IPMAT Indore 2023 (MCQ) - Free PYQs + Solutions

Q1:

Indore 2023

Number System

>

Unit Digit

Easy

Q1:

Let

p

be a positive integer such that the unit digit of

p ^ 3

is

4

. What are the possible unit digits of

(p + 3) ^ 3

3

1, 7, 9

4, 7

1, 3, 7

Correct Answer

Option: 1

Correct Answer

Explanation →

Q2:

Indore 2023

Number System

>

Integral Solutions

Medium

Q2:

Let

[x]

denote the greatest integer not exceeding

x

and {

x

}

= x - [x]

If

n

is a natural number, then the sum of all values of

x

satisfying the equation

2[x] = x + n

{

x

} is

\dfrac{n(n+2)}{2}

\dfrac{3}{2}

\dfrac{n(n+1)}{2}

n

Correct Answer

Option: 1

Correct Answer

Explanation →

Q3:

Indore 2023

Algebra

>

Inequalities

Easy

Q3:

The set of all real values of x satisfying the inequality

\dfrac{x^2(x+1)}{(x-1)(2x+1)^3} > 0

is

(-\infty, -1)

U

(-\dfrac{1}{2}, 0)

U

(1, +\infty)

(-1, -\dfrac{1}{2})

U

(1,+\infty)

(-1, 0)

U

(1,+\infty)

(-1, -\dfrac{1}{2})

U

(0,+\infty)

Correct Answer

Option: 2

Correct Answer

Explanation →

Q4:

Indore 2023

Arithmetic

>

Profit & Loss

Easy

Q4:

A goldsmith bought a large solid golden ball at INR 1,000,000 and melted it to make a certain number of solid spherical beads such that the radius of each bead was one-fifth of the radius of the original ball. Assume that the cost of making golden beads is negligible. If the goldsmith sold all the beads at 20% discount on the listed price and made a total profit of 20%, then the listed price or each golden bead, in INR, was

48000

12000

9600

24000

Correct Answer

Option: 2

Correct Answer

Explanation →

Q5:

Indore 2023

Geometry

>

Circles

Easy

Q5:

Which of the following straight lines are both tangent to the circle

x ^ 2 + y ^ 2 - 6x + 4y - 12 = 0

?

4x+3y+19=0, 4x+3y-31=0

4x+3y-19=0, 4x+3y+31=0

4x+3y-19=0, 4x+3y-31=0

4x+3y+19=0, 4x+3y+31=0

Correct Answer

Option: 1

Correct Answer

Explanation →

Q6:

Indore 2023

Modern Math

>

Matrices & Determinants

Medium

Q6:

If

A = \begin{bmatrix} 1 & 2 \newline 3 & a \end{bmatrix}

where

a

is a real number and det

(A ^ 3 - 3A ^ 2 - 5A) = 0

then one of the values of

a

can be

4

6

1

5

Correct Answer

Option: 2

Correct Answer

Explanation →

Q7:

Indore 2023

Arithmetic

>

Time, Speed & Distance

Easy

Q7:

A helicopter flies along the sides of a square field of side length 100 kms. The first side is covered at a speed of 100 kmph, and for each subsequent side the speed is increased by 100 kmph till it covers all the sides. The average speed of the helicopter is

250 kmph

184 kmph

192 kmph

200 kmph

Correct Answer

Option: 3

Correct Answer

Explanation →

Q8:

Indore 2023

Arithmetic

>

Ratio, Proportion & Variation

Easy

Q8:

\dfrac{(a + b)}{(b + c)} = \dfrac{(c + d)}{(d + a)}

which of the following statements is always true?

a + b + c + d = 0

a=c,

or

a+b+c+d = 0

a=c

a=c,

and

b=d

Correct Answer

Option: 2

Correct Answer

Explanation →

Q9:

Indore 2023

Algebra

>

Quadratic Equations

Medium

Q9:

If the harmonic mean of the roots of the equation

(5 + \sqrt{2}) x ^ 2 - bx + 8 + 2\sqrt{5} = 0

is

4

then the value of

b

is

2

4-\sqrt{5}

3

4+\sqrt{5}

Correct Answer

Option: 4

Correct Answer

Explanation →

Q10:

Indore 2023

DILR

>

Tournaments

Medium

Q10:

In a chess tournament there are 5 contestants. Each player plays against all the others exactly once. No game results in a draw. The winner in a game gets one point and the loser gets zero points. Which of the following sequences cannot represent the scores of the five players?

2, 2, 2, 2, 2

3, 2, 2, 2, 1

3, 3, 2, 1, 1

4, 4, 1, 1, 0

Correct Answer

Option: 4

Correct Answer

Explanation →

Q11:

Indore 2023

Arithmetic

>

Simple & Compound Interest

Easy

Q11:

If the difference between compound interest and simple interest for a certain amount of money invested for

3

years at an annual interest rate of

10\%

is INR

527

, then the amount invested in INR is

17000

15000

1500

170000

Correct Answer

Option: 1

Correct Answer

Explanation →

Q12:

Indore 2023

Algebra

>

Progression & Series

Medium

Q12:

Let

a_{1}, a_{2}, a_{3}

be three distinct real numbers in geometric progression. If the equations

a_{1} x ^ 2 + 2a_{2}x + a_{3} = 0

and

b_{1} x ^ 2 + 2b_{2}x + b_{3} = 0

have a common root, then which of the following is necessarily true?

