MOCK CAT SECTION – A 1. If m2 CAT Notes | EduRev

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CAT : MOCK CAT SECTION – A 1. If m2 CAT Notes | EduRev

 Page 1


MOCK CAT 
SECTION – A 
1. If m
2
a
2
 + (n
2
 + 1) b
2
 + c
2
 = 2b(mna – c), then which of the following statement(s) is/are necessarily true?
I. ma = nb
II. ma = – nc
III. ma = nc
(1) I only (2) only II and III (3) Only I and II (4) None of these  
2. In the adjacent figure ABCDEF is a regular hexagon. Find the
ratio of the radius of C
large
 to that of radius of C
small
.
(1)
1 2
1 2
-
+
  (2) 
3 2
3 2
-
+
(3) 
1
2
(4) Can’t say 
Directions for questions 3 – 4: Refer to the following data for the following questions. 
There are 4 cities A, B, C & D. There can be two types of routes between any two cities. One is a direct one 
while the other one indirect. A, B & C all have direct routes between them. While city D is connected only to A 
& C with only one road to each. There are a total of 18 routes between A & C, 27 routes between A & B and 
22 routes between B & C. 
3. How many direct roads are there between A & B?
(1) 4    (2)3 (3) 6  (4) 2 
4. How many direct roads are there between B & C?
(1) 4    (2)3 (3) 5  (4) 1 
5. On a certain pasture the grass grows at on even rate. It is known that 40 cows can graze on it for 40
days before the grass is exhausted, but 30 cows can graze there for as long as 60 days. How many
days would the pasture last if 20 cows were to graze on it.
(1) 90 days    (2) 80 days   (3) 100 days   (4) 120 days
Directions for questions 6 – 8: Refer to the following data for the following questions. 
A polynomial of the from a
1
1
n
x
 + a
2
2
n
x
 + ……. + a
i
i
n
x
 + …….. + a
k
k
n
x
 where n
1
 > n
2
 > …… > n
k
 and a
1
 ? 0 
and 0 = I < k is represented by the sequence (a
1
, n
1
, a
2
, n
2
, a
3
, n
3
, ….., a
k
, n
k
) 
6. The value of (3, 5, 2, 2, 4, 1) + (1, 5, 2, 4, 5, 1) is
(1) (3, 5, 2, 4, 2, 2, 9, 1) (2) (4, 5, 2, 4, 2, 3, 3, 2, 9, 1) 
(3) (4, 5, 2, 3, 5, 1) (4) None of these  
7. The value of (4, 2, 6, 1, 5, 0) × (1, 1, 1, 0) is
(1) (4, 3, 6, 1, 5, 0) (2) (4, 3, 6, 2, 5, 1) 
(3) (4, 3, 10, 2, 11, 1, 5, 0) (4) None of these  
•
A B 
F
D E
C
C
large
C
small
Page 2


MOCK CAT 
SECTION – A 
1. If m
2
a
2
 + (n
2
 + 1) b
2
 + c
2
 = 2b(mna – c), then which of the following statement(s) is/are necessarily true?
I. ma = nb
II. ma = – nc
III. ma = nc
(1) I only (2) only II and III (3) Only I and II (4) None of these  
2. In the adjacent figure ABCDEF is a regular hexagon. Find the
ratio of the radius of C
large
 to that of radius of C
small
.
(1)
1 2
1 2
-
+
  (2) 
3 2
3 2
-
+
(3) 
1
2
(4) Can’t say 
Directions for questions 3 – 4: Refer to the following data for the following questions. 
There are 4 cities A, B, C & D. There can be two types of routes between any two cities. One is a direct one 
while the other one indirect. A, B & C all have direct routes between them. While city D is connected only to A 
& C with only one road to each. There are a total of 18 routes between A & C, 27 routes between A & B and 
22 routes between B & C. 
3. How many direct roads are there between A & B?
(1) 4    (2)3 (3) 6  (4) 2 
4. How many direct roads are there between B & C?
(1) 4    (2)3 (3) 5  (4) 1 
5. On a certain pasture the grass grows at on even rate. It is known that 40 cows can graze on it for 40
days before the grass is exhausted, but 30 cows can graze there for as long as 60 days. How many
days would the pasture last if 20 cows were to graze on it.
(1) 90 days    (2) 80 days   (3) 100 days   (4) 120 days
Directions for questions 6 – 8: Refer to the following data for the following questions. 
