,6) and (-1,4). The coordinates of C are
a) 1,-2
b) 2,-1
c) 1,2
d) 2,3
Q10. If x 3–6x2+11x–6=0 then find the value of (3x–4)
a) 1,2,3
b) -1,2,5
c) -1,3,5
d) 2,3,5
Q11. Area of a rectangular garden is 8000 sq m. ratio in length and breath is 5:4. A path of uniform width runs all round the inside of the garden. if the path occupies 3200 sq m, what is its width?
a) 12 m
b) 6 m
c) 10 m
d) 14 m
Q12. The graph of straight line x=5 will be
a) Intersecting both the axis
b) parallel to Y axis
c) Parallel to X axis
d) None
Q13. If a > 0 and b < 0, it follows that
a) 1/a > 1/b
b) 1/a < 1/b
c) 1/a = 1/b
d) none of these
Q14. A factory manufactures 2 articles x and y. to manufacture article x, certain machine has to be worked for 1.5 Hr and in addition, a crafts man has to wok for 2 Hr. to manufacture article y, certain machine has to be worked for 2.5 Hr and in addition, a crafts man has to wok for 1.5 Hr. in a week, the factory can avail of 80 Hr of machine and 70 Hr of crafts man’s time. Let x units of article x and y units of article y be produced, then the constrains are
a) 1.5x + 2.5y ≥ 80 2x + 1.5y ≤ 70 x ≥ 0 , y ≥ 0
b) 1.5x + 2.5y ≤ 80 2x + 1.5y ≤ 70 x ≥ 0 , y ≥ 0
c) 1.5x + 2.5y ≤ 80 2x + 1.5y ≥ 70 x ≥ 0 , y ≥ 0
d) none of these
Q15. On the average, an experienced person does 7 units of work while a fresh person does 5 units of work daily but the employer has to maintain the output of at least 35 units of work per day. The situation can be expressed as
a) 7x + 5y < 35
b) 7x + 5y ≤ 35
c) 7x + 5y > 35
d) 7x + 5y ≥ 35
Q16. If 3x–4_____4≤512, the solution is
a) {x: 19/18 ≤ x ≥ 29/18}
b) {x: 7/9 ≤ x ≤ 17/9}
c) {x: -29/18 ≤ x ≤ -19/18}
d) None of these
Q17. Inequalities are statements which shows an ________ relationship between any two or more given quantities
a) Direct
b) unequal
c) circular
d) indirect
Q18. A car manufacturing company manufactures car of two types A and B. model A requires 150 men-hours for assembling, 50 men-hours for painting and 10 men-hours for checking and testing. Model B requires 60 men-hours for assembling, 40 men-hours for painting and 20 men-hours for checking and testing. There are available 30000 men-hours for assembling, 13000 men-hours for painting and 5000 men-hours for checking and testing. Express the above situation using linear inequalities. Let the company manufacture x units of type A model of carsand y units of type B model of cars. Then, the inequalities are.
a) 5x+2y ≥ 1000, 5x+4y ≥ 1300, x+2y ≤ 500, x ≥ 0, y ≥ 0
b) 5x+2y ≤ 1000, 5x+4y ≤ 1300, x+2y ≥ 500, x ≥ 0, y ≥ 0
c) 5x+2y ≤ 1000, 5x+4y ≤ 1300, x+2y ≤ 500, x ≥ 0, y ≥ 0
d) 5x+2y = 1000, 5x+4y ≥ 1300, x+2y = 500, x ≥ 0, y ≥ 0
Q19. The number of triangles that can be formed by choosing the vertices from a set of 12 points, seven of which lie on the same straight line is
a) 185
b) 175
c) 115
d) 105
Q20. A boy has 3 library tickets and 8 books of his interest in the library of these 8, he does not
want to borrow mathematics part-II unless mathematics part-I is also borrowed? In how many
ways can he choose the three books to be borrowed?
a) 41
b) 51
c) 61
d) 71
Q21. If 6Pr = 24 x 6Cr, then find r
a) 4
b) 6
c) 2
d) 1
Q22. In a bag there were 5 white, 3 red and 2 black balls.3 balls are drawn at a time. What is the
probability that the 3 balls drawn are white?