\dfrac{b_{1}}{a_{1}}, \dfrac{b_{2}}{a_{2}}, \dfrac{b_{3}}{a_{3}}

are in geometric progression

b_{1}, b_{2}, b_{3}

are in geometric progression

b_{1}, b_{2}, b_{3}

are in arithmetic progression

\dfrac{b_{1}}{a_{1}}, \dfrac{b_{2}}{a_{2}}, \dfrac{b_{3}}{a_{3}}

are in arithmetic progression

Correct Answer

Option: 4

Correct Answer

Explanation →

Q13:

Indore 2023

Geometry

>

Triangles

Medium

Q13:

In a triangle ABC, let D be the midpoint of BC, and AM be the altitude on BC. If the lengths of AB, BC and CA are in the ratio of 2:4:3, then the ratio of the lengths of BM and AD would be

11:4\sqrt{10}

12:11

11:12

4\sqrt{10}:11

Correct Answer

Option: 1

Correct Answer

Explanation →

Q14:

Indore 2023

Modern Math

>

Logarithms

Medium

Q14:

Let

a, b, c

be real numbers greater than 1, and

n

be a positive real number not equal to 1. If

log_n(log_2a) = 1; log_n(log_2b) = 2

and

log_n(log_2c) = 3

then which of the following is true?

(b-a)^n=(c-b)

a^n+b^n=c^n

a+b=c

(a^n+b)^n=ac

Correct Answer

Option: 4

Correct Answer

Explanation →

Q15:

Indore 2023

Modern Math

>

Permutation & Combination

Easy

Q15:

Consider an

8 \times 8

chessboard. The number of ways 8 rooks can be placed on the board such that no two rooks are in the same row and no two are in the same column is

7

7!

8

8!

Correct Answer

Option: 4

Correct Answer

Explanation →

Q16:

Indore 2023

Geometry

>

Circles

Easy

Q16:

The equation

x^2 + y^2 - 2x - 4y +5 = 0

represents

a pair of straight lines

a circle

an ellipse

a point

Correct Answer

Option: 4

Correct Answer

Explanation →

Q17:

Indore 2023

Algebra

>

Progression & Series

Hard

Q17:

A person standing at the centre of an open ground first walks 32 meters towards the east, takes a right turn and walks 16 meters, takes another right turn and walks 8 meters, and so on. How far will the person be from the original starting point after an infinite number of such walks in this pattern?

32

meters

\frac{32}{\sqrt{5}}

meters

64

meters

\frac{64}{\sqrt{5}}

meters

Correct Answer

Option: 4

Correct Answer

Explanation →

Q18:

Indore 2023

Modern Math

>

Logarithms

Medium

Q18:

If

\log_{(cos x)}(sin x) + \log_{(sin x)}(cos x) = 2,

then the value of

x

is

n\pi + \dfrac{\pi}{4}, n

is an integer

2n\pi + \dfrac{\pi}{4}, n

is an integer

\dfrac{n\pi}{4}, n

is an integer

\dfrac{n\pi}{4} + \dfrac{\pi}{4}, n

is an integer

Correct Answer

Option: 2

Correct Answer

Explanation →

Q19:

Indore 2023

Modern Math

>

Permutation & Combination

Medium

Q19:

A rabbit is sitting at the base of a staircase which has 10 steps. It proceeds to the top of the staircase by climbing either one step at a time or two steps at a time. The number of ways it can reach the top is

144

89

34

55

Correct Answer

Option: 2

Correct Answer

Explanation →

Q20:

Indore 2023

Modern Math

>

Probability

Medium

Q20:

The probability that a randomly chosen positive divisor of

10 ^ {2023}

is an integer multiple of

10 ^ {2001}

is

\dfrac{22}{2023}

\dfrac{23^2}{{2024}^2}

\dfrac{22}{2024}

\dfrac{22^2}{{2023}^2}

Correct Answer

Option: 2

Correct Answer

Explanation →

Q21:

Indore 2023

Modern Math

>

Set Theory

Easy

Q21:

In a group of 120 students, 80 students are from the Science stream and the rest are from the Commerce stream. It is known that 70 students support Mumbai Indians in the Indian Premier League; all the other students support Chennai Super Kings. The number of Science students who are supporters of Mumbai Indians is

Exactly 20

Between 15 and 25

30 or more

Between 20 and 25

Correct Answer

Option: 3

Correct Answer

Explanation →

Q22:

Indore 2023

Number System

>

Divisibility Rules

Medium

Q22:

If a three-digit number is chosen at random, what is the probability that it is divisible neither by 3 nor by 4?