A polynomial of the from a
1
1
n
x
 + a
2
2
n
x
 + ……. + a
i
i
n
x
 + …….. + a
k
k
n
x
 where n
1
 > n
2
 > …… > n
k
 and a
1
 ? 0 
and 0 = I < k is represented by the sequence (a
1
, n
1
, a
2
, n
2
, a
3
, n
3
, ….., a
k
, n
k
) 
6. The value of (3, 5, 2, 2, 4, 1) + (1, 5, 2, 4, 5, 1) is
(1) (3, 5, 2, 4, 2, 2, 9, 1) (2) (4, 5, 2, 4, 2, 3, 3, 2, 9, 1) 
(3) (4, 5, 2, 3, 5, 1) (4) None of these  
7. The value of (4, 2, 6, 1, 5, 0) × (1, 1, 1, 0) is
(1) (4, 3, 6, 1, 5, 0) (2) (4, 3, 6, 2, 5, 1) 
(3) (4, 3, 10, 2, 11, 1, 5, 0) (4) None of these  
•
A B 
F
D E
C
C
large
C
small
8. If (1, 2, 0) × y = (1, 2, 4, 1, 4, 0) and (1, 1, 2, 0) ? 0, then y =
(1) (1, 1, 2, 0)  (2) (1, 1, 4, 0) (3) (1, 2, 2, 1) (4) None of these  
9. For some digit ‘a’ we have 0.a25a25a25 ... =
810
K
, where K is a positive integer. Find the hundred place 
of K.
(1) 5    (2)7 (3) 9  (4) 3 
10. M is the largest multiple of 8 which has no two digits the same. What is remainder when M is divided by
1000?
(1) 240   (2) 312   (3) 120   (4) 100
11. At the Bus-stand, I noted that most of the buses had Blue number plates. Half the buses with White
plates moved off on the tour. After this the ratio of Blue to White is 12 : 1. Within an hour, 2 more Buses
with White number plates started out. Now the present ratio of Blue to White becomes 20 : 1. Now
guess at this stage how many buses with Blue number plates are there?
(1) 50    (2) 60    (3) 75    (4)90
12. According to the positions of minute hand & hour hand, it is now a certain number of minutes past eight
O’clock but it was six times as many minutes past seven O’clock 15 minutes ago. So guess what is the
time now?
(1) 8 : 07   (2) 8 : 09   (3) 8 : 45   (4) None of these
13. Last year my father organized my birthday party. He distributed chocolates to all the children & trying to
ensure each received an equal amount. But when we counted & found that each had 18 except one
who had only 12. I calculated that if the number of children was subtracted from the total number of
chocolates, it would equal to 1014. So guess how many children came in my birthday party?
 (1) 17    (2) 55    (3) 60    (4)65
14. A shopkeeper spent money in three equal parts in buying Pants, shirts & T-shirts. Each pant cost Rs.10
more than shirt & Rs.20 more than T-shirt. Altogether he bought 470 apparels. The number of shirts
exceeded that of the pants by as many T-shirts as he could have bought by Rs. 90. The number of
pants, shirts & T-shirts are respectively.
(1) 170, 120, 180  (2) 150, 130, 190  (3) 120, 150, 200  (4) None of these
15 The sequence 2, 3, 5, 6, 7, 10, 11, ... consists of all positive integers that are not a square or a cube. 
Find the 1000th term. 
  (1) 1038   (2) 1028   (3) 1039   (4) 1041 
16. Mr. Munish is a computer programmer. He is assigned with three jobs for which time allotted is in the
ratio of 5 : 4 : 2 (jobs are needed to be done individually). But due to some technical snag, 10%, 12.5%
and 25% of the time allotted for each job gets wasted respectively. He invests only 50%, 40% and 30%
of the hours of what was actually allotted to do the three jobs individually. Find how much percentage of
the total time allotted is the time wasted by Munish?
(1) 38.33%   (2) 39.4545%  (3) 49.09%           (4) Cannot be determined
Page 3


MOCK CAT 
SECTION – A 
1. If m
2
a
2
 + (n
2
 + 1) b
2
 + c
2
 = 2b(mna – c), then which of the following statement(s) is/are necessarily true?
I. ma = nb
II. ma = – nc
III. ma = nc
(1) I only (2) only II and III (3) Only I and II (4) None of these  
2. In the adjacent figure ABCDEF is a regular hexagon. Find the
ratio of the radius of C
large
 to that of radius of C
small
.
(1)
1 2
1 2
-
+
  (2) 
3 2
3 2
-
+
(3) 
1
2
(4) Can’t say 
Directions for questions 3 – 4: Refer to the following data for the following questions. 
There are 4 cities A, B, C & D. There can be two types of routes between any two cities. One is a direct one 
while the other one indirect. A, B & C all have direct routes between them. While city D is connected only to A 
& C with only one road to each. There are a total of 18 routes between A & C, 27 routes between A & B and 
22 routes between B & C. 
