1 IPMAT 2019 - Quantitative Aptitude

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

2 IPMAT 2019 - Quantitative Aptitude

Suppose that a, b and c are real numbers greater than 1. then the value of

3 IPMAT 2019 - Quantitative Aptitude

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________

4 IPMAT 2019 - Quantitative Aptitude

Let A, B, C be three 4 × 4 matrices such that det A = 5, Det B = − 3, det C =  1/2. Then the det (2AB^-1C³B^T) is______

5 IPMAT 2019 - Quantitative Aptitude

If A is a 3 × 3 non – zero matrix such that A² = 0 then determinant of [(I + A)⁵⁰ – 50A] is equal to_____

6 IPMAT 2019 - Quantitative Aptitude

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_______

7 IPMAT 2019 - Quantitative Aptitude

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__________

8 IPMAT 2019 - Quantitative Aptitude

For all real values of x, lies between 1 and k, and does not take any value above k. Then k equals__________.

9 IPMAT 2019 - Quantitative Aptitude

The maximum distance between the point (-5, 0) and a point on the circle x² + y² = 4  is________

10 IPMAT 2019 - Quantitative Aptitude

If x, y, z are positive real numbers such that x¹² = y¹⁶ = z²⁴, and the three quantities 3 log_yx, 4 log_zy, n log_xz are in arithmetic progression, then the value of n is______

11 IPMAT 2019 - Quantitative Aptitude

The number of pairs (x, y) satisfying the equation sinx siny= sin (x + y) and |x| + |y| = 1 is______

12 IPMAT 2019 - Quantitative Aptitude

The circle x² + y² - 6x - 10y + k = 0 does not touch or intersect the coordinate axes. If the point (1, 4) does not lie outside the circle, and the range of k is (a, b) then a + b is ________

13 IPMAT 2019 - Quantitative Aptitude

If a 3 x 3 matrix is filled with + 1’s and – 1’s such that the sum of each row and column of the matrix is 1, then the absolute value of its determinant is__________

14 IPMAT 2019 - Quantitative Aptitude

Let the set = {2, 3, 4,…, 25}. For each k ∈ P, define Q (k) = {x ∈ P such that x > k and k divides x}. Then the number of elements in the set

15 IPMAT 2019 - Quantitative Aptitude

The number of whole metallic tiles that can be produced by melting and recasting a circular metallic plate, if each of the tiles has a shape of a right – angled isosceles triangle and the circular plate has a radius equal in length to the longest side of the tile (Assume that the tiles and plate are of uniform thickness, and there is no loss of material in the melting and recasting process) is___________

16 IPMAT 2019 - Quantitative Aptitude

If |x| < 100 and |y| < 100, then the number of integer solutions of (x, y) satisfying the equation 4x + 7y = 3 is_______

17 IPMAT 2019 - Quantitative Aptitude

The average of five distinct integers is 110 and the smallest number among them is 100. The maximum possible value of the largest integer is ________

18 IPMAT 2019 - Quantitative Aptitude

Assume that all positive integers are written down consecutively from left to right as in 1234567891011……. The 6389th digit in this sequence is___________

19 IPMAT 2019 - Quantitative Aptitude

The number of pairs of integers whose sums are equal to their products is___________

20 IPMAT 2019 - Quantitative Aptitude

You have been asked to select a positive integer N which is less than 1000, such that it is either a multiple of 4, or a multiple of 6, or an odd multiple of 9. Then number of such numbers is_________.

21 IPMAT 2019 - Quantitative Aptitude

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.

22 IPMAT 2019 - Quantitative Aptitude

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

23 IPMAT 2019 - Quantitative Aptitude

The remainder when (29²⁹) is divided by 9 is

24 IPMAT 2019 - Quantitative Aptitude

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 ?

25 IPMAT 2019 - Quantitative Aptitude

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

26 IPMAT 2019 - Quantitative Aptitude

In class of 65 students 40 like cricket, 25 like football and 20 like hockey. 10 students like both cricket and football, 8 students like football and hockey and 5 students like all three sports. If all the students like at least on sport, then the number of students who like both cricket and hockey is

27 IPMAT 2019 - Quantitative Aptitude

If x ∈ (a, b) satisfies the inequality then the largest possible value of b – a is

28 IPMAT 2019 - Quantitative Aptitude

If a, b, c are real number a² + b² + c² = 1, then the set of values ab + bc +ca can take is -

29 IPMAT 2019 - Quantitative Aptitude

The inequality holds true for

30 IPMAT 2019 - Quantitative Aptitude

The set of values of x which satisfy the inequality < 0.343 is

31 IPMAT 2019 - Quantitative Aptitude

A chord is drawn inside a circle, such that the length of the chord is equal to the radius of the circle. Now, circle are drawn, one on each side of the chord, each touching the chord at its midpoint and the original circle. Let k be the ratio of the areas of the bigger inscribed circle and the smaller inscribed circle, then k equals –

32 IPMAT 2019 - Quantitative Aptitude

Points P, Q, R and S are taken on sides AB, BC, CD and DA of square ABCD respectively, so that AP : PB = BQ : QC = CR : RD = DS : SA = 1:

33 IPMAT 2019 - Quantitative Aptitude

On a circular path of radius 6m a boy starts from a point A on the circumference and walks along a chord AB of length 3m. He then walks along another chord BC of length 2m to reach point C. The point B lies on the minor are AC. The distance between point C from point A is -

