IPMAT 2021: Past Year Question Paper | IPMAT Mock Test Series - Commerce PDF Download

 Page 1


IPMAT 2021 INDORE
1. The number of positive integers that divide (1890)(130)(170) and are not divisible by 45 is
________
2. The sum up to 10 terms of the series 1.3 + 5.7 + 9.11 + .  . Is
3. It is given that the sequence {x
n
} satisfies x
1
= 0, x
n+1
= x
n
+ 1 + 2v(1+ )  for n = 1,2, . . . . . ?? ?? Then x
31
is _______
4. There are 5 parallel lines on the plane. On the same plane, there are ‘n’ other lines that are
perpendicular to the 5 parallel lines. If the number of distinct rectangles formed by these lines is
360, what is the value of n?
5. There are two taps, T1 and T2, at the bottom of a water tank, either or both of which may be
opened to empty the water tank, each at a constant rate. If T1 is opened keeping T2 closed, the
water tank (initially full) becomes empty in half an hour. If both T1 and T2 are kept open, the
water tank (initially full) becomes empty in 20 minutes. Then, the time (in minutes) it takes for
the water tank (initially full) to become empty if T2 is opened while T1 is closed is
6. A class consists of 30 students. Each of them has registered for 5 courses. Each course
instructor conducts an exam out of 200 marks. The average percentage marks of all 30 students
across all courses they have registered for, is 80%. Two of them apply for revaluation in a
course. If none of their marks reduce, and the average of all 30 students across all courses
becomes 80.02%, the maximum possible increase in marks for either of the 2 students is
7. What is the minimum number of weights which enable us to weigh any integer number of
grams of gold from 1 to 100 on a standard balance with two pans? (Weights can be placed only
on the left pan)
8. If one of the lines given by the equation = 0 coincides with one of those 2?? 2
 + ?? ?? ?? + 3?? 2
given by and the other lines represented by them are perpendicular then 2?? 2
 + ?? ?? ?? - 3?? 2
?? 2
+ = ?? 2
9. If a function f(a) = max (a, 0) then the smallest integer value of ‘x’ for which the equation f(x-3)
+ 2f(x+1) = 8 holds true is _______
10. In a class, 60% and 68% of students passed their Physics and Mathematics examinations
respectively. Then atleast percentage of students passed both their Physics and Mathematics
examinations.
Page 2


IPMAT 2021 INDORE
1. The number of positive integers that divide (1890)(130)(170) and are not divisible by 45 is
________
2. The sum up to 10 terms of the series 1.3 + 5.7 + 9.11 + .  . Is
3. It is given that the sequence {x
n
} satisfies x
1
= 0, x
n+1
= x
n
+ 1 + 2v(1+ )  for n = 1,2, . . . . . ?? ?? Then x
31
is _______
4. There are 5 parallel lines on the plane. On the same plane, there are ‘n’ other lines that are
perpendicular to the 5 parallel lines. If the number of distinct rectangles formed by these lines is
360, what is the value of n?
5. There are two taps, T1 and T2, at the bottom of a water tank, either or both of which may be
opened to empty the water tank, each at a constant rate. If T1 is opened keeping T2 closed, the
water tank (initially full) becomes empty in half an hour. If both T1 and T2 are kept open, the
water tank (initially full) becomes empty in 20 minutes. Then, the time (in minutes) it takes for
the water tank (initially full) to become empty if T2 is opened while T1 is closed is
6. A class consists of 30 students. Each of them has registered for 5 courses. Each course
instructor conducts an exam out of 200 marks. The average percentage marks of all 30 students
across all courses they have registered for, is 80%. Two of them apply for revaluation in a
course. If none of their marks reduce, and the average of all 30 students across all courses
becomes 80.02%, the maximum possible increase in marks for either of the 2 students is
7. What is the minimum number of weights which enable us to weigh any integer number of
grams of gold from 1 to 100 on a standard balance with two pans? (Weights can be placed only
on the left pan)
8. If one of the lines given by the equation = 0 coincides with one of those 2?? 2
 + ?? ?? ?? + 3?? 2
given by and the other lines represented by them are perpendicular then 2?? 2
 + ?? ?? ?? - 3?? 2
?? 2
+ = ?? 2
9. If a function f(a) = max (a, 0) then the smallest integer value of ‘x’ for which the equation f(x-3)
+ 2f(x+1) = 8 holds true is _______
10. In a class, 60% and 68% of students passed their Physics and Mathematics examinations
respectively. Then atleast percentage of students passed both their Physics and Mathematics
examinations.