3. How many direct roads are there between A & B?
(1) 4    (2)3 (3) 6  (4) 2 
4. How many direct roads are there between B & C?
(1) 4    (2)3 (3) 5  (4) 1 
5. On a certain pasture the grass grows at on even rate. It is known that 40 cows can graze on it for 40
days before the grass is exhausted, but 30 cows can graze there for as long as 60 days. How many
days would the pasture last if 20 cows were to graze on it.
(1) 90 days    (2) 80 days   (3) 100 days   (4) 120 days
Directions for questions 6 – 8: Refer to the following data for the following questions. 
A polynomial of the from a
1
1
n
x
 + a
2
2
n
x
 + ……. + a
i
i
n
x
 + …….. + a
k
k
n
x
 where n
1
 > n
2
 > …… > n
k
 and a
1
 ? 0 
and 0 = I < k is represented by the sequence (a
1
, n
1
, a
2
, n
2
, a
3
, n
3
, ….., a
k
, n
k
) 
6. The value of (3, 5, 2, 2, 4, 1) + (1, 5, 2, 4, 5, 1) is
(1) (3, 5, 2, 4, 2, 2, 9, 1) (2) (4, 5, 2, 4, 2, 3, 3, 2, 9, 1) 
(3) (4, 5, 2, 3, 5, 1) (4) None of these  
7. The value of (4, 2, 6, 1, 5, 0) × (1, 1, 1, 0) is
(1) (4, 3, 6, 1, 5, 0) (2) (4, 3, 6, 2, 5, 1) 
(3) (4, 3, 10, 2, 11, 1, 5, 0) (4) None of these  
•
A B 
F
D E
C
C
large
C
small
8. If (1, 2, 0) × y = (1, 2, 4, 1, 4, 0) and (1, 1, 2, 0) ? 0, then y =
(1) (1, 1, 2, 0)  (2) (1, 1, 4, 0) (3) (1, 2, 2, 1) (4) None of these  
9. For some digit ‘a’ we have 0.a25a25a25 ... =
810
K
, where K is a positive integer. Find the hundred place 
of K.
(1) 5    (2)7 (3) 9  (4) 3 
10. M is the largest multiple of 8 which has no two digits the same. What is remainder when M is divided by
1000?
(1) 240   (2) 312   (3) 120   (4) 100
11. At the Bus-stand, I noted that most of the buses had Blue number plates. Half the buses with White
plates moved off on the tour. After this the ratio of Blue to White is 12 : 1. Within an hour, 2 more Buses
with White number plates started out. Now the present ratio of Blue to White becomes 20 : 1. Now
guess at this stage how many buses with Blue number plates are there?
(1) 50    (2) 60    (3) 75    (4)90
12. According to the positions of minute hand & hour hand, it is now a certain number of minutes past eight
O’clock but it was six times as many minutes past seven O’clock 15 minutes ago. So guess what is the
time now?
(1) 8 : 07   (2) 8 : 09   (3) 8 : 45   (4) None of these
13. Last year my father organized my birthday party. He distributed chocolates to all the children & trying to
ensure each received an equal amount. But when we counted & found that each had 18 except one
who had only 12. I calculated that if the number of children was subtracted from the total number of
chocolates, it would equal to 1014. So guess how many children came in my birthday party?
 (1) 17    (2) 55    (3) 60    (4)65
14. A shopkeeper spent money in three equal parts in buying Pants, shirts & T-shirts. Each pant cost Rs.10
more than shirt & Rs.20 more than T-shirt. Altogether he bought 470 apparels. The number of shirts
exceeded that of the pants by as many T-shirts as he could have bought by Rs. 90. The number of
pants, shirts & T-shirts are respectively.
(1) 170, 120, 180  (2) 150, 130, 190  (3) 120, 150, 200  (4) None of these
15 The sequence 2, 3, 5, 6, 7, 10, 11, ... consists of all positive integers that are not a square or a cube. 
Find the 1000th term. 
  (1) 1038   (2) 1028   (3) 1039   (4) 1041 
16. Mr. Munish is a computer programmer. He is assigned with three jobs for which time allotted is in the
ratio of 5 : 4 : 2 (jobs are needed to be done individually). But due to some technical snag, 10%, 12.5%
and 25% of the time allotted for each job gets wasted respectively. He invests only 50%, 40% and 30%
of the hours of what was actually allotted to do the three jobs individually. Find how much percentage of
the total time allotted is the time wasted by Munish?
(1) 38.33%   (2) 39.4545%  (3) 49.09%           (4) Cannot be determined
17. An electronic lock has 10 digit codes. A combination is any subset of 5 digits. It can be opened by the
combination in any order. Let there be X combinations possible. Suppose it is redesigned to allow a
combination to be any subset of 1 to 9 digits. What is the approx. percentage increase in total
combinations?