34 IPMAT 2019 - Quantitative Aptitude

The area enclosed by the curve 2|x| + 3|y| = 6 is

35 IPMAT 2019 - Quantitative Aptitude

Two points on a ground are 1 m apart. If a cow moves in the field in such a way that is distance from the two points is always in ratio 2:3 then 

36 IPMAT 2019 - Quantitative Aptitude

Given that cos x + cos y = 1, the range of sin x – sin y is

37 IPMAT 2019 - Quantitative Aptitude

If sin θ + cos θ = m then sin⁶ θ + cos⁶ θ equals-

38 IPMAT 2019 - Quantitative Aptitude

If inverse of the matrix is , then the value of x is

39 IPMAT 2019 - Quantitative Aptitude

The function is

40 IPMAT 2019 - Quantitative Aptitude

For a > b > c > 0, the minimum value of the function f(x) = |x – a| + |x – b| + |x – c| is

41 IPMAT 2019 - Quantitative Aptitude

Let α, β be the roots of x² – x + p = 0 and γ, δ be the roots of x² – 4x + q = 0 where p and q are integers. If α, β, γ, δ are in geometric progression the p + q is

42 IPMAT 2019 - Quantitative Aptitude

43 IPMAT 2019 - Quantitative Aptitude

The number of terms common to both the arithmetic progressions 2, 5, 8, 11, …, 179 and 3, 5, 7, 9,…,101 is

44 IPMAT 2019 - Quantitative Aptitude

From a pack of 52 cards, we draw one by one, without replacement. If f(n) is the probability that an Ace will appear at the nth turn, then

45 IPMAT 2019 - Quantitative Aptitude

A die is thrown three times and the sum of the three numbers is found to be 15. The probability that the first throw was a four is

46 IPMAT 2019 - Quantitative Aptitude

In a given village there are only three sizes of families: families with 2 members, families with 4 members and families with 6 members. The proportion of families with 2, 4 and 6 members are roughly equal. A poll is conducted in this village wherein a person is chosen at random and asked about his/her family size. The average family size computed by sampling 1000 such persons from the village would be closest to

47 IPMAT 2019 - Quantitative Aptitude

The value of is

48 IPMAT 2019 - Quantitative Aptitude

The inequality log_a, {f(x)}< log_a {g(x)} implies that-

49 IPMAT 2019 - Quantitative Aptitude

Three cubes with integer edge lengths are given. It is known that the sum of their surface areas is 564 cm². Then the possible values of the sum of their volumes are

50 IPMAT 2019 - Quantitative Aptitude

Determine the greatest number among the following four numbers

51 IPMAT 2019 - Quantitative Aptitude

The number of points, having both co-ordinates as integers, that lie in the interior of the triangle with vertices (0, 0), (0, 31) and (31, 0) is

52 IPMAT 2019 - Quantitative Aptitude

Two small insects, which are x metres apart, take u minutes to pass each other when they are flying towards each other, and v minutes to meet each other when they are flying in the same direction. Then, the ratio of the speed of the slower insect to that of the faster insect is

53 IPMAT 2019 - Quantitative Aptitude

An alloy P has copper and zinc in the proportion of 5:2 (by weight), while another alloy Q has the same metals in the proportion of 3:4 (by weight).If these two alloys are mixed in the proportion of a : b (by weight), a new alloy R is formed, which has equal contents of copper and zinc. Then, the proportion of copper and zinc in the alloy S, formed by mixing the two alloys P and Q in the proportion of b : a (by weight) is 

54 IPMAT 2019 - Quantitative Aptitude

How many different numbers can be formed by using only the digits 1 and 3 which are smaller than 3000000?

55 IPMAT 2019 - Quantitative Aptitude

There are n numbers a₁, a₂, a₃, ……a_n each of them being + 1 or – 1. If it is known that a₁a₂ + a₂a₃ + a₃a₄ + a_n-1a_n + a₁a₁ = 0 then

56 IPMAT 2019 - Quantitative Aptitude

Analyse the given data for exports and imports of rubber in Rs. crores from 2006 to 2017 and answer the questions based on the analysis.


Average annual exports for the given periods (2006 – 2017) was approximately

57 IPMAT 2019 - Quantitative Aptitude

Analyse the given data for exports and imports of rubber in Rs. crores from 2006 to 2017 and answer the questions based on the analysis.

The percentage decline in exports during the period 2006 – 2011 is more than the percentage decline in exports during 2012 – 2017 by approximately ______ percent.

58 IPMAT 2019 - Quantitative Aptitude

Analyse the given data for exports and imports of rubber in Rs. crores from 2006 to 2017 and answer the questions based on the analysis.


The maximum difference between imports and exports is

59 IPMAT 2019 - Quantitative Aptitude

Analyse the given data for exports and imports of rubber in Rs. crores from 2006 to 2017 and answer the questions based on the analysis.


Balance of trade is defined as imports subtracted from exports (=imports – imports). Which of the following blocks of three years has witnessed the largest average negative balance of trade?

60 IPMAT 2019 - Quantitative Aptitude

Analyse the given data for exports and imports of rubber in Rs. crores from 2006 to 2017 and answer the questions based on the analysis.


The percentage increase in imports over the previous year is maximum during