BUSINESS MATHEMATICS, LOGICAL REASONING AND STATISTICS – MT 3

NATIONAL MANAGEMENT COLLEGE, THUDUPATHI.

 

PAPER – 3: BUSINESS MATHEMATICS, LOGICAL REASONING AND STATISTICS

Monthly  test 3 (28.11.2022)

 Time Allowed : 1 hour                                               Maximum Marks: 50

 

1)If  log₁₀ 3 =  , log₁₀ 4 =  , then the value of log₁₀ 120 =

1. a) b) ) c) ) d) ) 2

2)   for some   and   , then the value of   is

1. a) 8 b) 6 c) 4 d)  2

3) . if  the ratio of two numbers is 7 : 11.  If 7 is added to each number then the new ratio will be 2 : 3 then the numbers are.

(a) 49, 77 (b) 42, 45  (c) 43,42 (d) 39, 40

4) log _2√2 (512):log_3√2 (324 )  then,

(a) 128 : 81   (b) 2 : 3   (c) 3 : 2  (d) None

5)  Then  the value of

log₅ + log₅ + log₅  + …………..log₅

1. a) 2 b)3 c)5 d) none of these

6) The two numbers are in ratio 3 : 4. The difference between their squares is 28. Find the greater number

. (a) 12 (b) 8  (c) 16 (d) 10

7) In a class there are 30 boys and 12 girls. Determine the ratio of number of boys to girls.

1. a) 2 : 5 b) 3 : 6 c)  5 : 6 d)  5 : 2

8) A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets Rs. 1000 more than D, what is B’s share?

a)Rs. 500   b) Rs. 1500  c)Rs. 2000 d)None of these

9) Find sum of all values of “a” ,

=  log ₇ 2401

1. a) -2 b) -12 c)-18 d) -6

10)   then all x, y, z are greater than 0 , then

1. a)b)
2. c) d)

11) . The ratio of the present age of father to that of son is 7:2. After 10 years their ages will be in the ratio of 9:4. The present ages of the father is

1. 35 years                    b. 40 years c. 30 years                                 d. 25 years

12) Price of each article of type P, Q, and R is Rs. 300, Rs. 180 and Rs. 120 respectively. Suresh buys articles of each type in the ratio 3:2:3 in Rs. 6480. How many articles of type Q did he purchase?

1. 8                       b. 14                                   c. 20                              d. None

13) .If the ratio of present ages of Jeet and Jay is 5:7 and after 6 years the ratio will be 3:4, what is the present age of Jay?

1. 42                    b. 30                           c. 36                      d. None of these

14) The triplicate ratio of 1:2 is?

1. 8:1                 b. 1:8                            c. 2:1                      d. 1:2

15) . The compound ratio of 5:6, 3:2 and 4:5?

1. 12:13           b. 1:4                             c. 1:5                     d. 1:1

16)     value

1. a) 1/6                 b)  1/2                 c) 1/3 d) 1/8

17) . log 144 =

1. a) 2 log 4 + 2 log 2 b) 4 log 2 + 2 log 3
2. c) 3 log 2 + 4 log 3 d) 3 log 2 – 4 log 3

18) For p, q, r ,s > 0  for value of each ratio is

a)1/2   b) 1/3 c)1/4 c) 1/5

19. The mean proportional between 24 and 54 is
20. a) 33 b) 34 c) 35 d) 36

20) . Which of the numbers are not in proportion  ?

1. a)  6 , 8  , 5 , 7 b) 7 , 3 , 14 , 6
2. c) 18 , 27 , 12 , 18 d) 8 , 6 , 12 , 9

log0.01 (10,000) = x; Find the value of x?
(a) 1 (c) – 4	(b) (d)	– 2 2

21)

 

22)  What number is to added each of the ratio 7:9 to equal 15:16 ?

