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1 IPMAT 2021 - Quantitative Aptitude
The number of positive integers that divide (1890).(130).(170) and are not divisible by 45 is ________.
2 IPMAT 2021 - Quantitative Aptitude
The sum up to 10 terms of the series 1.3 + 5.7 + 9.11 +… is__________
3 IPMAT 2021 - Quantitative Aptitude
It is given that the sequence {xn} satisfies x1 = 0, xn+1 = xn + 1 + 2√(1 + xn) for n = 1, 2….. Then x31 is________
4 IPMAT 2021 - Quantitative Aptitude
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 IPMAT 2021 - Quantitative Aptitude
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 IPMAT 2021 - Quantitative Aptitude
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 IPMAT 2021 - Quantitative Aptitude
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 IPMAT 2021 - Quantitative Aptitude
If one of the lines given by the equation 2x2 + axy + 3y2 = 0 coincides with one of those given by 2x2 + axy + 3y2 = 0 and the other lines represented by them are perpendicular then a2 + b2 is ___________.
9 IPMAT 2021 - Quantitative Aptitude
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 IPMAT 2021 - Quantitative Aptitude
In a class, 60% and 68% of students passed their Physics and Mathematics examinations respectively. Then at least percentage of students passed both their Physics and Mathematics examinations.
11 IPMAT 2021 - Quantitative Aptitude
Suppose that a real – valued function f(x) of real number satisfies f(x + xy) = f(x) + f(xy) for all real x, y and that f(2020) = 1. Compute f(2021).
2021/2020
2020/2019
1
2020/2021
12 IPMAT 2021 - Quantitative Aptitude
Suppose that log2 [log3 (log4 a)] = log3 [log4 (log2 b)] = log4 [log2 (log3 c)]. Then the value of a + b + c is
105
71
89
37
13 IPMAT 2021 - Quantitative Aptitude
Let Sn be sum of the first n terms of an A.P. {an}. if S5 = S9, what is the ratio of a3 : a5
9 : 5
5 : 9
3 : 5
5 : 3
14 IPMAT 2021 - Quantitative Aptitude
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
B
A + B
I
15 IPMAT 2021 - Quantitative Aptitude
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
16 IPMAT 2021 - Quantitative Aptitude
The unit digit in (743)85 – (525)37 + (987)96 is _____
9
3
1
5
17 IPMAT 2021 - Quantitative Aptitude
The set of all real values of p for which the equation 3 sin2 x + 12 cos x – 3 = p has at least one solution is
[– 12, 12]
[– 12, 9]
[– 15, 9]
[– 15, 12]
18 IPMAT 2021 - Quantitative Aptitude
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
26
25
21
16
19 IPMAT 2021 - Quantitative Aptitude
The highest possible value of the ratio of a four-digit number and the sum of its four digits is
1000
277.75
900.1
999
20 IPMAT 2021 - Quantitative Aptitude
Consider the polynomials f(x) = ax2 + bx + c, where a > 0, b, c are real, and g(x) = – 2x. If f(x) cuts x-axis at (– 2, 0) and g(x) passes through (a, b), then the minimum value of f(x) + 9a + 1 is__________.
0
1
2
3
21 IPMAT 2021 - Quantitative Aptitude
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
22%
25%
30%
38%
22 IPMAT 2021 - Quantitative Aptitude
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.
3 AM next day
4 AM next day
8 AM next day
11 PM the same day
23 IPMAT 2021 - Quantitative Aptitude
The number of 5-digit numbers consisting of distinct digits that can be formed such that only odd digits occur at odd places is
5250
6240
2520
3360
24 IPMAT 2021 - Quantitative Aptitude
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
10
25
35
36
25 IPMAT 2021 - Quantitative Aptitude
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
2
0.5
4
6
26 IPMAT 2021 - Quantitative Aptitude
Direction for Qs. 26 - 30: Refer to the following information and answer the following questions.
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):
It is known that: (1) Team B defeated Team C, and (2) Team C defeated Team D.
Total number of matches ending in draw is
12
4
5
6
27 IPMAT 2021 - Quantitative Aptitude
Direction for Qs. 26 - 30: Refer to the following information and answer the following questions.
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):
It is known that: (1) Team B defeated Team C, and (2) Team C defeated Team D.
Which team has the highest number of draws
Team A
Team C
Team D
Team E
28 IPMAT 2021 - Quantitative Aptitude
Direction for Qs. 26 - 30: Refer to the following information and answer the following questions.
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):
It is known that: (1) Team B defeated Team C, and (2) Team C defeated Team D.
Total points Team F scored was
0
1
2
3
29 IPMAT 2021 - Quantitative Aptitude
Direction for Qs. 26 - 30: Refer to the following information and answer the following questions.
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):
It is known that: (1) Team B defeated Team C, and (2) Team C defeated Team D.
Which team was not defeated by team A
B
C
D
F
30 IPMAT 2021 - Quantitative Aptitude
Direction for Qs. 26 - 30: Refer to the following information and answer the following questions.
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):
It is known that: (1) Team B defeated Team C, and (2) Team C defeated Team D.
Team E was defeated by
Teams A and B only
Only Team A
Only Team B
Teams A, B and D only