a) 1/12
b) 1/24
c) 1/120
d) None of these
Q23. How many members not exceeding 1000 can be made from the digits 1, 2, 3, 4, 5, 6, 7, 8, 9
if repetition is not allowed
a) 364
b) 585
c) 728
d) 819
Q24. 7 books are to be arranged in such a way so that two particular books are always at first and
last place. Final the number of arrangements.
a) 60
b) 120
c) 240
d) 480
Q25. If the simple interest on Rs 1400 for 3 Yrs, is less than the simple interest on Rs 1800 for the
same period by Rs 80, then the rate of interest is
a) 5.67%
b) 6.67%
c) 7.20%
d) 5.00%
Q26. A company may obtain a machine either by leasing it for 5 yr at an annual rent of Rs 2000 or
by purchasing the machine for Rs 8100.if the company can borrow money at 18% p.a, which
alternative is preferable?
a) Leasing
b) Purchasing
c) Can’t say
d) None of these
Q27. A sum of Rs 44000 is divided into 3 parts such that the corresponding interest earned after
2 yr, 3 yr and 6 yr may be equal. If the rates of simple interest are 6%, 8% and 6% p.a. then the
smallest part of the sum will be
a) Rs. 4000
b) Rs. 8000
c) Rs. 10000
d) Rs. 12000
Q28. If the simple interest on Rs. 1400 for 3 Yrs, is less than the simple interest on Rs. 1800 for
the same period by Rs. 80, then the rate of interest is
a) 5.67%
b) 6.67%
c) 7.20%
d) 5.00%
Q29. The SI on a sum of money is 4/9 of the principal and the no. of years is equal to the rate of
interest p.a. Find the rate of interest p.a?
a) 5%
b) 20/3%
c) 22/7%
d) 6%
Q30. Rs. 8000 becomes Rs. 10000 in 2 years at simple interest. The amount that will become Rs.
6875 in 3 years at the same rate of interest is
a) Rs. 4850
b) Rs. 5000
c) Rs. 5500
d) Rs. 5275
Q31. ∑n2 defines
a) n(n+1)(2n+1)/2
b) n(n+1)/2
c) n+1/2
d) none of these
Q32. A contractor who fails to complete a building in a certain specified time is compelled to
forfeit Rs. 200 for the first day of extra time required and thereafter forfeited amount is
increased by Rs 25 for every day. If he loses Rs. 9450, for how many days did he over run the
contract time?
a) 19 days
b) 21 days
c) 23 days
d) 25 days
Q33. If the first term of a G.P exceeds the second term by 2 and the sum to infinity is 50, the
series is:
a) 10, 8, 32/5..........
b) 10, 8, 5/2..........
c) 10, 10/3, 10/9.............
d) none of these
Q34. The 4th term of 3 times the first and the 7th term exceeds the third term by 1. Find the first
term a and the common difference d
a) a = 3, d = 2
b) a = 4, d = 3
c) a = 5, d = 4
d) a = 6d = 5
Q35. If the sum of n terms of an AP be 2n2 + 5n, then its nth term is
a) 4n-2
b) 3n-4
c) 4n+3
d) 3n+4
Q36. The sum of all 2 digit odd numbers is
a) 2475
b) 2575
c) 4950
d) 5049
Q37. In a class of 80 students, 35% students can play only cricket, 45% students can play only
table tennis and the remaining students can play both the games. In all how many students can
play cricket?
a) 55
b) 44
c) 33
d) 22
Q38. Let A = {1, 2, 3} and B = {6, 4, 7} then, the relation R = {(2, 4)(3, 6)} will be
a) Function from A to B
b) Function from B to A
c) Both A and B
d) Not a function
Q39. For a group of 200 persons, 100 are interested in music, 70 in photography and 40 in swimming. Further more 40 are interested in both music and photography, 30 in both music and swimming, 20 in photography and swimming and 10 in all the three. How many are interested in photography but not in music and swimming?