(a) 23 (b) 16 (c) 31 (d) 13

23) .  If  =  =  then z is equal to

1. a)  xy                         b) c) d)

24) . If  2^x -2^x-1 =4  then X^x =

1. a) 7                                b) 3                              c) 27                                              d) 9

25) . Find the value of x, if x (x)^1/2  = (x^1/2)^x

a). 3                            b) 4                              c) 2                                                            d) 6

26) How many number divisible by 5 of 6 digit can be made from the digit 2, 3, 4, 5, 6, 7

(a) 120        (b) 600 (c) 240  (d) none

27) 5 boys and 3 girls are to be seated together such that no two girls are together

(a) 14,400 (b) 2400 (c) 720  (d) None of these

28) Out of 6 Boys & 4 girls, Find the number of ways for selecting 5 member committee in

which there is exactly two girls ?

(a) 120 (b) 1440 (c) 720  (d) 71

29) if  ⁿP₅ :ⁿP₃  is 2:1 than value of n is

(a) 2  (b) -5 (c) -2 (d) 5

30) If  ¹¹C_x =¹¹C_2x-4   if   then the value of ⁷C_x =

(a) 20 (b) 21 (c) 22  (d) 23

31)The number of four letter words can be formed using the letter of the word “DICTIONARY” is

a)5040 b)720 c)90 d)30240

32)The number of the words that can be formed using the letter of “PETROL” such that the words do not have “P” in the first position is,

1. a) 720 b)120 c)600 d)540

33)ⁿP₂ =12 then the value of n is

a)2 b)5 c)4 d)3

34)The number of different ways the letters of the word “DETAIL”  can be arranged in such a way that the vowels can be occupy only the odd position is ,

a)32 b)36 c)48 d)60

35) A person has 4 coins if different denominations. What is the number of different sums of money the person can form?

1. A) 12        B) 15              C) 11             D) 16

36) There are three dice each of them having faces with a number from 1 to 6. These dices are rolled. Find the number of possible outcomes such that at least one of the dice shows the number 2.

1. a) 36 b) 91              c) 81              d) 116

37) If ¹⁰c₃ + 2. ¹⁰c₄ +¹⁰c₅ = ⁿc₅ then the value of n = ________

(a) 10 (b) 11 (c) 12  (d) 13

38) The numbers of parallelograms that can be formed by a set of 6 parallel lines intersected by the another set of 4 parallel lines is ____________:

(a) 360 (b) 90     (c) 180        (d) 45

39) A man has 5 friends’. In how many ways can be invite one or more of his friends to dinner?

(a) 30 (b) 31 (c) 32 (d) 10

40) From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?

a)564 b)645   c)735   d)756

41) Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?             a)210 b)1050 c)25200 d)21400

42) If ⁹P₅ + 5 . ⁹P₄ = ¹⁰P_r . then r =

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

3be drawn from the box, if at least one black ball is to be included in the draw?

a)32 b)48 c)64 d)96

44) An intelligence agency forms a code of two distinct digits selected from 0, 1, 2, …., 9 such that the first digit of the code is nonzero. The code, handwritten on a slip, can however potentially create confusion, when read upside down-for example, the code 91 may appear as 16. How many codes are there for which no such confusion can arise?

1. a) 80 b) 78 c) 71 d) 69

45) If a refrigerator contains 12 cans such that 7 blue cans and 5 red cans. In how many ways can we remove 8 cans so that at least 1 blue can and 1 red can remains in the refrigerator.

1. a) 513 b) 455 c) 627 d) 369

46) How many diagonals a decagon has?

a)45 b)35 c)55 d)65

47) Find the number of ways of selecting 3 books from 8 different mathematics books that a particular book is not included.

a)33 b)39 c)38 d)35

48) There are 10 lamps in a hall and each one of them can be switched on independently. Find the total number of ways in which the hall can be illuminated?

a)10² b)1023 c)2¹⁰ d)2⁹

49) A train is going from Mumbai to Pune and makes 15 stops on the way. 3 persons enter the train after it has started from Mumbai with 3 different tickets. How many different sets of tickets they may have had?

a)¹⁵p₃ b) 3×¹⁵P₃ c)¹⁵C₃ d)¹⁵C₃  / 3

50) 7 persons are to be arranged  at a circular table .If two particular person among  them are not  to be side by side . then the total number of arrangement is

a)480 ways b)440 ways c) 240 ways d ) 420 ways

CLICK TO DOWNLOAD