(1) 210   (2) 305   (3) 83    (4) 350
18. If M = 107, N = 108, O = 109, P = 110 then the square root of (1 + (M + 1)(N + 1)(O + 1)(P + 1))
(1) 11989   (2) 11909   (3) 10979   (4) 9069
19. Five consecutive positive integers are such whose sum is a cube and sum of the middle three is a
square, find the smallest possible middle integer.
(1) 27    (2) 125   (3) 675   (4) 225
20. If 16
101
 + 8
101
 + 4
101
 + 2
101
 + 1 is divided by 2
100
 + 1, then the remainder is
(1) 0    (2) 11    (3)4 (4) 2 
21. At how many points does the graph of
y = (x – 2) (2x
2
 – 5x + 4) (2x
2
 – 7x + 4) intersect the x-axis?
(1) 0           (2) 1         (3) 2   (4) 3 
22. A child starts counting all the natural numbers starting from one. After sometime he stops and finds that
he has not counted one of the numbers and also that he has counted one other number thrice. To his
surprise he finds that the final count is the same as he would have got without making any mistake.
What is the total number of such combinations possible if the count was 496?
(1) 14    (2) 15    (3) 16    (4) None of these
23. Give that 1025/1024 = 1.0009765625, what is the sum of the digits of 5
10
?
(1) 36    (2) 40    (3)41 (4) 50 
24. f(x, y) is defined for positive integers x, y and satisfies f(x, x) = x, f(x, y) = f(y, x), f(x, x + y) = (1 + x/y)
f(x, y). Find f(14, 52).
(1) 246   (2) 424   (3) 190   (4) 364
25. A biased coin has probability p of coming up tails. If it is tossed five times, the probability of just two tails
is the same as the probability of just one tail. Find the probability of just three tails in five tosses.
(1)
5
3
40
(2) 
16
5
(3) 
5
3
25
(4)
5
3
10
Page 4


MOCK CAT 
SECTION – A 
1. If m
2
a
2
 + (n
2
 + 1) b
2
 + c
2
 = 2b(mna – c), then which of the following statement(s) is/are necessarily true?
I. ma = nb
II. ma = – nc
III. ma = nc
(1) I only (2) only II and III (3) Only I and II (4) None of these  
2. In the adjacent figure ABCDEF is a regular hexagon. Find the
ratio of the radius of C
large
 to that of radius of C
small
.
(1)
1 2
1 2
-
+
  (2) 
3 2
3 2
-
+
(3) 
1
2
(4) Can’t say 
Directions for questions 3 – 4: Refer to the following data for the following questions. 
There are 4 cities A, B, C & D. There can be two types of routes between any two cities. One is a direct one 
while the other one indirect. A, B & C all have direct routes between them. While city D is connected only to A 
& C with only one road to each. There are a total of 18 routes between A & C, 27 routes between A & B and 
22 routes between B & C. 
3. How many direct roads are there between A & B?
(1) 4    (2)3 (3) 6  (4) 2 
4. How many direct roads are there between B & C?
(1) 4    (2)3 (3) 5  (4) 1 
5. On a certain pasture the grass grows at on even rate. It is known that 40 cows can graze on it for 40
days before the grass is exhausted, but 30 cows can graze there for as long as 60 days. How many
days would the pasture last if 20 cows were to graze on it.
(1) 90 days    (2) 80 days   (3) 100 days   (4) 120 days
Directions for questions 6 – 8: Refer to the following data for the following questions. 
A polynomial of the from a
1
1
n
x
 + a
2
2
n
x
 + ……. + a
i
i
n
x
 + …….. + a
k
k
n
x
 where n
1
 > n
2
 > …… > n
k
 and a
1
 ? 0 
and 0 = I < k is represented by the sequence (a
1
, n
1
, a
2
, n
2
, a
3
, n
3
, ….., a
k
, n
k
) 
6. The value of (3, 5, 2, 2, 4, 1) + (1, 5, 2, 4, 5, 1) is
(1) (3, 5, 2, 4, 2, 2, 9, 1) (2) (4, 5, 2, 4, 2, 3, 3, 2, 9, 1) 
(3) (4, 5, 2, 3, 5, 1) (4) None of these  
7. The value of (4, 2, 6, 1, 5, 0) × (1, 1, 1, 0) is
(1) (4, 3, 6, 1, 5, 0) (2) (4, 3, 6, 2, 5, 1) 
(3) (4, 3, 10, 2, 11, 1, 5, 0) (4) None of these  
•
A B 
F
D E
C
C
large
C
small
8. If (1, 2, 0) × y = (1, 2, 4, 1, 4, 0) and (1, 1, 2, 0) ? 0, then y =
(1) (1, 1, 2, 0)  (2) (1, 1, 4, 0) (3) (1, 2, 2, 1) (4) None of these  
9. For some digit ‘a’ we have 0.a25a25a25 ... =
810
K
, where K is a positive integer. Find the hundred place 
of K.