11. Suppose that a real-valued function f(x) of real numbers satisfies f(x + xy) = f(x) + f(xy) for all
real x, y, and that f(2020) = 1. Compute f(2021).
A.
2021
2020
B.
2020
2019
C.   1
D.
2020
2021
12. Suppose that  log
2
[log
3
(log
4
a)]  =  log
3
[log
4
(log
2
b)] =  log
4
[log
2
(log
3
c)]  =  0 then the value of a
+ b + c  is
A. 105
B.  71
C.  89
D.  37
13. Let S
n
be sum of the first n terms of an A.P. {a
n
}. If S
5
= S
9
, what is the ratio of a
3
: a
5
A. 9: 5        B.  5: 9        C.  3: 5          D.  5: 3
14. If A,B and A + B are non singular matrices and AB = BA then
2A - B – A(A + B)
-1
A + B(A + B)
-1
B equals
A. A
B.  B
C.  A + B
D. I
15. If the angles A, B, C of a triangle are in arithmetic progression such
that sin(2A + B) = 1/2 then sin(B + 2C) is equal to
A.
-1
2
B.
1
2
C.
-1
v2
D.
3
v2
16. The unit digit in (743)
85
– (525)
37
+ (987)
96
is ________
A. 9
B. 3
C. 1
D. 5
17. The set of all real value of p for which the equation
Page 3


IPMAT 2021 INDORE
1. The number of positive integers that divide (1890)(130)(170) and are not divisible by 45 is
________
2. The sum up to 10 terms of the series 1.3 + 5.7 + 9.11 + .  . Is
3. It is given that the sequence {x
n
} satisfies x
1
= 0, x
n+1
= x
n
+ 1 + 2v(1+ )  for n = 1,2, . . . . . ?? ?? Then x
31
is _______
4. There are 5 parallel lines on the plane. On the same plane, there are ‘n’ other lines that are
perpendicular to the 5 parallel lines. If the number of distinct rectangles formed by these lines is
360, what is the value of n?
5. There are two taps, T1 and T2, at the bottom of a water tank, either or both of which may be
opened to empty the water tank, each at a constant rate. If T1 is opened keeping T2 closed, the
water tank (initially full) becomes empty in half an hour. If both T1 and T2 are kept open, the
water tank (initially full) becomes empty in 20 minutes. Then, the time (in minutes) it takes for
the water tank (initially full) to become empty if T2 is opened while T1 is closed is
6. A class consists of 30 students. Each of them has registered for 5 courses. Each course
instructor conducts an exam out of 200 marks. The average percentage marks of all 30 students
across all courses they have registered for, is 80%. Two of them apply for revaluation in a
course. If none of their marks reduce, and the average of all 30 students across all courses
becomes 80.02%, the maximum possible increase in marks for either of the 2 students is
7. What is the minimum number of weights which enable us to weigh any integer number of
grams of gold from 1 to 100 on a standard balance with two pans? (Weights can be placed only
on the left pan)
8. If one of the lines given by the equation = 0 coincides with one of those 2?? 2
 + ?? ?? ?? + 3?? 2
given by and the other lines represented by them are perpendicular then 2?? 2
 + ?? ?? ?? - 3?? 2
?? 2
+ = ?? 2
9. If a function f(a) = max (a, 0) then the smallest integer value of ‘x’ for which the equation f(x-3)
+ 2f(x+1) = 8 holds true is _______
10. In a class, 60% and 68% of students passed their Physics and Mathematics examinations
respectively. Then atleast percentage of students passed both their Physics and Mathematics
examinations.
