IPMAT 2022 | Past Year Question Paper

Question 1.

$logx2y$ + $logy2x$ = 1 and y = x² - 30, then the value of x² + y² is:

Question 2.

The set of real values of x for which the inequality $log278$ ≤ $log3x$ < $91log23$ holds is

A

[2, 81)

B

(2, 27)

C

[2, 81]

D

(2, 27]

Question 3.

The main point the writer makes is that fruit-bearing plants

A

of all kinds need to be studied, not just those consumed by humans.

B

and other plant species' propagation cannot be studied accurately.

C

are better protected than other plant species and can propagate easily.

D

have the same problems in propagation as other plants.

Question 4.

The set of all possible values of f(x) for which (81)^x+ (81)^f(x)= 3 is

A

(0.25, 3)

B

(-∞, 4)

C

(-∞, 0.25)

D

(3, 4)

Question 5.

The area enclosed by 2|x| + 3|y| ≤ 6 is ____________ sq. units.

Question 6.

The study has been based on

A

fruits that are consumed by humans.

B

fruits available at the University of Tokyo.

C

wild fruits consumed by animals.

D

fruits sourced by greengrocers.

Question 7.

When Geeta increases her speed from 12km/hr to 20km/hr, she takes one hour less than the usual time to cover the distance between her home and office. The distance between her home and office is ___________ km.

Question 8.

Which one of the following options means "arboreal" and "camouflage"?

A

tree-dwelling and disguised

B

ground-dwelling and hidden

C

protected and fortified

D

covered and variegated

Question 9.

The value of k for which the following lines

x − y − 1 = 0
2x + 3y − 12 = 0
2x − 3y + k = 0

are concurrent is

A

1

B

-1

C

0

D

12

Question 10.

The lengths of the sides of a triangle are x, 21 and 40, where x is the shortest side. A possible value of x is

A

18

B

20

C

19

D

16

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IPMAT indore 2022 Complete Paper Solution

Question 1.

$logx2y$ + $logy2x$ = 1 and y = x² - 30, then the value of x² + y² is:

Question 2.

The set of real values of x for which the inequality $log278$ ≤ $log3x$ < $91log23$ holds is

Question 3.

The main point the writer makes is that fruit-bearing plants

Question 4.

The set of all possible values of f(x) for which (81)^x+ (81)^f(x)= 3 is

Question 5.

The area enclosed by 2|x| + 3|y| ≤ 6 is ____________ sq. units.

Question 6.

The study has been based on

Question 7.

When Geeta increases her speed from 12km/hr to 20km/hr, she takes one hour less than the usual time to cover the distance between her home and office. The distance between her home and office is ___________ km.

Question 8.

Which one of the following options means "arboreal" and "camouflage"?

Question 9.

The value of k for which the following lines

x − y − 1 = 0
2x + 3y − 12 = 0
2x − 3y + k = 0

are concurrent is

Question 10.

The lengths of the sides of a triangle are x, 21 and 40, where x is the shortest side. A possible value of x is

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FREE CONTENT

IPMAT indore 2022 Complete Paper Solution

Question 1.

logx2ylogx2ylogx2y + logy2xlogy2xlogy2x = 1 and y = x2 - 30, then the value of x2 + y2 is:

Question 2.

The set of real values of x for which the inequality log278log278log278 ≤ log3xlog3xlog3x < 91log2391log2391log23 holds is

Question 3.

The main point the writer makes is that fruit-bearing plants

Question 4.

The set of all possible values of f(x) for which (81)x + (81)f(x) = 3 is

Question 5.

The area enclosed by 2|x| + 3|y| ≤ 6 is ____________ sq. units.

Question 6.

The study has been based on

Question 7.

When Geeta increases her speed from 12km/hr to 20km/hr, she takes one hour less than the usual time to cover the distance between her home and office. The distance between her home and office is ___________ km.

Question 8.

Which one of the following options means "arboreal" and "camouflage"?

Question 9.

The value of k for which the following lines x − y − 1 = 0 2x + 3y − 12 = 0 2x − 3y + k = 0 are concurrent is

Question 10.

The lengths of the sides of a triangle are x, 21 and 40, where x is the shortest side. A possible value of x is

$logx2y$ + $logy2x$ = 1 and y = x² - 30, then the value of x² + y² is:

The set of real values of x for which the inequality $log278$ ≤ $log3x$ < $91log23$ holds is

The set of all possible values of f(x) for which (81)^x+ (81)^f(x)= 3 is

The value of k for which the following lines

x − y − 1 = 0
2x + 3y − 12 = 0
2x − 3y + k = 0

are concurrent is