Mock Test: Business Mathematics, Logical Reasoning and Statistics(Paper-3) - Series-II(Dec. 2023) | Mock Tests & Past Year Papers for CA Foundation PDF Download

 Page 1


1 
MOCK TEST PAPER - II 
FOUNDATION COURSE 
PAPER 3: BUSINESS MATHEMATICS, LOGICAL REASONING AND STATISTICS 
Time: 2 Hours       Marks: 100 
Part A: Business Mathematics and Logical Reasoning 
1. If x = 2 +v3 and y = 2 -v3 then value of x
2
 + y
2
 = 
(a)  14  
(b)  4  
(c)  2  
(d)  6 
2.   If (25)
150
 = (25x)
50
; then the value of x will be: 
(a) 5
3
  
(b) 5
4
  
(c) 5
2
  
(d) 5 
3. On solving the equation log t + log (t-3) = 1 we get the value of t as 
(a)  5  
(b)  2  
(c)  3  
(d)  0 
4.  If log 2 = 0.3010 and log 3 = 0.4771, then the value of log 24 is : 
(a)  1.0791 
(b)  1.7323 
(c)  1.3801 
(d)  1.8301 
5.   If four numbers 
1
2
,
1
3
,
1
5
,
1
x
 are proportional then x = 
(a)  
6
5
 
(b)  
5
6
  
(c)  
15
2
 
(d) none 
6.    A box contains 276 coins of 5 rupees, 2 rupees and 1 rupee. The value of each kind of coins are in the 
ratio 2:3:5 respectively. The number of 2 rupees coin is 
(a)  52 
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Page 2


1 
MOCK TEST PAPER - II 
FOUNDATION COURSE 
PAPER 3: BUSINESS MATHEMATICS, LOGICAL REASONING AND STATISTICS 
Time: 2 Hours       Marks: 100 
Part A: Business Mathematics and Logical Reasoning 
1. If x = 2 +v3 and y = 2 -v3 then value of x
2
 + y
2
 = 
(a)  14  
(b)  4  
(c)  2  
(d)  6 
2.   If (25)
150
 = (25x)
50
; then the value of x will be: 
(a) 5
3
  
(b) 5
4
  
(c) 5
2
  
(d) 5 
3. On solving the equation log t + log (t-3) = 1 we get the value of t as 
(a)  5  
(b)  2  
(c)  3  
(d)  0 
4.  If log 2 = 0.3010 and log 3 = 0.4771, then the value of log 24 is : 
(a)  1.0791 
(b)  1.7323 
(c)  1.3801 
(d)  1.8301 
5.   If four numbers 
1
2
,
1
3
,
1
5
,
1
x
 are proportional then x = 
(a)  
6
5
 
(b)  
5
6
  
(c)  
15
2
 
(d) none 
6.    A box contains 276 coins of 5 rupees, 2 rupees and 1 rupee. The value of each kind of coins are in the 
ratio 2:3:5 respectively. The number of 2 rupees coin is 
(a)  52 
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(b)  60 
(c)  76 
(d)  85 
7.   What must be added to each term of the ratio 49 : 68, so that it becomes 3 : 4 ? 
(a)  3 
(b)  5  
(c)  8 
(d)  9 
8.   If u = 3t
4
 + 5t
3
 + 2t
2
+ t + 4, then the value of 
du
dt
 at t = -1 is : 
(a)  0 
(b)  1 
(c)  2 
(d)  5 
9.   if y = e
a log x
 + e
x log a
, then 
dy
dx
= 
(a) ?? ?? + ?? ?? 
(b) ?? ?? ??-1
+ ?? ?? log ?? 
(c) ?? ?? ??-1
+ ?? ?? ??-1
 
(d) ?? ?? + ?? ?? 
10.  ? (2x + 5) dx
4
1
 and the value is: 
(a)  10  
(b)  3  
(c)  30  
(d)  None 
11.   Evaluate ? ??. ?? ?? dx 
(a) ?? ?? (?? + 1 ) + ??  
(b) ?? ?? (?? - 1 ) + ??  
(c) ?? ?? + ??  
(d) ?? - ?? ?? + ?? 
12. Insert 4 A.M.'s between 3 and 18: 
(a)  12, 15, 9, 6   
(b)  6, 9, 12, 15   
(c)  9, 6, 12, 15   
(d)  15, 12, 9, 6  
13. Find the sum to infinity of the following series:  
1 - 1 + 1 - + 1 - 1 + ......................... ? 
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1 
MOCK TEST PAPER - II 
FOUNDATION COURSE 
PAPER 3: BUSINESS MATHEMATICS, LOGICAL REASONING AND STATISTICS 
Time: 2 Hours       Marks: 100 
Part A: Business Mathematics and Logical Reasoning 
1. If x = 2 +v3 and y = 2 -v3 then value of x
2
 + y
2
 = 
(a)  14  
(b)  4  
(c)  2  
(d)  6 
2.   If (25)
150
 = (25x)
50
; then the value of x will be: 
(a) 5
3
  