(1) 5    (2)7 (3) 9  (4) 3 
10. M is the largest multiple of 8 which has no two digits the same. What is remainder when M is divided by
1000?
(1) 240   (2) 312   (3) 120   (4) 100
11. At the Bus-stand, I noted that most of the buses had Blue number plates. Half the buses with White
plates moved off on the tour. After this the ratio of Blue to White is 12 : 1. Within an hour, 2 more Buses
with White number plates started out. Now the present ratio of Blue to White becomes 20 : 1. Now
guess at this stage how many buses with Blue number plates are there?
(1) 50    (2) 60    (3) 75    (4)90
12. According to the positions of minute hand & hour hand, it is now a certain number of minutes past eight
O’clock but it was six times as many minutes past seven O’clock 15 minutes ago. So guess what is the
time now?
(1) 8 : 07   (2) 8 : 09   (3) 8 : 45   (4) None of these
13. Last year my father organized my birthday party. He distributed chocolates to all the children & trying to
ensure each received an equal amount. But when we counted & found that each had 18 except one
who had only 12. I calculated that if the number of children was subtracted from the total number of
chocolates, it would equal to 1014. So guess how many children came in my birthday party?
 (1) 17    (2) 55    (3) 60    (4)65
14. A shopkeeper spent money in three equal parts in buying Pants, shirts & T-shirts. Each pant cost Rs.10
more than shirt & Rs.20 more than T-shirt. Altogether he bought 470 apparels. The number of shirts
exceeded that of the pants by as many T-shirts as he could have bought by Rs. 90. The number of
pants, shirts & T-shirts are respectively.
(1) 170, 120, 180  (2) 150, 130, 190  (3) 120, 150, 200  (4) None of these
15 The sequence 2, 3, 5, 6, 7, 10, 11, ... consists of all positive integers that are not a square or a cube. 
Find the 1000th term. 
  (1) 1038   (2) 1028   (3) 1039   (4) 1041 
16. Mr. Munish is a computer programmer. He is assigned with three jobs for which time allotted is in the
ratio of 5 : 4 : 2 (jobs are needed to be done individually). But due to some technical snag, 10%, 12.5%
and 25% of the time allotted for each job gets wasted respectively. He invests only 50%, 40% and 30%
of the hours of what was actually allotted to do the three jobs individually. Find how much percentage of
the total time allotted is the time wasted by Munish?
(1) 38.33%   (2) 39.4545%  (3) 49.09%           (4) Cannot be determined
17. An electronic lock has 10 digit codes. A combination is any subset of 5 digits. It can be opened by the
combination in any order. Let there be X combinations possible. Suppose it is redesigned to allow a
combination to be any subset of 1 to 9 digits. What is the approx. percentage increase in total
combinations?
(1) 210   (2) 305   (3) 83    (4) 350
18. If M = 107, N = 108, O = 109, P = 110 then the square root of (1 + (M + 1)(N + 1)(O + 1)(P + 1))
(1) 11989   (2) 11909   (3) 10979   (4) 9069
19. Five consecutive positive integers are such whose sum is a cube and sum of the middle three is a
square, find the smallest possible middle integer.
(1) 27    (2) 125   (3) 675   (4) 225
20. If 16
101
 + 8
101
 + 4
101
 + 2
101
 + 1 is divided by 2
100
 + 1, then the remainder is
(1) 0    (2) 11    (3)4 (4) 2 
21. At how many points does the graph of
y = (x – 2) (2x
2
 – 5x + 4) (2x
2
 – 7x + 4) intersect the x-axis?
(1) 0           (2) 1         (3) 2   (4) 3 
22. A child starts counting all the natural numbers starting from one. After sometime he stops and finds that
he has not counted one of the numbers and also that he has counted one other number thrice. To his
surprise he finds that the final count is the same as he would have got without making any mistake.
What is the total number of such combinations possible if the count was 496?
(1) 14    (2) 15    (3) 16    (4) None of these
23. Give that 1025/1024 = 1.0009765625, what is the sum of the digits of 5
10
?
(1) 36    (2) 40    (3)41 (4) 50 
24. f(x, y) is defined for positive integers x, y and satisfies f(x, x) = x, f(x, y) = f(y, x), f(x, x + y) = (1 + x/y)
f(x, y). Find f(14, 52).
(1) 246   (2) 424   (3) 190   (4) 364
25. A biased coin has probability p of coming up tails. If it is tossed five times, the probability of just two tails
is the same as the probability of just one tail. Find the probability of just three tails in five tosses.
(1)
5
3
40
(2) 
16
5
(3) 
5
3
25
(4)
5
3
10
SECTION – B 
Directions for questions 26 – 28: Read the following and answer the questions that follow the BSNL 
announced a cut in the STD rates on 27 December 2001. The new rates and slabs are given in the table 
below and are to be implemented from the 14 January 2002. 
