**NATIONAL MANAGEMENT COLLEGE, THUDUPATHI.**

**CA FOUNDATION**

**PAPER – 3: BUSINESS MATHEMATICS, LOGICAL REASONING AND STATISTICS**

**50% REVISION TEST 1 (02.05.2022)**

** ****Time ****Allowed**** ****: 1 hour**** ** ** ****Maximum ****Marks:**** ****50**

**Part A**

**1) A bag contains 4 red, 3 black and 2 white balls . In how many ways 3 balls can be drawn from this bag so that they include at least one black ball ?**

- a) 46 b)64 c)86 d) none of these

**2)In how many ways can the word ‘CHRISTMAS ‘ be arranged so that the letters C and M are never adjacent ?**

a)8! b)9! c)8! d)9!

**3) how many 3 digit odd numbers can be formed from the digits 5,6,7,8,9 if the digits can be repeated**

a)60 b)24 c)75 d)72

**4) A.M and G.M of two positive integers a and b (a<b) are respectively 5 and 4; then a and b are**

a)6,4 b) 2,8 C) 8,2 D) 4,6

**5) There are five roads leading to a town from a village. the number of different ways in which a villager can go to the town and return back is**

- a) 5 b) 10 c) 20 `d) 25

**6) ) Find the sum of the series:2+7+12+…………297.**

- a) 8970 b) 8870 c) 7630 d)9875

**7) A locker in bank has 3 digit lock. Mahesh forgot his password and was trying all possible combinations. He took 6 seconds for each try. The problem was that each digit can be from 0 to 9. How much time will be needed to by Mahesh to try all the combinations?**

a)90 miniutes b) 120 miniutes c) 60 miniutes d) 100 miniutes

**8) If ^{9}P_{5} + 5 . ^{9}P_{4} = ^{10}P_{r} . then r =**

a)2 b) 3 c)5 d)7

**9) A sequence is called ___________ if a _{n+1} = a_{n }+ d**

- a) Arithmatic progression b) geometric progression c) harmonic progression d) special progression

**10) Find the sum of first twenty-five terms of A.P. series whose n ^{th} term**

a)105 b)115 c)125 d)135

**11) If in an A.P ., first term is 20 and 12 ^{th} term is 120 . find sum upto 12^{th } term,**

a)420 b)840 c)140 d)1680

**12)If sum of n terms of an A.P., is then find general term**

- a) n+1 b)2n c)3n d)

**13) In a college of 300 students, every student reads 5 newspapers and every newspaper is read by 60 students. The number of newspapers is ________**

a)35 b)27 c)25 d)30

**14) If A = {1, 2, 3} , B = {1, 4, 6, 9} and R is a relation from A to B defined by ‘x is greater than y’. The range of R is**

a){1, 4, 6, 9} b){4, 6, 9} c){1} D)None of these

**15) Let R be an equivalence relation on a finite set A having n elements. Then the number of ordered pairs in R is**

a)Greater than or equal to n b)Less than n

c)Less than or equal to n d)none

**16) In a class of 100 students, 55 students have passed in Mathematics and 67 students have passed in Physics. Then the number of students who have passed in Physics only is**

a)33 b)45 c)22 d)10

**17)if y = then =**

- a) b) c) d)none of these

**18) If , the equation of a curve Y = f(x) passing through the point (1,0) is given by**

- a) b) c) d) none

**19) dx =**

- a) 1 b)5/2 c)2/5 d)5

**20) The cost of C of a product is a function of the quantity x of the product: C(x) = x ^{2} – 400x + 50. Find the quantity for which the cost is minimum.**

- a) 1000 b) 1500 c)2000 d) 3000

**Part B**

**21) If wall is called window, window is called door, door is called floor, floor is called roof and roof is called ventilator, what will a person stand on ?**

- A) Window B) Wall C) Floor D) Roof

**22)If “A” means “subtraction”, “B” means “division”, “C” means “addition” and “D” means “multiplication”, then**

**330 B 6 A 32 C 45 D 12 = ?**

- A) 525 B) 547 C) 582 D) 563

**23)find odd man out 10, 25, 45, 54, 60, 75, 80**

a)10 b)45 c)54 d) 80

**24) Insert the missing number.**

16, 33, 65, 131, 261, (….)