(b) 5
4
  
(c) 5
2
  
(d) 5 
3. On solving the equation log t + log (t-3) = 1 we get the value of t as 
(a)  5  
(b)  2  
(c)  3  
(d)  0 
4.  If log 2 = 0.3010 and log 3 = 0.4771, then the value of log 24 is : 
(a)  1.0791 
(b)  1.7323 
(c)  1.3801 
(d)  1.8301 
5.   If four numbers 
1
2
,
1
3
,
1
5
,
1
x
 are proportional then x = 
(a)  
6
5
 
(b)  
5
6
  
(c)  
15
2
 
(d) none 
6.    A box contains 276 coins of 5 rupees, 2 rupees and 1 rupee. The value of each kind of coins are in the 
ratio 2:3:5 respectively. The number of 2 rupees coin is 
(a)  52 
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(b)  60 
(c)  76 
(d)  85 
7.   What must be added to each term of the ratio 49 : 68, so that it becomes 3 : 4 ? 
(a)  3 
(b)  5  
(c)  8 
(d)  9 
8.   If u = 3t
4
 + 5t
3
 + 2t
2
+ t + 4, then the value of 
du
dt
 at t = -1 is : 
(a)  0 
(b)  1 
(c)  2 
(d)  5 
9.   if y = e
a log x
 + e
x log a
, then 
dy
dx
= 
(a) ?? ?? + ?? ?? 
(b) ?? ?? ??-1
+ ?? ?? log ?? 
(c) ?? ?? ??-1
+ ?? ?? ??-1
 
(d) ?? ?? + ?? ?? 
10.  ? (2x + 5) dx
4
1
 and the value is: 
(a)  10  
(b)  3  
(c)  30  
(d)  None 
11.   Evaluate ? ??. ?? ?? dx 
(a) ?? ?? (?? + 1 ) + ??  
(b) ?? ?? (?? - 1 ) + ??  
(c) ?? ?? + ??  
(d) ?? - ?? ?? + ?? 
12. Insert 4 A.M.'s between 3 and 18: 
(a)  12, 15, 9, 6   
(b)  6, 9, 12, 15   
(c)  9, 6, 12, 15   
(d)  15, 12, 9, 6  
13. Find the sum to infinity of the following series:  
1 - 1 + 1 - + 1 - 1 + ......................... ? 
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(a)  1   
(b)  ?  
(c)  1/2   
(d)  Does not exist  
14. Find the product of: 
 (243), (243)
1/6
, (243)
1/36
, .......... ? 
(a)  1,024   
(b)  27   
(c)  729   
(d)  243  
15.   The sum of the series 1 + 11 + 111 + ...................... to n terms is __________. 
(a) 
1
27
(10
n+1
- 9n - 10)   
(b) 10
n+1
- 9n - 10 
(c) 
1
81
(10
n+1
- 9n - 10)   
(d) None of these 
16.  The roots of the cubic equation ?? 3
- 7?? + 6 = 0 are: 
(a)  1, 2 and 3  
(b)  1, -2 and 3  
(c)  1, 2 and -3  
(d)  1, -2 and -3 
17. If A = {p, q, r, s}, B = {q, s, t}, C = {m, q, n}. Find C - [A n B] 
(a)  {m, n}  
(b)  {p, q}  
(c)  {r, s}  
(d)  {p, r} 
18.  If arithmetic mean between roots of a quadratic equation is 8 and the geometric mean between them is 
5, the equation is_______. 
(a)  x
2
-
-
16x – 25 = 0   
(b)  x
2
- 16x + 25 = 0 
(c) x
2
 - 16x + 5 = 0   
(d)  None of these. 
19.   A man starts his job with a certain monthly salary and earns a fixed increment every year. If his salary 
was ` 1,500 after 4 years of service and ` 1,800 after 10 years of service, what was his starting salary 
and what is the annual increment in rupees? 
(a)  ` 1,300, ` 50 
(b)  ` 1,100, ` 50 
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1 
MOCK TEST PAPER - II 
FOUNDATION COURSE 
PAPER 3: BUSINESS MATHEMATICS, LOGICAL REASONING AND STATISTICS 
Time: 2 Hours       Marks: 100 
Part A: Business Mathematics and Logical Reasoning 
1. If x = 2 +v3 and y = 2 -v3 then value of x
2
 + y
2
 = 
(a)  14  
(b)  4  
(c)  2  
(d)  6 
2.   If (25)
150
 = (25x)
50
; then the value of x will be: 
(a) 5
3
  