SLAB DETAILS 
Rates (Rs./min) 
Distance Peak Rates Off Peak 
Old New Old New
50 – 200 4.8 2.4 1.2 1.2 
200 – 500 11.6 4.8 3 2.4 
500 – 1000 17.56 9.00 4.5 4.5 
1000+ 17.56 9.00 6 4.5
26. The maximum percentage reduction in costs will be experienced for calls over which of the following
distances?
(1) 50-200   (2) 500-1000   (3) 1000+   (4) 200-500
27. The percentage difference in the cost of a set of telephone calls made on the 13
th
 and 14
th
 January
having durations of 4 minutes over a distance of 350 km, 3 minutes for a distance of 700 km and 3
minutes for a distance of 1050 kms is (if all the three calls are made in peak times)
(1) 51.2%   (2) 51.76%   (3) 59.8%           (4) Cannot be determined
28. If one of the three calls in question 48 were made in an off peak time on both days, then the percentage
reduction in the total cost of the calls between 13
th
 and 14
th
 January will
(1) Definitely reduce
(2) Definitely increase
(3) Will depend on which particular call was made in an off peak time
(4) Cannot be determined
Directions for questions 29 – 31: Refer to the graphs below: 
 
 
 
 
 
2869.7
2330.8
2135.5
3352.1
3790.9
93-94
92-93
91-92
90-91
89-90
Flls & Public 
40.29%
Fls 42.84%
Tata Group 
7%
Directors 
0.03%
Foreign 
Companies 
1.50%
Other 
Companies 
4.14%
Bank & 
Mutual Funds 
4.17
Govt 
Companies 
0.03%
180.8
127.1
214.1
160.1
148.5
93-94
92-93
91-92
90-91
89-90
SHARE HOLDING PATTERN 
SALES                      FOR ALL THE YEARS   PROFIT 
Figures in Rs. Crores 
Figures in Rs. Crores 
Page 5


MOCK CAT 
SECTION – A 
1. If m
2
a
2
 + (n
2
 + 1) b
2
 + c
2
 = 2b(mna – c), then which of the following statement(s) is/are necessarily true?
I. ma = nb
II. ma = – nc
III. ma = nc
(1) I only (2) only II and III (3) Only I and II (4) None of these  
2. In the adjacent figure ABCDEF is a regular hexagon. Find the
ratio of the radius of C
large
 to that of radius of C
small
.
(1)
1 2
1 2
-
+
  (2) 
3 2
3 2
-
+
(3) 
1
2
(4) Can’t say 
Directions for questions 3 – 4: Refer to the following data for the following questions. 
There are 4 cities A, B, C & D. There can be two types of routes between any two cities. One is a direct one 
while the other one indirect. A, B & C all have direct routes between them. While city D is connected only to A 
& C with only one road to each. There are a total of 18 routes between A & C, 27 routes between A & B and 
22 routes between B & C. 
3. How many direct roads are there between A & B?
(1) 4    (2)3 (3) 6  (4) 2 
4. How many direct roads are there between B & C?
(1) 4    (2)3 (3) 5  (4) 1 
5. On a certain pasture the grass grows at on even rate. It is known that 40 cows can graze on it for 40
days before the grass is exhausted, but 30 cows can graze there for as long as 60 days. How many
days would the pasture last if 20 cows were to graze on it.
(1) 90 days    (2) 80 days   (3) 100 days   (4) 120 days
Directions for questions 6 – 8: Refer to the following data for the following questions. 
A polynomial of the from a
1
1
n
x
 + a
2
2
n
x
 + ……. + a
i
i
n
x
 + …….. + a
k
k
n
x
 where n
1
 > n
2
 > …… > n
k
 and a
1
 ? 0 
and 0 = I < k is represented by the sequence (a
1
, n
1
, a
2
, n
2
, a
3
, n
3
, ….., a
k
, n
k
) 
6. The value of (3, 5, 2, 2, 4, 1) + (1, 5, 2, 4, 5, 1) is
(1) (3, 5, 2, 4, 2, 2, 9, 1) (2) (4, 5, 2, 4, 2, 3, 3, 2, 9, 1) 
(3) (4, 5, 2, 3, 5, 1) (4) None of these  
7. The value of (4, 2, 6, 1, 5, 0) × (1, 1, 1, 0) is
(1) (4, 3, 6, 1, 5, 0) (2) (4, 3, 6, 2, 5, 1) 
(3) (4, 3, 10, 2, 11, 1, 5, 0) (4) None of these  
•
A B 
F
D E
C
C
large
C
small
8. If (1, 2, 0) × y = (1, 2, 4, 1, 4, 0) and (1, 1, 2, 0) ? 0, then y =
(1) (1, 1, 2, 0)  (2) (1, 1, 4, 0) (3) (1, 2, 2, 1) (4) None of these  
9. For some digit ‘a’ we have 0.a25a25a25 ... =
810
K
, where K is a positive integer. Find the hundred place 
of K.