a) 30
b) 15
c) 25
d) 20
Q40. If A = {±2, ±3}, B = {1, 4, 9} and F = {(2, 4),(-2, 4),(3, 9),(-3, 9)} then F is defined as:
a) one to one function from A into B
b) one to one function from A onto B
c) many to one function from A onto B
d) many to one function from A into B
Q41. If A = {1, 2, 3, 4}
B = {2, 4, 6, 8}
f(1) = 2, f(2) = 4, f(3) = 6 and f(4) = 8
f: A→B then f – 1 is
a) {(2,1),(4,2),(6,3),(8,4)}
b) {(1,2),(2,4),(3,6)(4,8)}
c) {(1,4),(2,2),(3,6),(4,8)}
d) none of these
Q42. In a survey of 300 companies, the number of companies using different media-
Newspapers(N), Radio(R) and Television(T) are as follows: n(N)=200, n(R)=100, n(T)=40, n(N∩R) = 50, n(R∩T) = 20, n(N∩T) = 25 and n(N∩R∩T) = 5. Find the number of companies using none ofthese media:
a) 20
b) 30
c) 40
d) 50
Q43. A is mother of D who is father of G. B is grandfather of E and husband of A. D who has only two children is brother of C. A has two children both of same gender. J is aunt of H who is sister of G.
a) J is sister of D
b) J is mother of D
c) J is aunt of D
d) None of these
Q44. What is the relation between C and E?
a) C is brother of E
b) C is father of E
c) C is uncle of E
d) Cannot be determined
Q45. At least how many male members can be predicted by the given relations?
a) 2
b) 3
c) 4
d) 5
Q46. If P + Q means P is the sister of Q, P - Q means P is brother of Q, P*Q means P is daughter of Q. Which of the following shows the relation that K is a uncle of O.
a) O*F-K
b) K*F+O
c) F*K+O
d) None of these
Q47. M and N are sisters. X and Y are brothers. M‟s daughter is X‟s sister. What is N‟s relation to Y?
a) Aunt
b) Sister
c) Mother-in-law
d) Daughter
Q48. A is the uncle of B, who is the daughter of C and C is the daughter – in – law of P. How is A related to P?
a) Brother
b) Son
c) Son - in - law
d) None of these
Q49. Find out the wrong number.
73, 57, 49, 44, 43, 42
a) 73
b) 57
c) 49
d) 44
Q50. 16, 21, ?, 48, 74, 111
a) 31
b) 32
c) 24
d) 25
Q51. Find out the wrong number.
1 1 2 6 24 96 720
a) 720
b) 96
c) 24
d) 6
Q52. 11, ?, 18, 35, 100, 357
a) 13
b) 15
c) 16
d) 17
Q53. Kashmira facing towards south moved straight 8 km and from there turned to her right 90° and travelled 7 km. Then she took a 45° turn to her left and travelled 4 km. Where would she be now with respect to the starting point?
a) South
b) South-west
c) North-east
d) South-east
Q54. A girl leaves from her home. She first walks 30 metres in North–west direction and then 30
metres in South–west direction. Next, she walks 30 metres in South-east direction. Finally, she
turns towards her house. In which direction is she moving?
a) North–East
b) North–West
c) South–East
d) South–East
Q55. Starting from a point S, Mahesh walked 25m towards South. He turned to his left and
walked 50m. He, then again turned to his left and walked 25m. He again turned to his left and
walked 60m and reached a point T. How far Mahesh is from point S and in which direction?
a) 10m, West
b) 25m, North
c) 10m, East
d) 25m, West
Q56. Two buses start from the opposite points of a main road, 150km apart. The first bus runs for
25 km and takes a right turn and then runs for 15km. It then turns left and runs for another
25km and takes the direction back to reach the main road. In the mean time, due to the minor
break down the other bus has run only 35km along the main road. What would be the distance
between the two buses at this point?
a) 65km
b) 80km
c) 75km
d) 85km
Q57. Anoop starts walking towards South. After walking 15m he turns towards North. After
walking 20m, he turns towards East and walks 10m. He, then turns towards South and walks
5m. How far is he from his original position in which direction?