(b) 5
4
  
(c) 5
2
  
(d) 5 
3. On solving the equation log t + log (t-3) = 1 we get the value of t as 
(a)  5  
(b)  2  
(c)  3  
(d)  0 
4.  If log 2 = 0.3010 and log 3 = 0.4771, then the value of log 24 is : 
(a)  1.0791 
(b)  1.7323 
(c)  1.3801 
(d)  1.8301 
5.   If four numbers 
1
2
,
1
3
,
1
5
,
1
x
 are proportional then x = 
(a)  
6
5
 
(b)  
5
6
  
(c)  
15
2
 
(d) none 
6.    A box contains 276 coins of 5 rupees, 2 rupees and 1 rupee. The value of each kind of coins are in the 
ratio 2:3:5 respectively. The number of 2 rupees coin is 
(a)  52 
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(b)  60 
(c)  76 
(d)  85 
7.   What must be added to each term of the ratio 49 : 68, so that it becomes 3 : 4 ? 
(a)  3 
(b)  5  
(c)  8 
(d)  9 
8.   If u = 3t
4
 + 5t
3
 + 2t
2
+ t + 4, then the value of 
du
dt
 at t = -1 is : 
(a)  0 
(b)  1 
(c)  2 
(d)  5 
9.   if y = e
a log x
 + e
x log a
, then 
dy
dx
= 
(a) ?? ?? + ?? ?? 
(b) ?? ?? ??-1
+ ?? ?? log ?? 
(c) ?? ?? ??-1
+ ?? ?? ??-1
 
(d) ?? ?? + ?? ?? 
10.  ? (2x + 5) dx
4
1
 and the value is: 
(a)  10  
(b)  3  
(c)  30  
(d)  None 
11.   Evaluate ? ??. ?? ?? dx 
(a) ?? ?? (?? + 1 ) + ??  
(b) ?? ?? (?? - 1 ) + ??  
(c) ?? ?? + ??  
(d) ?? - ?? ?? + ?? 
12. Insert 4 A.M.'s between 3 and 18: 
(a)  12, 15, 9, 6   
(b)  6, 9, 12, 15   
(c)  9, 6, 12, 15   
(d)  15, 12, 9, 6  
13. Find the sum to infinity of the following series:  
1 - 1 + 1 - + 1 - 1 + ......................... ? 
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(a)  1   
(b)  ?  
(c)  1/2   
(d)  Does not exist  
14. Find the product of: 
 (243), (243)
1/6
, (243)
1/36
, .......... ? 
(a)  1,024   
(b)  27   
(c)  729   
(d)  243  
15.   The sum of the series 1 + 11 + 111 + ...................... to n terms is __________. 
(a) 
1
27
(10
n+1
- 9n - 10)   
(b) 10
n+1
- 9n - 10 
(c) 
1
81
(10
n+1
- 9n - 10)   
(d) None of these 
16.  The roots of the cubic equation ?? 3
- 7?? + 6 = 0 are: 
(a)  1, 2 and 3  
(b)  1, -2 and 3  
(c)  1, 2 and -3  
(d)  1, -2 and -3 
17. If A = {p, q, r, s}, B = {q, s, t}, C = {m, q, n}. Find C - [A n B] 
(a)  {m, n}  
(b)  {p, q}  
(c)  {r, s}  
(d)  {p, r} 
18.  If arithmetic mean between roots of a quadratic equation is 8 and the geometric mean between them is 
5, the equation is_______. 
(a)  x
2
-
-
16x – 25 = 0   
(b)  x
2
- 16x + 25 = 0 
(c) x
2
 - 16x + 5 = 0   
(d)  None of these. 
19.   A man starts his job with a certain monthly salary and earns a fixed increment every year. If his salary 
was ` 1,500 after 4 years of service and ` 1,800 after 10 years of service, what was his starting salary 
and what is the annual increment in rupees? 
(a)  ` 1,300, ` 50 
(b)  ` 1,100, ` 50 
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(c)  ` 1,500, ` 30 
(d)  None 
20. On an average, an experienced person does 5 units of work whereas an unexperienced does one 3 
units work daily but the employer have to maintain the output of at least 30 units of work per day. The 
situation can be expressed as. 
(a) 5x + 3y = 30  
(b) 5x + 3y =3 0  
(c) 5x + 3y = 30  
(d) None of these 
21.  From a group of 200 persons, 100 are interested in music, 70 in photography and 40 in swimming, 
furthermore 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 
22.  If ?? (?? ) = 2?? + 2 and ?? (?? ) = ?? 2
, then the value of fog (4) is: 
(a)  18 
(b)  22 
(c)  34 
(d)  128 
23.  A Supreme Court Bench consists of 5 judges. In how many ways, the bench can give a majority 
decision? 
(a)  10  
(b)  5  
(c)  15  
(d)  16 
24.   The maximum number of points of intersection of 10 circles will be : 
(a)  2 
(b)  20 
(c)  90 
(d)  180 
25.  If 
15
C3r = 
15
Cr+3, then 'r' is equal is  
(a)  2  
(b)  3  
(c)  4  
(d)  5 
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1 
MOCK TEST PAPER - II 
FOUNDATION COURSE 
PAPER 3: BUSINESS MATHEMATICS, LOGICAL REASONING AND STATISTICS 
Time: 2 Hours       Marks: 100 
Part A: Business Mathematics and Logical Reasoning 
1. If x = 2 +v3 and y = 2 -v3 then value of x
2
 + y
2
 = 
(a)  14  
(b)  4  
(c)  2  
(d)  6 
2.   If (25)
150
 = (25x)
50
; then the value of x will be: 
(a) 5
3
  