- A) 523 B) 521 C) 613 D) 721

**25) Find out the wrong number in the given sequence of numbers.**

56, 72, 90, 110, 132, 150

- A) 72 B) 110 C) 132 D) 150

**26) Pointing to Gopi, Nalni says, “I am the daughter of the only son of his grandfather.” How Nalni is related to Gopi?**

- Niece B. Daughter C. Sister D. Mother

**27) B5D means B is the father of D.**

B9D means B is the sister of D.

B4D means B is the brother of D.

B3D means B is the wife of D.

Which of the following means F is the mother of K?

- A) F3M5K B) F5M3K C) F9M4N3K D) F3M5N3K

**28)Pointing to a photograph Lata says, “He is the son of the only son of my grandfather.” How is the man in the photograph related to Lata?**

- Brother B. Uncle C. Cousin D. Data is inadequate

**29) A and B are brothers , C and D are sisters. A’s son is D’s brother. How is B related to C?**

- a) father b )brother c) uncle d) grandfather

**30) If A + B means A is the mother of B; A – B means A is the brother B; A % B means A is the father of B and A x B means A is the sister of B, which of the following shows that P is the maternal uncle of Q?**

- A) Q – N + M x P B) P + S x N – Q C) P – M + N x Q D) Q – S % P

**Part C**

**31) The difference between upper limit and lower limit of a class is called:**

(a) Class interval (b) Class boundaries (c) Mid-value (d) Frequency

**32) Histogram is used for finding**

(a) Mode (b) Mean (c) First Quartile (d) None

**33) Ogive graph is used for finding**

(a) Mean (b) Mode (c) Median (d) None

**34) A National Institude arranged its students data in accordance with different states. This arrangemnt of data is known as**

- a) Temperal data b)geographical data c) ordinal data d)cardinal data-

**35) A student marks in five subject S1, S2 , S3, S4 and S5 are 86, 79, 90,88 and 89 . If we need to draw a Pie chart to represent these marks, then what will be the Central angle for S3?**

a)103.2^{0} b) 75^{0} c)105.6^{0} d)94.8^{0}

**36) Multiple axis line chart is considered when**

- a) There is more than one time series
- b) The units of the variables are different
- c) In any case

d)If there are more than one time series and unit of vairables are different

**37) If avarage mark for a group of 30 girls is 80, a group of boys is 70 and combined average is 76, then how many are in the boy’s group ?**

- a) 21 b)20 c)22 d) 19

**38) If two variables a and b are related by c = ab the G.M of c is equal to**

- a) G.M of a + G.m of b b) G.m of a × G.M of b

c ) G.M of a – G.m of b d) ) G.M of a / G.m of b

**39) for a moderately skewed distribution, the median is twice the mean , then the mode is ________ times the median**

- a) 3 b) 2 c) 2/3 d) 3/2

**40 ) The median value of the set of observations 48,36,72,87,19,66,56,91 is**

- a) 53 b)87 c)61 d) 19

**41) SD of first five consecutive natural numbers is**

(a)√10 (b) √8 (c) √3 (d) √2

**42) Ifσ ^{2}=100 and coefficient of variation = 20% then A.M is**

(a) 60 (b) 70 (c) 80 (d) 50

**43) The sum of mean and SD of a series is a+b, if we add 2 to each observation of the series then the sum of mean and SD is**

(a) a + b + 2 (b) 6 + a + b (c) 4 + a – b (d) a + b + 4

**44) Sum of the squares of deviations is minimum when deviations are taken from**

(a) Mean (b) Median (c) Mode (d) An arbitrary value

**45) P(A) =1 , then the event A is,**

- a) sure event b) impossible event c) not sure event d) none

**46) The chance of getting 7 or 11 in a throw of 2 dice is**

(a) 7/9 (b) 5/9 (c) 2/9 (d) None of these

**47) If the overall percentage of success in an exam is 60, what is the probability that out of a group of 4 students, at least one has passed?**

(a) 0.6525 (b) 0.9744 (c) 0.8704 (d) 0.0256

**48) All possible outcomes of a random experiment forms the**

a)Exhaustive Events b) Sample space c) Both d) None

**49) A bag contains 3 red marbles and 4 blue marbles. Two marbles are drawn at random without replacement. If the first marble drawn is red, what is the probability the second marble is blue?**

a)3/7 b) 1/2 c) 4/7 d) 2/3

**50) If P(A)=5/9, then the odds against the event A is**

- a) 4:5 b) 5:9 c) 4:9 d) 5:4