NATIONAL MANAGEMENT COLLEGE, THUDUPATHI.
PAPER – 3: BUSINESS MATHEMATICS, LOGICAL REASONING AND STATISTICS
Monthly test 4 (24.12.2022)
Time Allowed : 1 hour Maximum Marks: 50
1)6 men and 8 women can do as much work in a given time as 3 men and 13 women. The capacities of a man and a woman are in the ratio
- 3:8 b. 3:5 c. 5:3 d. 5:8
2) In the first four papers each of 100 marks, Rishi got 95, 72, 73, 83 marks. If he wants an average of greater than or equal to 75 marks and less than 80 marks, find the range of marks he should score in the fifth paper .
A.52 ≤ × < 77 B.73 ≤ × < 100 C.25 ≤ × < 75 D.75 ≤ × < 80
3) Inequations involved in the given region are___________
- a) 2x+3y>6 b) 2x+3y<6 c) 2x+3y≥6 d) 2x+3y≤6
4) If , then:
- a) b) c) d)
5)
is equal to
- a) 1 b)3/2 c) 0 d) 3
6)The value of
a)725 b) 5 c) 6 d) 3125
7) A mixture contains alcohol and water in the ratio 4 : 3. If 5 liters of water is added to the mixture, the ratio becomes 4: 5. Find the quantity of alcohol in the given mixture.
- a) 10 b) 12 c) 15 d) 18
8) There are three numbers such that one number is 20% more than a third number and the second number is 50% more than a first number. The ratio of two numbers is?
- 2 : 3 B. 3: 4 C. 4: 6 D. 3: 2
9) If 0.75 : x :: 5 : 8, then x is equal to:
A)1.12 B)1.2 C)1.25 D)1.30
10) A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. Find the speed of the train.
- a) 30 km/hr (b) 40 km/hr (c) 50 km/hr (d) 60 km/hr
11) The quadratic equation x2 + 7x – 60 has
(a) two equal roots (b) two real and unequal roots
(b) no real roots (d) two equal complex roots
12) The maximum number of roots for a quadratic equation is equal to
(a) 1 (b) 2 (c) 3 (d) 4
13) compute the net present value or NPV for 3 years projects costing Rs.28000 with revenue generation expectancy of Rs. 8000 for year 1 , Rs. 12000 for year2 , and Rs.17,000 for year 3 with 3% as applicable discount rate ,
- a) Rs.6635 b) Rs.6653 c) Rs.6356 d) Rs.3460
14) The value of log(13 + 23 + 33 +………..n3 ) is equal to:
(a)3 log 1 + 3 log 2 + ….. + 3 log n (b)2 log n + 2 log (n + 1) – 2 log 2
(c)log n + log (n + 1) + log (2n + 1) – log 6 (d)1
15) . Roots of equation 2x2 + 3x + 7 = 0 are α and β. The value of αβ-1 + βα-1 is
(a)2 (b) 7/2 (c)3/7 (d) -19/14
16) By mistake a clerk, calculated the simple interest on principal for 5 months at 6.5% p.a. instead of 6 months at 5.5% p.a. If the error in calculation was Rs 25.40. The original sum of principal was______
(a)Rs 60, 690 (b)Rs 60,960 (c) Rs 90, 660 (d) Rs 90,690
17) In what will a sum of money double its y at 6.25% p.a simple interest?
(a)5 years (b)8 years (c) 12 years (d) 16 years
18) The partners A and B together lent Rs 3,903 at 4% per annum interest compounded annually. After a span of 7 years, A gets the same amount as B gets after 9 years. The share of A in the sum of Rs 3,903 would have been:
(a)Rs 1,875 (b) Rs 2,028 (c)Rs 2,280 (d) Rs 2,820
19) The future value of an annuity of Rs 1,000 made annually for 5 years at the interest of 14% compounded annually is:
(a)Rs 5,610 (b)Rs 6,610 c) Rs 6,160 (d) Rs 5,160
20) Suppose your parent decides to open a PPF (Public Provident Fund) account in a bank towards your name with Rs 10,000 every year starting from today for next 15 years. When you receive and get 8.5% per annum interest rate compounded annually. What is the present value of this annuity?
(a)83,042 (b)1,66,084 (c) 93,042 (d) 8,30,423
21) In how many years will a sum of money become four times at 12% p.a simple interest?
(a)18 years (b)21 years (c) 25 years (d) 28 years
22) Find the number of arrangements of 5 things taken out of 12 things, in which one particular thing must always be included.
(a)39,000 (b)37,600 (c) 39,600 (d) 36,000
23) There are 5 books on English, 4 books on Tamil and 3 books on Hindi. In how many ways can these books be placed in a shelf if the books on the same subjects are to be together?
