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IPMAT indore 2022 Complete Paper Solution

Question 1.

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logx2ylogx2y + logy2xlogy2x = 1 and y = x2 - 30, then the value of x2 + y2 is:

A
B
C
D

Question 2.

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The set of real values of x for which the inequality log278log278 ≤ log3xlog3x < 91log2391log23 holds is

A
[2, 81)
B
(2, 27)
C
[2, 81]
D
(2, 27]

Question 3.

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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.

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

A
(0.25, 3)
B
(-∞, 4)
C
(-∞, 0.25)
D
(3, 4)

Question 5.

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

A
B
C
D

Question 6.

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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.

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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.

A
B
C
D

Question 8.

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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.

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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.

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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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