\frac{1}{4}

\frac{1}{2}

\frac{2}{3}

\frac{1}{3}

Correct Answer

Option: 2

Correct Answer

Explanation →

Q23:

Indore 2023

Modern Math

>

Probability

Easy

Q23:

The minimum number of times a fair coin must be tossed so that the probability of getting at least one head exceeds 0.8 is

5

6

3

7

Correct Answer

Option: 3

Correct Answer

Explanation →

Q24:

Indore 2023

Geometry

>

Trigonometry

Medium

Q24:

If

cos \alpha

+

cos \beta

= 1 then the maximum value of

sin \alpha - sin \beta

is

\sqrt{2}

2

\sqrt{3}

1

Correct Answer

Option: 3

Correct Answer

Explanation →

Q25:

Indore 2023

Number System

>

Remainder

Medium

Q25:

A polynomial

P(x)

leaves a remainder

2

when divided by

(x - 1)

and a remainder

1

when divided by

(x - 2)

The remainder when

P(x)

is divided by

(x - 1)(x - 2)

is

3-x

3

x-3

2

Correct Answer

Option: 1

Correct Answer

Explanation →

Q26:

Indore 2023

DILR

>

Arrangements

Easy

Q26:

A pharmaceutical company has tested five drugs on three different organisms. The following incomplete table reports if a drug works on the given organism. For example, drug A works on organism R while B and C work on Q.

Drug	Organism Q	Organism R
A		✔
B	✔
C	✔
D
E

Following additional information is available:

Each drug works on at least one organism but not more than two organisms.

\newline

Each organism can be treated with at least two and at most three of these five drugs.

\newline

On whichever organism A works, B also works. Similarly, on whichever organism C works. D also works.

\newline

D and E do not work on the same organism.

Drug E works on

P & R

Q & R

Only P

Only R

Correct Answer

Option: 4

Correct Answer

Explanation →

Q27:

Indore 2023

DILR

>

Arrangements

Easy

Q27:

A pharmaceutical company has tested five drugs on three different organisms. The following incomplete table reports if a drug works on the given organism. For example, drug A works on organism R while B and C work on Q.

Drug	Organism Q	Organism R
A		✔
B	✔
C	✔
D
E

Following additional information is available:

Each drug works on at least one organism but not more than two organisms.

\newline

Each organism can be treated with at least two and at most three of these five drugs.

\newline

On whichever organism A works, B also works. Similarly, on whichever organism C works. D also works.

\newline

D and E do not work on the same organism.

Drug D works on:

P & Q

Only P

Only Q

Q & R

Correct Answer

Option: 1

Correct Answer

Explanation →

Q28:

Indore 2023

DILR

>

Arrangements

Easy

Q28:

A pharmaceutical company has tested five drugs on three different organisms. The following incomplete table reports if a drug works on the given organism. For example, drug A works on organism R while B and C work on Q.

Drug	Organism Q	Organism R
A		✔
B	✔
C	✔
D
E

Following additional information is available:

Each drug works on at least one organism but not more than two organisms.

\newline

Each organism can be treated with at least two and at most three of these five drugs.

\newline

On whichever organism A works, B also works. Similarly, on whichever organism C works. D also works.

\newline

D and E do not work on the same organism.

The organism(s) that can be treated with three of these five drugs is(are)

Only P

Only Q

P and Q

Q and R

Correct Answer

Option: 4

Correct Answer

Explanation →

Q29:

Indore 2023

DILR

>

Arrangements

Easy

Q29:

A pharmaceutical company has tested five drugs on three different organisms. The following incomplete table reports if a drug works on the given organism. For example, drug A works on organism R while B and C work on Q.

Drug	Organism Q	Organism R
A		✔
B	✔
C	✔
D
E

Following additional information is available:

Each drug works on at least one organism but not more than two organisms.

\newline

Each organism can be treated with at least two and at most three of these five drugs.

\newline

On whichever organism A works, B also works. Similarly, on whichever organism C works. D also works.

\newline

D and E do not work on the same organism.

Organism R can be treated with

A, B and C

Only A and E

Only A and B

A, B and E

Correct Answer

Option: 4

Correct Answer

Explanation →

Q30:

Indore 2023

DILR

>

Arrangements

Easy

Q30:

A pharmaceutical company has tested five drugs on three different organisms. The following incomplete table reports if a drug works on the given organism. For example, drug A works on organism R while B and C work on Q.

Drug	Organism Q	Organism R
A		✔
B	✔
C	✔
D
E

Following additional information is available:

Each drug works on at least one organism but not more than two organisms.

\newline

Each organism can be treated with at least two and at most three of these five drugs.

\newline

On whichever organism A works, B also works. Similarly, on whichever organism C works. D also works.

\newline

D and E do not work on the same organism.

Organism P can be treated with:

Only C and D

B, C and D

Only B and D

A, B, and D

Correct Answer

Option: 1

Correct Answer

Explanation →

IPMAT Indore 2023 (MCQ) PYQs

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IPMAT Indore 2023 MCQ Past Year Questions (Free PDF Download)