a) 10m, North
b) 10m, South
c) 10m, West
d) 10m, East
Directions (Q. 58-62): Study the following information carefully to answer the given questions:
Eight friends A, B, C, D, E, F, G and H are sitting around a circular table with equal distance between them but not necessarily in the same order. Some of them are facing the centre with some face outside (i.e. opposite to centre). C sits second to the right of F, F faces the centre. Only two people sit between C and B (either form C’s right or C’s left).G sits second to the right of C. H sits to the immediate right of B. G and B face opposite direction. Immediate neighbour of G face the same direction. Only three people sit between D and E. Neither D nor A is an immediate neighbour of F. E sits second to the right of A. Both H and E face a direction opposite to that of C.
Q58. How many persons sit between E and H? (Count from E, anti clockwise)
a) Three
b) Four
c) Five
d) Two
Q59. D sits to the immediate right of
a) A
b) G
c) Both G and H
d) C
Q60. How many persons facing outside?
a) 5
b) 4
c) 3
d) 2
Q61. Which of the following statement is false?
a) C sits immediate left of E
b) B and D faces the same direction
c) G sits opposite to F
d) H sits second to the right of F
Q62. Which of the following statement is true?
a) H and C faces the same direction
b) G is the immediate neighbour of A and C
c) B sits third to the left of G
d) E sits second to the right of A
Direction (Q.63-67): Study the following information carefully and answer the questions given below. Twelve persons are sitting in two parallel rows containing six persons each, in such a way that there is an equal distance between the adjacent persons. In row1 P, Q, R, S, T, U are facing south. In row 2 J, K, L, M, N and O are facing north. J is sitting third to the right of M. Either M or J is sitting at the extreme ends of the row. Q is facing J. U is sitting third to the right of Q. S not sits at the middle position of the row. Nis sitting third to the right of K and is not sitting at the extreme ends of the row. T is sitting immediate right of Q. S is facing K. L is an immediate neighbour of neither N nor J. N is facing R.
Q63. In the row facing south who is sitting at the extreme ends of the row?
a) R,S
b) R,P
c) S,Q
d) R,Q
Q64. Who is sitting immediate right of N?
a) M
b) O
c) L
d) J
CAtestseries.org (Since 2015) – CA Final Inter Foundation online Test Series Page 24
65. Who are the immediate neighbours of U?
a) S and P
b) S and R
c) P and R
d) S and T
Q66. If K is interchanges his position with M, similarly L with N and J with O, then who among the following is facing P?
a) L
b) M
c) J
d) N
Q67. Four of the following five are alike in a certain way based on the given arrangement and so form a group. Which is the one that does not belong to that group?
a) PU
b) RT
c) ML
d) KL
Q68. Time frame to complete a transaction in bank is classified as
a) Parameters
b) Process
c) Mixer
d) Sampler
Q69. Procedures of descriptive statistics and control charts which are used to improve process are classified as
a) Statistical tools
b) Parallel tools
c) Serial tools
d) Behavioral tools
Q70. Model which consists of management philosophy, behavioral tools and statistical methods as key steps towards improvement is considered as
a) Serial improvement process model
b) Behavioral improvement process model
c) Quality improvement process model
d) Statistics improvement process model
Q71. Scale used in statistics which provides difference of proportions as well as magnitude of differences is considered as
a) Satisfactory scale
b) Ratio scale
c) Goodness scale
d) Exponential scale
Q72. “An average is an attempt to find one single figure to describe the whole of figures”. This definition is given by
-a) Croxton and Cowden
b) Simpson and Kafka
c) Clark and Sekkade
d) None of these
Q73. Objectives and significance of statistical averages.
a) To present huge mass of data in a summarized form
b) To facilitate comparison of different sets of data
c) To help in decision making
d) All of above
Q74. Which of the following sentence is/ are wrong in relation to ‘mode’?
a) It can be determined for a distribution with open ends.
b) It is not based on all the observations
c) It is affected by extreme observations
d) All of above
Q75. Consider following observation relating to marks obtained by 10 students in CS Foundation Exam:
210, 202, 207, 222, 276, 201, 246, 212, 285, 312.