11. Suppose that a real-valued function f(x) of real numbers satisfies f(x + xy) = f(x) + f(xy) for all
real x, y, and that f(2020) = 1. Compute f(2021).
A.
2021
2020
B.
2020
2019
C.   1
D.
2020
2021
12. Suppose that  log
2
[log
3
(log
4
a)]  =  log
3
[log
4
(log
2
b)] =  log
4
[log
2
(log
3
c)]  =  0 then the value of a
+ b + c  is
A. 105
B.  71
C.  89
D.  37
13. Let S
n
be sum of the first n terms of an A.P. {a
n
}. If S
5
= S
9
, what is the ratio of a
3
: a
5
A. 9: 5        B.  5: 9        C.  3: 5          D.  5: 3
14. If A,B and A + B are non singular matrices and AB = BA then
2A - B – A(A + B)
-1
A + B(A + B)
-1
B equals
A. A
B.  B
C.  A + B
D. I
15. If the angles A, B, C of a triangle are in arithmetic progression such
that sin(2A + B) = 1/2 then sin(B + 2C) is equal to
A.
-1
2
B.
1
2
C.
-1
v2
D.
3
v2
16. The unit digit in (743)
85
– (525)
37
+ (987)
96
is ________
A. 9
B. 3
C. 1
D. 5
17. The set of all real value of p for which the equation
3 sin
2
x + 12 cos x – 3 = p  has one solution is
A. [-12, 12]
B. [-12, 9]
C. [-15, 9]
D. [-15, 12]
18. ABCD is a quadrilateral whose diagonals AC and BD intersect at O. If triangles AOB and
COD have areas 4 and 9 respectively, then the minimum area that ABCD can have is
A. 26
B. 25
C. 21
D. 16
19. The highest possible value of the ratio of a four-digit number and the sum of its four digits is
A. 1000
B. 277.75
C. 900.1
D. 999
20. Consider the polynomials f(x) = ax
2
+ bx + c, where a > 0, b, c are real, g(x) = -2x. If f(x) cuts
the x-axis at (-2, 0) and g(x) passes through (a, b), then the minimum value of f(x) + 9a + 1 is
__________
A. 0
B. 1
C. 2
D. 3
21. In a city, 50% of the population can speak in exactly one language among Hindi, English and
Tamil, while 40% of the population can speak in at least two of these three languages.
Moreover, the number of people who cannot speak in any of these three languages is twice the
number of people who can speak in all these three languages. If 52% of the population can
speak in Hindi and 25% of the population can speak exactly in one language among English
and Tamil, then the percentage of the population who can speak in Hindi and in exactly one
more language among English and Tamil is
A. 22%
B. 25%
C. 30%
D. 38%
22. A train left point A at 12 noon. Two hours later, another train started from point A in the same
direction. It overtook the first train at 8 PM. It is known that the sum of the speeds of the two
trains is 140 km/hr. Then, at what time would the second train overtake the first train, if instead
Page 4


IPMAT 2021 INDORE
1. The number of positive integers that divide (1890)(130)(170) and are not divisible by 45 is
________
2. The sum up to 10 terms of the series 1.3 + 5.7 + 9.11 + .  . Is
3. It is given that the sequence {x
n
} satisfies x
1
= 0, x
n+1
= x
n
+ 1 + 2v(1+ )  for n = 1,2, . . . . . ?? ?? Then x
31
is _______
4. There are 5 parallel lines on the plane. On the same plane, there are ‘n’ other lines that are
perpendicular to the 5 parallel lines. If the number of distinct rectangles formed by these lines is
360, what is the value of n?
