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IPM Question Paper 2021 | IPM Indore Quants

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IPMAT 2021 Question Paper Indore Quants. Solve questions from IPMAT 2021 Question Paper from IPM Indore and check the solutions to get adequate practice.

IPMAT 2021 Question Paper - IPM Indore Quants

The number of positive integers that divide (1890).(130).(170) and are not divisible by 45 is ________

320
IPMAT 2021 Question Paper - IPM Indore Quants

The sum up to 10 terms of the series 1.3 + 5.7 + 9.11 + . . is

5310
IPMAT 2021 Question Paper - IPM Indore Quants

It is given that the sequence {x_n} satisfies x₁ = 0,
x_n+1 = x_n + 1 + 2√(1+x_n) for n = 1,2, . . . . . Then x₃₁ is _______

960
IPMAT 2021 Question Paper - IPM Indore Quants

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?

9
IPMAT 2021 Question Paper - IPM Indore Quants

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 T₁ 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

60
IPMAT 2021 Question Paper - IPM Indore Quants

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

6
IPMAT 2021 Question Paper - IPM Indore Quants

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)

7
IPMAT 2021 Question Paper - IPM Indore Quants

If one of the lines given by the equation 2𝑥² + axy + 3y² = 0 coincides with one of those given by 2x² + b𝑥𝑦 - 3𝑦² = 0 and the other lines represented by them are perpendicular then 𝑎² + 𝑏² =
IPMAT 2021 Question Paper - IPM Indore Quants

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 _______

3
IPMAT 2021 Question Paper - IPM Indore Quants

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.

28
IPMAT 2021 Question Paper - IPM Indore Quants

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).
1. \(\frac{2021}{2020}\)
2. \(\frac{2020}{2019}\)
3. 1
4. \(\frac{2020}{2021}\)
Choice A
\(\frac{2021}{2020}\)
IPMAT 2021 Question Paper - IPM Indore Quants

Suppose that log₂[log₃ (log₄a)] = log₃ [log₄ (log₂b)] = log₄ [log₂ (log₃c)] = 0 then the value of a + b + c is
1. 105
2. 71
3. 89
4. 37
Choice C
89
IPMAT 2021 Question Paper - IPM Indore Quants

Let S_n be sum of the first n terms of an A.P. {a_n }. If S₅ = S₉ , what is the ratio of a₃ : a₅
1. 9:5
2. 5:9
3. 3:5
4. 5:3
Choice A
9:5
IPMAT 2021 Question Paper - IPM Indore Quants

If A, B and A + B are non singular matrices and AB = BA then
2A - B - A(A + B)^-1A + B(A + B)^-1B equals
1. A
2. B
3. A + B
4. I
Choice D
I
IPMAT 2021 Question Paper - IPM Indore Quants

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
1. \(\frac{-1}{2}\)
2. \(\frac{1}{2}\)
3. \(\frac{-1}{\sqrt{2}}\)
4. \(\frac{3}{\sqrt{2}}\)
Choice A
\(\frac{-1}{2}\)
IPMAT 2021 Question Paper - IPM Indore Quants

The unit digit in (743)⁸⁵ – (525)³⁷ + (987)⁹⁶ is ________
1. 9
2. 3
3. 1
4. 5
Choice A
9
IPMAT 2021 Question Paper - IPM Indore Quants

The set of all real value of p for which the equation 3 sin²x + 12 cos x – 3 = p has one solution is
1. [-12, 12]
2. [-12, 9]
3. [-15, 9]
4. [-15, 12]
Choice D
[-15, 12]
IPMAT 2021 Question Paper - IPM Indore Quants

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
1. 26
2. 25
3. 21
4. 16
Choice B
25
IPMAT 2021 Question Paper - IPM Indore Quants

The highest possible value of the ratio of a four-digit number and the sum of its four digits is
1. 1000
2. 277.75
3. 900.1
4. 999
Choice A
1000
IPMAT 2021 Question Paper - IPM Indore Quants

Consider the polynomials f(x) = ax² + 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
1. 0
2. 1
3. 2
4. 3
Choice D
3
IPMAT 2021 Question Paper - IPM Indore Quants

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
1. 22%
2. 25%
3. 30%
4. 38%
Choice A
22%
IPMAT 2021 Question Paper - IPM Indore Quants

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.
1. 3 AM the next day
2. 4 AM the next day
3. 8 AM the next day
4. 11 PM the same day
Choice C
8 AM the next day
IPMAT 2021 Question Paper - IPM Indore Quants

The number of 5-digit numbers consisting of distinct digits that can be formed such that only odd digits occur at odd places is
1. 5250
2. 6240
3. 2520
4. 3360
Choice C
2520
IPMAT 2021 Question Paper - IPM Indore Quants

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
1. 10
2. 25
3. 35
4. 36
Choice D
36
IPMAT 2021 Question Paper - IPM Indore Quants

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
1. 2
2. 0.5
3. 4
4. 6
Choice D
6

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 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

IPMAT 2021 Question Paper - IPM Indore Quants

Total number of matches ending in draw is
1. 12
2. 4
3. 5
4. 6
Choice D
6
IPMAT 2021 Question Paper - IPM Indore Quants

Which team has the highest number of draws
1. A
2. C
3. D
4. E
Choice D
E
IPMAT 2021 Question Paper - IPM Indore Quants

Total points Team F scored was
1. 0
2. 1
3. 2
4. 3
Choice C
2
IPMAT 2021 Question Paper - IPM Indore Quants

Which team was not defeated by team A
1. B
2. C
3. D
4. F
Choice C
D
IPMAT 2021 Question Paper - IPM Indore Quants

Team E was defeated by
1. Teams A and B only
2. Only team A
3. Only team B
4. Teams A, B and D only
Choice C
Only team B