Arithmetic mean=?
a) 206
b) 237.3
c) 217.2
d) 216.1
Q76. If the profit of a company remains the same for the last 10 months, then the standard deviation of profits for these 10 months would be?
a) Positive
b) Negative
c) Zero
d) (A) or (C)
Q77. Objectives and significance of dispersion:-
a) To test the reliability of an average
b) To compare the extent of variability in two or more distributions
c) To facilitate the computation of other statistical measures
d) All of the above
Q78. P(B/A) is defined only when-a) A is a sure event
b) B is a sure event
c) A is not an impossible event
d) B is an impossible event
Q79. An experiment is known to be random if the results of the experiment-
a) Cannot be predicted
b) Can be predicted
c) Can be split into further experiments
d) Can be selected at random
Q80. A box contains tickets numbered from 1 to 16. 3 tickets are to be chosen to give 3 prizes.
What is the probability that at least 2 tickets contain a number which is multiple of 4?
a) 19/140
b) 11/240
c) 43/250
d) 9/80
Q81. There are 2 people who are going to take part in race. The probability that the first one will win is 2/7 and that of other winning is 3/5. What is the probability that one of them will win?
a) 14/35
b) 21/35
c) 17/35
d) 19/35
Q82. A speak truth in 60% cases and B in 80% cases. In what percent of cases they likely to contradict each other narrating the same incident?
a) 9/25
b) 7/25
c) 11/25
d) 13/25
Q83. A 4- digit number is formed by the digits 0, 1, 2, 5 and 8 without repetition. Find the probability that the number is divisible by 5.
a) 1/5
b) 2/5
c) 3/5
d) 4/5
Q84. The curve of _________ distribution is uni modal and bell shaped with the highest point over the mean
(a) Poisson
(b) Normal
(c) Binomial
(d) None
Q85. In Normal distribution the probability decreases gradually on either side of the mean but never touches the axis.
(a) True
(b) False
(c) both
(d) None
Q86. The Number of methods for fitting the normal curve is
(a) 1
(b) 2
(c) 3
(d) 4
Q87. ________ distribution has a greater spread than Normal distribution curve
(a) t
(b) Binomial
(c) Poisson
(d) none
Q88. In Normal distribution the quartiles are equidistant from
(a) median
(b) Mode
(c) Mean
(d) None
Q89. In rank correlation coefficient only an increasing/decreasing relationship is required.
(a) false
(b) true
(c) both
(d) none
Q90. Karl Pearson’s coefficient is defined from
(a) ungrouped data
(b) grouped data
(c) both
(d) none.
Q91. “Unemployment index and the purchasing power of the common man“____ Correlation is
(a) positive
(b) negative
(c) zero
(d) none
Q92. ___________ is a relative measure of association between two or more variables.
(a) Coefficient of correlation
(b) Coefficient of regression
(c) both
(d) none
Q93. In linear equations Y = a + bX and X= a + bY ‘a‘ is the
(a) intercept of the line
(b) slope
(c) both
(d) none
Q94. The line X = a + bY represents the regression equation of
(a) Y on X
(b) X onY
(c) both
(d) none
Q95. _______ measure the general changes in the price level from one period to another.
a) Value Index Numbers
b) Quantity Index Numbers
c) Price Index Numbers
d) None of above
Q96. The best average for constructing an index numbers is-
a) Arithmetic Mean
b) Harmonic Mean
c) Geometric Mean
d) None of above
Q97. Index nos. show .......... changes rather than absolute amount of change.
a) Relative
b) Percentage
c) Both (A) and (B)
d) None of above
Q98. The circular test is satisfied by-
a) Fisher's index number
b) Paasche's index number
c) Laspeyre's index number
d) None of above
Q99. The price level of a country in a certain year has increased 25% over the base period. The index number is-
a) 25
b) 125
c) 225
d) 2500
d) 2500
Q100. _____________ requires that the formula for calculating an index number should give consistence results in both the directions, i.e. forward and backward.