5. There are two taps, T1 and T2, at the bottom of a water tank, either or both of which may be
opened to empty the water tank, each at a constant rate. If T1 is opened keeping T2 closed, the
water tank (initially full) becomes empty in half an hour. If both T1 and T2 are kept open, the
water tank (initially full) becomes empty in 20 minutes. Then, the time (in minutes) it takes for
the water tank (initially full) to become empty if T2 is opened while T1 is closed is
6. A class consists of 30 students. Each of them has registered for 5 courses. Each course
instructor conducts an exam out of 200 marks. The average percentage marks of all 30 students
across all courses they have registered for, is 80%. Two of them apply for revaluation in a
course. If none of their marks reduce, and the average of all 30 students across all courses
becomes 80.02%, the maximum possible increase in marks for either of the 2 students is
7. What is the minimum number of weights which enable us to weigh any integer number of
grams of gold from 1 to 100 on a standard balance with two pans? (Weights can be placed only
on the left pan)
8. If one of the lines given by the equation = 0 coincides with one of those 2?? 2
 + ?? ?? ?? + 3?? 2
given by and the other lines represented by them are perpendicular then 2?? 2
 + ?? ?? ?? - 3?? 2
?? 2
+ = ?? 2
9. If a function f(a) = max (a, 0) then the smallest integer value of ‘x’ for which the equation f(x-3)
+ 2f(x+1) = 8 holds true is _______
10. In a class, 60% and 68% of students passed their Physics and Mathematics examinations
respectively. Then atleast percentage of students passed both their Physics and Mathematics
examinations.
11. Suppose that a real-valued function f(x) of real numbers satisfies f(x + xy) = f(x) + f(xy) for all
real x, y, and that f(2020) = 1. Compute f(2021).
A.
2021
2020
B.
2020
2019
C.   1
D.
2020
2021
12. Suppose that  log
2
[log
3
(log
4
a)]  =  log
3
[log
4
(log
2
b)] =  log
4
[log
2
(log
3
c)]  =  0 then the value of a
+ b + c  is
A. 105
B.  71
C.  89
D.  37
13. Let S
n
be sum of the first n terms of an A.P. {a
n
}. If S
5
= S
9
, what is the ratio of a
3
: a
5
A. 9: 5        B.  5: 9        C.  3: 5          D.  5: 3
14. If A,B and A + B are non singular matrices and AB = BA then
2A - B – A(A + B)
-1
A + B(A + B)
-1
B equals
A. A
B.  B
C.  A + B
D. I
15. If the angles A, B, C of a triangle are in arithmetic progression such
that sin(2A + B) = 1/2 then sin(B + 2C) is equal to
A.
-1
2
B.
1
2
C.
-1
v2
D.
3
v2
16. The unit digit in (743)
85
– (525)
37
+ (987)
96
is ________
A. 9
B. 3
C. 1
D. 5
17. The set of all real value of p for which the equation
3 sin
2
x + 12 cos x – 3 = p  has one solution is
A. [-12, 12]
B. [-12, 9]
C. [-15, 9]
D. [-15, 12]
18. ABCD is a quadrilateral whose diagonals AC and BD intersect at O. If triangles AOB and
COD have areas 4 and 9 respectively, then the minimum area that ABCD can have is
A. 26
B. 25
C. 21
D. 16
19. The highest possible value of the ratio of a four-digit number and the sum of its four digits is
A. 1000
B. 277.75
C. 900.1
D. 999
20. Consider the polynomials f(x) = ax
2
+ bx + c, where a > 0, b, c are real, g(x) = -2x. If f(x) cuts
the x-axis at (-2, 0) and g(x) passes through (a, b), then the minimum value of f(x) + 9a + 1 is
__________
A. 0
B. 1
C. 2
D. 3
21. In a city, 50% of the population can speak in exactly one language among Hindi, English and
Tamil, while 40% of the population can speak in at least two of these three languages.
Moreover, the number of people who cannot speak in any of these three languages is twice the
number of people who can speak in all these three languages. If 52% of the population can
speak in Hindi and 25% of the population can speak exactly in one language among English
and Tamil, then the percentage of the population who can speak in Hindi and in exactly one
more language among English and Tamil is
A. 22%
B. 25%
C. 30%
D. 38%
22. A train left point A at 12 noon. Two hours later, another train started from point A in the same
direction. It overtook the first train at 8 PM. It is known that the sum of the speeds of the two
trains is 140 km/hr. Then, at what time would the second train overtake the first train, if instead
the second train had started from point A in the same direction 5 hours after the first train?
