banner

IPMAT indore 2019 Complete Paper Solution

Question 1.

The sum of the interior angles of a convex n-sided polygon is less than 20192019^{\circ}. The maximum possible value of n is

A
B
C
D

Question 2.

Suppose that a, b, and c are real numbers greater than 1. Then the value of 11+loga2bca+11+logb2cab+11+logc2abc\dfrac{1}{1+\log_{a^2b}\dfrac{c}{a}} + \dfrac{1}{1+\log _{b^2c}\dfrac{a}{b}} + \dfrac{1}{1+\log_{c^2a}\dfrac{b}{c}} is .............

A
B
C
D

Question 3.

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 4.

Let A, B, C be three 4x4 matrices such that det A = 5, det B = -3, and det C=12C = \frac{1}{2}. Then the det (2AB1C3BT)(2AB^{-1}C^{3}B^{T}) is ........

A
B
C
D

Question 5.

If A is a 3 X 3 non-zero matrix such that A2=0A^{2} = 0 then determinant of [(1+A)250A][(1 + A)^{2}- 50A] is equal to

A
B
C
D

Question 6.

Three friends divided some apples in the ratio 3 : 5 : 7 among themselves. After consuming 16 apples they found that the remaining number of apples with them was equal to largest number of apples received by one of them at the beginning. Total number of apples these friends initially had was

A
B
C
D

Question 7.

A shopkeeper reduces the price of a pen by 25% as a result of which the sales quantity increased by 20%. If the revenue made by the shopkeeper decreases by x%, then x is

A
B
C
D

Question 8.

For all real values of x, 3x26x+12x2+2x+4\dfrac{3x^{2} - 6x + 12}{x^{2} + 2x + 4} lies between 1 and k, and does not take any value above k. Then k equals...........

A
B
C
D

Question 9.

The maximum distance between the point (-5, 0) and a point on the circle X2+Y2=4X^{2} + Y^{2} = 4 is .......

A
B
C
D

Question 10.

If x, y, z are positive real numbers such that x12=y16=z24x^{12} = y^{16} = z^{24}, and the three quantities 3logyx,4logzy,nlogxz3\log_{y}x, 4 \log_{z}y, n\log_{x}z are in arithmetic progression, then the value of n is

A
B
C
D
cat-foundation
HOME
Recorded Course
Past Papers
More
YoutubeInstagramTelegramWhatsapp