a) Circular test
b) Time reversal test
c) Factor reversal test
d) Unit test
Answers
1. A
Explanation:
Let the income of A and B be 3x and 2x
Expenditure of A and B be 5y and 3y
Then, 3x-5y = 1500..........(i)
2x-3y = 1500...........(ii)
By solving i and ii we get
X = 3000 and y = 1500
Hence, B’s income = 2x = 2 x 3000 = Rs6000
2. C
3. A
Explanation:
Here, A:B:C = 1/4:1/5:1/6 = 15:12:10/60 = 15:12:10
A’s share = 407*15/37 = Rs. 165
B’s share = 407*12/37 = Rs. 132
C’s share = 407*10/37 = Rs. 110
4. C
5. A
6. C
7. C
8. A
Explanation:
Let starting salary be x and annual increment be y
Then, x+4y=1500 ........... 1 and x+10y=1800......... 2
By solving 1&2 we get x=1300=starting salary and y=50= annual increment
9. B
Explanation:
Let coordinates of C be (x,y)
centroid = X1+X2+X3/3,Y1+Y2+Y3/3
Then, 5+(-1)+x/3=2,6+4+y/3=3
4+x=6, 10+y=9
x=2, y=-1
Coordinates of C are (2,-1)
10. B
11. C
12. B
13. A
Explanation:
Since a is a positive number therefore its reciprocal i.e. 1/a will also be positive
Since b is a negative number therefore its reciprocal i.e. 1/b will also be negative
So, we can conclude that 1/a is > 1/b
14. B
15. D
Explanation:
Let experience person = x units work per day
Fresh one = y units work per day
Therefore, 7x + 5y ≥ 35
16. B
17. B
18. C
19. A
Explanation:
The number of triangles that can be formed from a set of 12 points = 12C3 since 7 points are on
the same line, therefore no triangle can be formed from these points i.e. number of triangles =
12C3 – 7C3 = 220 – 35 = 185
20. A
Explanation:
There are two cases possible:
CASE 1:- When mathematics part-II is borrowed (i.e it means part-I has also been borrowed)
Number of ways = 6C1 = 6 ways
CASE 2:-when mathematics part-II is not borrowed (i.e.3 3 books are to be selected out of 7)
Number of ways = 7C3 = 35 ways
Hence, total number of ways = 35 + 6 = 41 ways
21. A
Explanation:
6Pr = 24 x 6Cr6! (6 – r)! = 24 x 6!r! x (6 – r)!4! = 24r!r! = 244!r! = 4!r = 4
22. A
Explanation:
No. of ways of drawing 3 balls at a time = 120 ways
No. of ways of drawing 3 white balls out of 5 white balls = 10 ways
Total no .of ways = favourable cases/total no. of cases = 10/129 = 1/12
23. B
Explanation:
Total no. of 2 digits that can be formed = 9 × 8 = 72
Total no. of 3 digits that can be formed = 9 x 8 x 7 = 504
Total no. of 1 digits that can be formed = 9
Total numbers that can be formed = 9 + 72 + 504 = 585
24. C
Explanation:
Since 2 particular books are to be kept always at the first and last place, so if we fix places, the
remaining 5 books can be arranged in 5! Ways
Those, 2 books can also change their places in 2! ways
The total number of arrangements are = 5! X 2! = 120 × 2 = 240 ways
25. B
Explanation:
CASE I P=Rs 1400, T=3Yrs, R = X%
SI = PRT/100 = 1400 x X x 3/100 = 42X
CASE II P = Rs 1800, T = 3Yrs, R = X%
SI = PRT/100 = 1800 x X x 3/100 = 54X
Given, case I – case II = 80
54X – 42X = 80
X = 80/12 = 6.67% = R
26. A
Explanation:
Purchase cost of machine at present =Rs 8100
Present value of the lease rental = a/i[(1 + i)n – 1/(1 + i)n] = 2000/0.18[(1 + 0.18)5 – 1/(1 +
0.18)5] = 11111 x 0.5629 = Rs. 6254.34 (aprox)
27. B
28. B
Explanation:
CASE I P = Rs 1400, T = 3Yrs, R = X%
SI = PRT/100 = 1400 x X x 3/100 = 42X
CASE II P = Rs 1800, T = 3Yrs, R = X%
SI = PRT/100 = 1800 x X x 3/100 = 54X
Given, case I – case II = 80
54X – 42X = 80
X = 80/12 = 6.67% = R
29. B
Explanation:
Given say principal P
SI = 4/9P
T = R
SI = PRT/100
4/9P = P x R x T/100
R = 20/3%
30. B
Explanation:
A=P[1 + rt/100]
10000 = 8000[1 + r x 2/100]
10000/8000 = 100 + 2r/100
2r = 125 - 100
R = 25/2 = 12.5% p.a.