Assume that both the trains travel at constant speeds.
A. 3 AM next day
B. 4 AM next day
C. 8 AM next day
D. 11 PM the same day
23. The number of 5-digit numbers consisting of distinct digits that can be formed such that only
odd digits occur at odd places is
A. 5250
B. 6240
C. 2520
D. 3360
24. There are 10 points in the plane, of which 5 points are collinear and no three among the
remaining are collinear. Then the number of distinct straight lines that can be formed out of
these 10 points is
A. 10
B. 25
C. 35
D. 36
25. The x-intercept of the line that passes through the intersection of the lines x + 2y = 4 and 2x
+ 3y = 6, and is perpendicular to the line 3x – y = 2 is
A.2
B.0.5
C.4
D.6
26
In a football tournament six teams A, B, C, D, E and F participated. Every pair of teams had
exactly one match among them. For any team, a win fetches 2 points, a draw fetches 1 point,
and a loss fetches no points. Both the teams E and F ended with less than 5 points. At the end
of the tournament points table is as follows (some of the entries are not shown):
Teams Played Wins Losses Draws Points
A 5 0 8
B 5 2 6
C 5 2 5
D 5 1 5
Page 5


IPMAT 2021 INDORE
1. The number of positive integers that divide (1890)(130)(170) and are not divisible by 45 is
________
2. The sum up to 10 terms of the series 1.3 + 5.7 + 9.11 + .  . Is
3. It is given that the sequence {x
n
} satisfies x
1
= 0, x
n+1
= x
n
+ 1 + 2v(1+ )  for n = 1,2, . . . . . ?? ?? Then x
31
is _______
4. There are 5 parallel lines on the plane. On the same plane, there are ‘n’ other lines that are
perpendicular to the 5 parallel lines. If the number of distinct rectangles formed by these lines is
360, what is the value of n?
5. There are two taps, T1 and T2, at the bottom of a water tank, either or both of which may be
opened to empty the water tank, each at a constant rate. If T1 is opened keeping T2 closed, the
water tank (initially full) becomes empty in half an hour. If both T1 and T2 are kept open, the
water tank (initially full) becomes empty in 20 minutes. Then, the time (in minutes) it takes for
the water tank (initially full) to become empty if T2 is opened while T1 is closed is
6. A class consists of 30 students. Each of them has registered for 5 courses. Each course
instructor conducts an exam out of 200 marks. The average percentage marks of all 30 students
across all courses they have registered for, is 80%. Two of them apply for revaluation in a
course. If none of their marks reduce, and the average of all 30 students across all courses
becomes 80.02%, the maximum possible increase in marks for either of the 2 students is
7. What is the minimum number of weights which enable us to weigh any integer number of
grams of gold from 1 to 100 on a standard balance with two pans? (Weights can be placed only
on the left pan)
8. If one of the lines given by the equation = 0 coincides with one of those 2?? 2
 + ?? ?? ?? + 3?? 2
given by and the other lines represented by them are perpendicular then 2?? 2
 + ?? ?? ?? - 3?? 2
?? 2
+ = ?? 2
9. If a function f(a) = max (a, 0) then the smallest integer value of ‘x’ for which the equation f(x-3)
+ 2f(x+1) = 8 holds true is _______
10. In a class, 60% and 68% of students passed their Physics and Mathematics examinations
respectively. Then atleast percentage of students passed both their Physics and Mathematics
examinations.
11. Suppose that a real-valued function f(x) of real numbers satisfies f(x + xy) = f(x) + f(xy) for all
real x, y, and that f(2020) = 1. Compute f(2021).
A.
2021
2020
B.
2020
2019
C.   1
D.