(1) 5    (2)7 (3) 9  (4) 3 
10. M is the largest multiple of 8 which has no two digits the same. What is remainder when M is divided by
1000?
(1) 240   (2) 312   (3) 120   (4) 100
11. At the Bus-stand, I noted that most of the buses had Blue number plates. Half the buses with White
plates moved off on the tour. After this the ratio of Blue to White is 12 : 1. Within an hour, 2 more Buses
with White number plates started out. Now the present ratio of Blue to White becomes 20 : 1. Now
guess at this stage how many buses with Blue number plates are there?
(1) 50    (2) 60    (3) 75    (4)90
12. According to the positions of minute hand & hour hand, it is now a certain number of minutes past eight
O’clock but it was six times as many minutes past seven O’clock 15 minutes ago. So guess what is the
time now?
(1) 8 : 07   (2) 8 : 09   (3) 8 : 45   (4) None of these
13. Last year my father organized my birthday party. He distributed chocolates to all the children & trying to
ensure each received an equal amount. But when we counted & found that each had 18 except one
who had only 12. I calculated that if the number of children was subtracted from the total number of
chocolates, it would equal to 1014. So guess how many children came in my birthday party?
 (1) 17    (2) 55    (3) 60    (4)65
14. A shopkeeper spent money in three equal parts in buying Pants, shirts & T-shirts. Each pant cost Rs.10
more than shirt & Rs.20 more than T-shirt. Altogether he bought 470 apparels. The number of shirts
exceeded that of the pants by as many T-shirts as he could have bought by Rs. 90. The number of
pants, shirts & T-shirts are respectively.
(1) 170, 120, 180  (2) 150, 130, 190  (3) 120, 150, 200  (4) None of these
15 The sequence 2, 3, 5, 6, 7, 10, 11, ... consists of all positive integers that are not a square or a cube. 
Find the 1000th term. 
  (1) 1038   (2) 1028   (3) 1039   (4) 1041 
16. Mr. Munish is a computer programmer. He is assigned with three jobs for which time allotted is in the
ratio of 5 : 4 : 2 (jobs are needed to be done individually). But due to some technical snag, 10%, 12.5%
and 25% of the time allotted for each job gets wasted respectively. He invests only 50%, 40% and 30%
of the hours of what was actually allotted to do the three jobs individually. Find how much percentage of
the total time allotted is the time wasted by Munish?
(1) 38.33%   (2) 39.4545%  (3) 49.09%           (4) Cannot be determined
17. An electronic lock has 10 digit codes. A combination is any subset of 5 digits. It can be opened by the
combination in any order. Let there be X combinations possible. Suppose it is redesigned to allow a
combination to be any subset of 1 to 9 digits. What is the approx. percentage increase in total
combinations?
(1) 210   (2) 305   (3) 83    (4) 350
18. If M = 107, N = 108, O = 109, P = 110 then the square root of (1 + (M + 1)(N + 1)(O + 1)(P + 1))
(1) 11989   (2) 11909   (3) 10979   (4) 9069
19. Five consecutive positive integers are such whose sum is a cube and sum of the middle three is a
square, find the smallest possible middle integer.
(1) 27    (2) 125   (3) 675   (4) 225
20. If 16
101
 + 8
101
 + 4
101
 + 2
101
 + 1 is divided by 2
100
 + 1, then the remainder is
(1) 0    (2) 11    (3)4 (4) 2 
21. At how many points does the graph of
y = (x – 2) (2x
2
 – 5x + 4) (2x
2
 – 7x + 4) intersect the x-axis?
(1) 0           (2) 1         (3) 2   (4) 3 
22. A child starts counting all the natural numbers starting from one. After sometime he stops and finds that
he has not counted one of the numbers and also that he has counted one other number thrice. To his
surprise he finds that the final count is the same as he would have got without making any mistake.
What is the total number of such combinations possible if the count was 496?
(1) 14    (2) 15    (3) 16    (4) None of these
23. Give that 1025/1024 = 1.0009765625, what is the sum of the digits of 5
10
?
(1) 36    (2) 40    (3)41 (4) 50 
24. f(x, y) is defined for positive integers x, y and satisfies f(x, x) = x, f(x, y) = f(y, x), f(x, x + y) = (1 + x/y)
f(x, y). Find f(14, 52).
(1) 246   (2) 424   (3) 190   (4) 364
25. A biased coin has probability p of coming up tails. If it is tossed five times, the probability of just two tails
is the same as the probability of just one tail. Find the probability of just three tails in five tosses.