(b) 5
4
  
(c) 5
2
  
(d) 5 
3. On solving the equation log t + log (t-3) = 1 we get the value of t as 
(a)  5  
(b)  2  
(c)  3  
(d)  0 
4.  If log 2 = 0.3010 and log 3 = 0.4771, then the value of log 24 is : 
(a)  1.0791 
(b)  1.7323 
(c)  1.3801 
(d)  1.8301 
5.   If four numbers 
1
2
,
1
3
,
1
5
,
1
x
 are proportional then x = 
(a)  
6
5
 
(b)  
5
6
  
(c)  
15
2
 
(d) none 
6.    A box contains 276 coins of 5 rupees, 2 rupees and 1 rupee. The value of each kind of coins are in the 
ratio 2:3:5 respectively. The number of 2 rupees coin is 
(a)  52 
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2 
(b)  60 
(c)  76 
(d)  85 
7.   What must be added to each term of the ratio 49 : 68, so that it becomes 3 : 4 ? 
(a)  3 
(b)  5  
(c)  8 
(d)  9 
8.   If u = 3t
4
 + 5t
3
 + 2t
2
+ t + 4, then the value of 
du
dt
 at t = -1 is : 
(a)  0 
(b)  1 
(c)  2 
(d)  5 
9.   if y = e
a log x
 + e
x log a
, then 
dy
dx
= 
(a) ?? ?? + ?? ?? 
(b) ?? ?? ??-1
+ ?? ?? log ?? 
(c) ?? ?? ??-1
+ ?? ?? ??-1
 