2020
2021
12. Suppose that  log
2
[log
3
(log
4
a)]  =  log
3
[log
4
(log
2
b)] =  log
4
[log
2
(log
3
c)]  =  0 then the value of a
+ b + c  is
A. 105
B.  71
C.  89
D.  37
13. Let S
n
be sum of the first n terms of an A.P. {a
n
}. If S
5
= S
9
, what is the ratio of a
3
: a
5
A. 9: 5        B.  5: 9        C.  3: 5          D.  5: 3
14. If A,B and A + B are non singular matrices and AB = BA then
2A - B – A(A + B)
-1
A + B(A + B)
-1
B equals
A. A
B.  B
C.  A + B
D. I
15. If the angles A, B, C of a triangle are in arithmetic progression such
that sin(2A + B) = 1/2 then sin(B + 2C) is equal to
A.
-1
2
B.
1
2
C.
-1
v2
D.
3
v2
16. The unit digit in (743)
85
– (525)
37
+ (987)
96
is ________
A. 9
B. 3
C. 1
D. 5
17. The set of all real value of p for which the equation
3 sin
2
x + 12 cos x – 3 = p  has one solution is
A. [-12, 12]
B. [-12, 9]
C. [-15, 9]
D. [-15, 12]
18. ABCD is a quadrilateral whose diagonals AC and BD intersect at O. If triangles AOB and
COD have areas 4 and 9 respectively, then the minimum area that ABCD can have is
A. 26
B. 25
C. 21
D. 16
19. The highest possible value of the ratio of a four-digit number and the sum of its four digits is
A. 1000
B. 277.75
C. 900.1
D. 999
20. Consider the polynomials f(x) = ax
2
+ bx + c, where a > 0, b, c are real, g(x) = -2x. If f(x) cuts
the x-axis at (-2, 0) and g(x) passes through (a, b), then the minimum value of f(x) + 9a + 1 is
__________
A. 0
B. 1
C. 2
D. 3
21. In a city, 50% of the population can speak in exactly one language among Hindi, English and
Tamil, while 40% of the population can speak in at least two of these three languages.
Moreover, the number of people who cannot speak in any of these three languages is twice the
number of people who can speak in all these three languages. If 52% of the population can
speak in Hindi and 25% of the population can speak exactly in one language among English
and Tamil, then the percentage of the population who can speak in Hindi and in exactly one
more language among English and Tamil is
A. 22%
B. 25%
C. 30%
D. 38%
22. A train left point A at 12 noon. Two hours later, another train started from point A in the same
direction. It overtook the first train at 8 PM. It is known that the sum of the speeds of the two
trains is 140 km/hr. Then, at what time would the second train overtake the first train, if instead
the second train had started from point A in the same direction 5 hours after the first train?
Assume that both the trains travel at constant speeds.
A. 3 AM next day
B. 4 AM next day
C. 8 AM next day
D. 11 PM the same day
23. The number of 5-digit numbers consisting of distinct digits that can be formed such that only
odd digits occur at odd places is
A. 5250
B. 6240
C. 2520
D. 3360
24. There are 10 points in the plane, of which 5 points are collinear and no three among the
remaining are collinear. Then the number of distinct straight lines that can be formed out of
these 10 points is
A. 10
B. 25
C. 35
D. 36
25. The x-intercept of the line that passes through the intersection of the lines x + 2y = 4 and 2x
+ 3y = 6, and is perpendicular to the line 3x – y = 2 is
A.2
B.0.5
C.4
D.6
26
In a football tournament six teams A, B, C, D, E and F participated. Every pair of teams had
exactly one match among them. For any team, a win fetches 2 points, a draw fetches 1 point,
and a loss fetches no points. Both the teams E and F ended with less than 5 points. At the end
of the tournament points table is as follows (some of the entries are not shown):
Teams Played Wins Losses Draws Points
A 5 0 8
B 5 2 6
C 5 2 5
D 5 1 5
E 5 1
F 5
It is known that: (1) Team B defeated Team C, and (2) Team C defeated Team D.
26.1
Total number of matches ending in draw is
A.12
B.4
C.5
D.6
26.2
Which team has the highest number of draws
A.A
B.C
C.D
D.E
26.3
Total points Team F scored was
A.0
B.1
C.2
D.3
26.4
Which team was not defeated by team A
A.B
B.C
C.D
D.F
26.5
Team E was defeated by
A.Teams A and B only
B.Only team A
C.Only team B
D.Teams A, B and D only