(1)
5
3
40
(2) 
16
5
(3) 
5
3
25
(4)
5
3
10
SECTION – B 
Directions for questions 26 – 28: Read the following and answer the questions that follow the BSNL 
announced a cut in the STD rates on 27 December 2001. The new rates and slabs are given in the table 
below and are to be implemented from the 14 January 2002. 
SLAB DETAILS 
Rates (Rs./min) 
Distance Peak Rates Off Peak 
Old New Old New
50 – 200 4.8 2.4 1.2 1.2 
200 – 500 11.6 4.8 3 2.4 
500 – 1000 17.56 9.00 4.5 4.5 
1000+ 17.56 9.00 6 4.5
26. The maximum percentage reduction in costs will be experienced for calls over which of the following
distances?
(1) 50-200   (2) 500-1000   (3) 1000+   (4) 200-500
27. The percentage difference in the cost of a set of telephone calls made on the 13
th
 and 14
th
 January
having durations of 4 minutes over a distance of 350 km, 3 minutes for a distance of 700 km and 3
minutes for a distance of 1050 kms is (if all the three calls are made in peak times)
(1) 51.2%   (2) 51.76%   (3) 59.8%           (4) Cannot be determined
28. If one of the three calls in question 48 were made in an off peak time on both days, then the percentage
reduction in the total cost of the calls between 13
th
 and 14
th
 January will
(1) Definitely reduce
(2) Definitely increase
(3) Will depend on which particular call was made in an off peak time
(4) Cannot be determined
Directions for questions 29 – 31: Refer to the graphs below: 
 
 
 
 
 
2869.7
2330.8
2135.5
3352.1
3790.9
93-94
92-93
91-92
90-91
89-90
Flls & Public 
40.29%
Fls 42.84%
Tata Group 
7%
Directors 
0.03%
Foreign 
Companies 
1.50%
Other 
Companies 
4.14%
Bank & 
Mutual Funds 
4.17
Govt 
Companies 
0.03%
180.8
127.1
214.1
160.1
148.5
93-94
92-93
91-92
90-91
89-90
SHARE HOLDING PATTERN 
SALES                      FOR ALL THE YEARS   PROFIT 
Figures in Rs. Crores 
Figures in Rs. Crores 
29. If profits have to be distributed in the ratio of the shareholding, the difference of profit of Tata Group in
90-91 and profit of Banks and mutual funds in 93-94, will be (Rs.) :
(1) 3.66 crores  (2) 4.98 crores  (3) 3.15 crores   (4) 2.34 crores
30. The angles subtended by the FIs and FIIs & public (at the center of the pie chart) differ by :
(1) 8.36
o
   (2) 8.8
o
   (3) 9.18
o
   (4) 9.36
o
31. The approximate Average annual growth rate of ‘sales’ from 89-90 to 92-93 is:
(1) 19%   (2) 21%   (3) 17% (4) 22% 
Directions for questions 32 – 36:  
The chart below shows the distances in km between four villages A, B, C and D which are connected by 
straight roads. 
– A B C D 
A – 15 13 24 
B 15 – 12 28 
C 13 12 – 21
D 24 28 21 – 
32. If a health visitor has to visit all the villages starting form B and to return to B, which is the shortest route
he should take?
(1) B A C D B   (2) B A D C B  (3) B D C A B  (4) B D A C B
33. Health camps have to be set up in two of the four villages, so that the distances from the remaining two
villages to the health camps may be the least. Which two villages should be selected?
(1) B and C   (2) A and C   (3) A and D   (4) C and D
34. If a village E is 8 km from A on the road to B, what is E’s distance from C?
(1) 10 km   (2) 18 km   (3) 9 km (4) 20 km 
35. If the bus fare along route ABD is Re.0.25 per km and along ACD it is Re.0.18 per km, which route is
less expensive and by how much?
(1) ABD by Rs. 2.83     (2) ACD by Rs. 4.63
(3) ABD by Rs. 1.25     (4) ACD by Rs. 1.35
36. If a village is equidistant from B, C and A, what is its distance from B?
(1) 10 km   (2) 12 km   (3) 8 km (4) 16 km 
Directions for questions 37 – 41: Study the data and answer the following questions. 
Two machines X and Y can produce three different types of spare parts A, B and C for motor vehicles. X can 
produce 1, 4 and 3 of A, B and C respectively in one hour while Y takes ½, 3/8, and 1/8 hour respectively to 
produce one A, B and C. Each machine can produce only one article at a time and can work for 20 hours per 
day. 
37. 70 of A, 30 of B and 60 of C are required to be produced. Which machine will take less time to produce
these?
(1)X (2) Y 
(3) Both will take same time (4) Cannot be found 
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