Let the amount which will become Rs 6875 be P. then,
6875 = p[1 + 12.5 x 3/100]
6875 = p[100 + 37.5/100]
p=6875 x 100/1375
p = Rs. 5000
31. A
32. B
Explanation:
Here, a = 200, d = 25 and Sn = 9450 Assume that the contract time is over run for n days. Then
Sn = n2[2a + (n – 1)d]9450 = n2[2 x 200 + (n – 1)25]18900 = n[400 + 25n – 25]18900 = n(375 +
25n)18900 = 375n + 25n225n2 + 375n – 18900 = 0n2 + 15n – 756 = 0 n2 + 36n – 21n – 756 =
0n(n + 36) –21(n +36) = 0(n – 21)(n + 36) = 0n = 21 or n = –36 hence, no. of days can’t be
negative so n = 21 days
33. A
Explanation:
Let the first terms of G.P be a, then its second term = a - 2
Common ratio i.e. r=a-2/a
Sum of infinity=50
a/1 – r = 50
a/1 - (a - 2)/a = 50
a/a – a + 2/a = 50
a = 10
r = 10 -2/10 = 8/10 = 4/5
Therefore, the required series is 10, 8, 32/5........
34. A
35. C
Explanation:
Given, Sn = 2n2 + 5nSn – 1 = 2(n –1)2 +5(n –1)
= 2n2 + 2 – 4n + 5n – 5
= 2n2 + n – 3nth term (Tn) = Sn – Sn – 1
= (2n2 + 5n) – (2n2 + n – 3)
= 4n + 3
36. A
37. B
38. A
Explanation:
A = {1, 2, 3} and B = {6, 4, 7}
Relation R = {(2, 4)(3, 6)} will be function from A to B.
39. D
Explanation:
Let photography = P
Music = M
Swimming = S
n(PUMUS = 200, n(M) = 100, n(P) = 70, n(S) =40
n(M∩P) = 40, n(M∩S) = 30, n(P∩S) = 20
n(P∩M∩S) = 10
n(P∩M’∩S’) = n(P) - n(P∩M) -n(P∩S) + n(P∩M∩S)
= 70 – 40 – 20 + 10 = 80 – 60 = 20
40. C
Explanation:
F: A→B 2→4–2→4 3→9–3→9many one function from A onto B
41. A
Explanation:
If A = {1, 2, 3, 4}
B = {2, 4, 6, 8}
When f: A→B, f = {(1, 2), (2, 4), (3, 6),(4, 8)}f – 1implies f: B→Af – 1 = {(2, 1), (4, 2),(6, 3), (8, 4)}
42. D
Explanation:
n(NURUT) = n(N) + n(R) + n(T) - n(N∩R) - n(N∩T) - n(R∩T) + n(N∩R∩T)
= 200 + 100 + 40 – 50 – 25 – 20 + 5
= 250
No. of companies not using any media
= n(S) - n(NURUT)
= 300 - 250
= 50
43. D
Explanations:
H is sister of G and G is child of D.
So Hand G children of D.
J is aunt of H.
So J can be wife of D‘s brother C or J can be sister of D‘s wife.
In both cases J will be sister in law of D.
44. B
Explanation:
B and A are husband wife, who have 2 children of same sex. A is mother of D who is father of G.
