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IPMAT indore 2019 Complete Paper Solution

Question 1.

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If the compound interest earned on a certain sum for 2 years is twice the amount of simple interest for 2 years, then the rate of interest per annum is _______ percent

A
200%
B
2%
C
4%
D
400%

Question 2.

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The sum of the interior angles of a convex n-sided polygon is less than 2019°. The maximum possible value of n is

A
B
C
D

Question 3.

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The maximum value of the natural number n for which 21n divides 50! is

A
6
B
7
C
8
D
9

Question 4.

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Suppose that a, b, and c are real numbers greater than 1. Then the value of 11+loga2bca11+loga2bca + 11+logb2cab11+logb2cab + 11+logc2abc11+logc2abc is

A
B
C
D

Question 5.

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A real-valued function f satisfies the relation f(x)f(y) = f(2xy + 3) + 3f(x + y) - 3f(y) + 6y, for all real numbers x and y, then the value of f(8) is

A
B
C
D

Question 6.

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The remainder when 292929292929 is divided by 9 is

A
1
B
2
C
3
D
4

Question 7.

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Placing which of the following two digits at the right end of 4530 makes the resultant six digit number divisible by 6,7 and 9?

A
96
B
78
C
42
D
54

Question 8.

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Let A, B, C be three 4 X 4 matrices such that det A = 5, det B = -3, and det C = 1/2. Then the det (2AB-1C3BT) is

A
B
C
D

Question 9.

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If A is a 3 X 3 non-zero matrix such that A2 = 0 then determinant of [(1 + A)2 - 50A] is equal to

A
B
C
D

Question 10.

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In a school 70% of the boys like cricket and 50% like football. If x% like both Cricket and Football, then

A
20 ≤ x ≤ 50
B
x ≤ 20
C
x ≥ 50
D
10 ≤ x ≤ 70
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