(d) ?? ?? + ?? ?? 
10.  ? (2x + 5) dx
4
1
 and the value is: 
(a)  10  
(b)  3  
(c)  30  
(d)  None 
11.   Evaluate ? ??. ?? ?? dx 
(a) ?? ?? (?? + 1 ) + ??  
(b) ?? ?? (?? - 1 ) + ??  
(c) ?? ?? + ??  
(d) ?? - ?? ?? + ?? 
12. Insert 4 A.M.'s between 3 and 18: 
(a)  12, 15, 9, 6   
(b)  6, 9, 12, 15   
(c)  9, 6, 12, 15   
(d)  15, 12, 9, 6  
13. Find the sum to infinity of the following series:  
1 - 1 + 1 - + 1 - 1 + ......................... ? 
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(a)  1   
(b)  ?  
(c)  1/2   
(d)  Does not exist  
14. Find the product of: 
 (243), (243)
1/6
, (243)
1/36
, .......... ? 
(a)  1,024   
(b)  27   
(c)  729   
(d)  243  
15.   The sum of the series 1 + 11 + 111 + ...................... to n terms is __________. 
(a) 
1
27
(10
n+1
- 9n - 10)   
(b) 10
n+1
- 9n - 10 
(c) 
1
81
(10
n+1
- 9n - 10)   
(d) None of these 
16.  The roots of the cubic equation ?? 3
- 7?? + 6 = 0 are: 
(a)  1, 2 and 3  
(b)  1, -2 and 3  
(c)  1, 2 and -3  
(d)  1, -2 and -3 
17. If A = {p, q, r, s}, B = {q, s, t}, C = {m, q, n}. Find C - [A n B] 
(a)  {m, n}  
(b)  {p, q}  
(c)  {r, s}  
(d)  {p, r} 
18.  If arithmetic mean between roots of a quadratic equation is 8 and the geometric mean between them is 
5, the equation is_______. 
(a)  x
2
-
-
16x – 25 = 0   
(b)  x
2
- 16x + 25 = 0 
(c) x
2
 - 16x + 5 = 0   
(d)  None of these. 
19.   A man starts his job with a certain monthly salary and earns a fixed increment every year. If his salary 
was ` 1,500 after 4 years of service and ` 1,800 after 10 years of service, what was his starting salary 
and what is the annual increment in rupees? 
(a)  ` 1,300, ` 50 
(b)  ` 1,100, ` 50 
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(c)  ` 1,500, ` 30 
(d)  None 
20. On an average, an experienced person does 5 units of work whereas an unexperienced does one 3 
units work daily but the employer have to maintain the output of at least 30 units of work per day. The 
situation can be expressed as. 
(a) 5x + 3y = 30  
(b) 5x + 3y =3 0  
(c) 5x + 3y = 30  
(d) None of these 
21.  From a group of 200 persons, 100 are interested in music, 70 in photography and 40 in swimming, 
furthermore 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 
22.  If ?? (?? ) = 2?? + 2 and ?? (?? ) = ?? 2
, then the value of fog (4) is: 
(a)  18 
(b)  22 
(c)  34 
(d)  128 
23.  A Supreme Court Bench consists of 5 judges. In how many ways, the bench can give a majority 
decision? 
(a)  10  
(b)  5  
(c)  15  
(d)  16 
24.   The maximum number of points of intersection of 10 circles will be : 
(a)  2 
(b)  20 
(c)  90 
(d)  180 
25.  If 
15
C3r = 
15
Cr+3, then 'r' is equal is  
(a)  2  
(b)  3  
(c)  4  
(d)  5 
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5 
26. There are 5 books on English, 4 Books on Tamil and 3 books on Hindi. In how many ways can these 
books be placed on a shelf if the books on the same subjects are to be together? 
(a)  1,36,800 
(b)  1,83,600 
(c)  1,03,680 
(d)  1,63,800 
27. The simple interest on `600 for 9 months is `27. Find the interest rate. 
(a)  6% 
(b) 12% 
(c)  2.2 % 
(d) None of these 
28.  Miss Liza lent ` 4,000 in such a way that some amount was given to Mr. A at 3% p.a. S.I. and rest 
amount to was given to B at 5% p.a. S.I., the annual interest from both is ` 144, Find the amount lent to 
Mr. A 
(a)  ` 2,800 
(b)  ` 1,200 
(c)  ` 2,500 
(d)  None 
29. A certain sum of money was put at S.I. for 2.5 years at a certain rate of S.I. p.a. Had it been put at 4% 
higher rate, it would have fetched ` 500 more. Find the sum of money. 
(a)  ` 4000 
(b)  ` 5000 
(c)  ` 6000 
(d)  None 
30. ` 1,25,000 is borrowed at compound interest at the rate of 2% for the 1st year, 3% for the second year 
and 4% for the 3rd year. Find the amount to be paid after 3 years. 
(a)  ` 125678 
(b)  ` 136587 
(c)  ` 163578 
(d)  ` 136578 
31. If the Compound Interest on a certain sum of money for 2 years at 4% p.a. be `510, then its simple 
Interest (S.I) of same time at same rate of interest is 
(a)  `500 
(b) `510 
(c) `450 
(d)  None 
32. How long will it take for a principal to double if money is worth 12% compounded monthly? 
(a) 4.25 years. 
(b) 5.81 years 
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