This means both children are males. D is brother of C, so C and D both are sons of A and B. D
also has two children – G and H. If B is grandfather of E then C must be father of E.
45. B
Explanation:
B, C, and D are certainly males H and J are females. Gender of E and G not known.
46. D
47. A
48. B
49. D
Explanation:
73, 57, 49, 44, 43, 42
73 – 57 = 16
57 – 49 = 8
49 – 45 = 4
45 – 43 = 2
43 – 42 = 1
Differences between the consecutive numbers are in Geometric Progression (G.P)
Hence, 44 is the wrong number.
50. A
Explanation:
21 – 16 = 5
31 – 21 = 10
48 – 31 = 17
74 – 48 = 26; 10 – 5 = 5; 17 – 10 = 7; 26 –17 = 9
51. B
Explanation:
1 × 1 = 1
1 × 2 = 2
2 × 3 = 6
6 × 4 = 24
24 × 5 = 120 not 96
120 × 6= 720
96 is wrong
52. A
Explanation:
11 + 12 + 1= 13
13 + 22 + 1= 18
18 + 42 + 1= 35........
53. B
Explanation:
54. A
Explanation:
The movements of the girl are as shown in Fig. (A to B, B to C, C to D, D to A). Clearly, she is
finally moving in the direction DA i.e. North east.
55. A
Explanation:
According to the question, the direction diagram is as follows
S = Starting point, T = Finishing point
AS = BC = 25m
AB = SC = 50m
CT = 60m
Required distance, ST = CT – SC = 60 – 50 =10m
Clearly, at point T, Mahesh is 10 m West from S.
56. A
Explanation:
Required distance = PQ = 150 – (25 + 25 + 35) = 65km
57. D
Explanation:
According to the question, the direction diagram is as follows
A = Original position, E = Finishing point
BC =20, AB = 15m, AC = ED = 5m, CD =AE = 10m
Clearly, at finishing point E, Anoop is 10 m East from original position A.
Directions (Q. 58-62):
58. B
59. C
60. A
61. D
62. D
Direction (Q 63-67):
ROW 1 S P U R T Q Facing south
ROW 2 K L M N O J Facing north
63. C
Explanation:
In the south facing row, S and Q are sitting at the extreme ends of the row.
64. B
Explanation:
O is sitting immediate right of N
65. C
Explanation:
P and R are the immediate neighbours of U.
66. D
Explanation:
L and N are interchanges their position hence, P faces N.
67. D
Explanation:
First person is sitting immediate right of second person in all the option except option d).
68. B
69. A
70. C
71. B
72. C
73. D
74. C
75. B
76. C
77. D
78. C
79. D
80. A
Explanation:
From 1 to 16, there are 4 numbers which are multiple of 4
1st 2 are multiple of 4, and one any other number from (16 - 4) = 12 tickets
4c2*12c1/16c3 = 72/560
2nd all are multiples of 4.
4c3/16c3=4/560
Add both 72/560 + 4/560. = 76/560 = 19/140
81. D
Explanation:
Prob. of 1st winning = 2/7, so not winning
= 1 – 2/7 = 5/7
Prob. of 2nd winning = 3/5, so not winning
= 1 – 3/5 = 2/5
So required prob. = 2/7 * 2/5 + 3/5 * 5/7 = 19/35
82. C
Explanation:
P(A) = 3/5 and P(B) = 4/5. Now they are contradicting means one is telling truth and other
telling the lie. So,
Probability = (3/5)*(1/5) + (2/5)*(4/5)
= 3/25 + 8/25 = 11/25
83. B
Explanation:
Total possibility = 5*4*3*2
Favourable outcomes = 2*4*3*2 (to be divisible by 5 unit digit can be filled with only 0 or 5, so
only two possibilities are there, then the remaining can be filled in 4, 3 and 2 ways respectively)
So probability = 2/5
84. B
85. A
86. B
87. A
88. C
89. B
90. B
91. B
92. A
93. A
94. B
95. C
96. C
97. B
98. A
99. B
100. B