(a)1,36,800 (b) 1,03,680 (c)1,83,600 (d) 1,63,800
24)
- a) 6 b) 7 c) 8 d) 9
25) The graph of linear inequalities 7x+9y ≤63, x+y ≥1,0 ≤x ≤6 and
(a) BCDB and DEFD (b) Unbounded (c) HFGH (d) ABDFHKA
26) A machine is depreciated at the rate of 20% on reducing balance. The original cost of the machine was Rs. 1,00,000 and its ultimate scrap value was Rs. 30,000. The effective life of the machine is
(a) 4.5 years (appx.) (b) 5.4 years (appx.) (c) 5 years (appx.) (d) none of these
26) In an examination paper, there are two groups each containing 4 questions. A candidate is required to attempt 5 questions but not more than 3 questions from any group. In how many ways can 5 questions be selected?
- a) 24 b) 48 c) 56 d0 96
27) In how many ways can 5 different toys be packed in 3 identical boxes such that no box is empty, if any of the boxes may hold all of the toys?
- a) 20 b) 25 c) 30 d) 30
28) If |x – 2| + |x – 3| = 7 then, ‘x’ will be equal to
(a)6 (b) 6 and -1 (c)-1 (d) none of the above
29) The difference between compound and simple interest on a certain sum of money for 2 years at 4% p.a is Rs 1. The sum (in Rs) is:
(a)625 (b)630 (c) 640 (d) 635
30) A certain sum of money was invested at simple rate of interest for three years. If the same has been invested at a rate that was seven percent higher, the interest amount would have been Rs 882 more. The amount of sum invested is:
(a)Rs 12,600 (b)Rs 6,800 (c) Rs 4,200 (d) Rs 2,800
31) Let a and b be roots of x2 – 3x + p = 0 and let c and d be the roots of x2 – 12x + q = 0, where a, b, c, d form an increasing G.P. Then the ratio of (q + p) : (q – p) is equal to
(a) 8 : 7 (b) 11 : 10 (c) 17 : 15 (d) None of these
32) ) In an examination there are three multiple choice questions and each question has 4 choices. The number of ways in which a student can fail to get all answer correct is
a)11 b) 27 c) 12 d) 63
33) A committee of 5 members is to be formed by selecting out of 4 men and 5 women. In how many different ways the committee can be formed if it should have at least 1 man?
A)115 B) 120 C) 125 D) 140
34) There are six teachers. Out of them two are primary teachers and two are secondary teachers. They are to stand in a row, so as the primary teachers, middle teachers and secondary teachers are always in a set. The number of ways in which they can do so, is
- a) 52 b) 48 c) 37 d) none of these
35) What is the nature of relation R, if R is defined as R = {(x, y) : 2x + y = 41, x, y = N}?
- a) Reflexive b) transitive c) symmetric d) none of these
36) A certain ball when dropped to the ground rebounds to 4/5th of the height from which it falls; it is dropped from a height of 100 meters find the total distance it travels before finally coming to rest :
- a) 600m b) 700m c) 900m d) 200m
37) If X = 1 + , Y = 1 + find XY
- a) 2 b) 1 c) 8/9 d) ½
38) A code word is to consist of two English alphabets followed by two distinct numbers between 1 and 9 . How many such code words are there?
- a) 6,15,800 b) 46,800 c) 7,19,500 d) 4,10,800
39) Given P (7,K) =60 P(7,K-3) then
- a) k = 9 b) k = 8 c) k = 5 d) k = 0
40) 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
41) ) Let A = {1, 2, 3} and consider the relation R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1, 3)}. Then R is
a.symmetric and transitive b.reflexive but not transitive
c.reflexive but not symmetric d.neither symmetric, nor transitive
42) Let R = { ( 3, 3 ) ( 6, 6 ) ( ( 9, 9 ) ( 12, 12 ), ( 6, 12 ) ( 3, 9 ) ( 3, 12 ), ( 3, 6 ) } be a relation on the setA = { 3, 6, 9, 12 }. The relation is
( a ) reflexive and transitive ( b ) reflexive only
( c ) an equivalence relation ( d ) reflexive and symmetric only
43) If f(x) = x3 – (1/x3), then f(x) + f(1/x) is equal to
(a) 2x3 (b) 2/x3 (c) 0 (d) 1
44) 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!
45) 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
- If n(A× B) = 6 and A = {1, 3} then n(B) is
A.)1 B)2 C)3 D)6
47) ) If f (x) = 2x + h then find f(x+h) – 2f(x)
a)h -2x b)2x-h c)2x+h d) none of these
48) Find the root of the equations. if and
- a) 2,1 b) -2,1 c)1,-2 d)1,2
49) The sum of n terms of an A.P is 3n2 +5n . The series is
- a) 8,14,20,26,…. b) 8,22 , 42,68,….. c)22,68,114,… d)8,14,28,44,……
50) 2+ 2 = ______
- A) 2 B)3 C) 4 D) NONE OF THESE
