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IPMAT Indore 2019 (MCQ) PYQs

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IPMAT Indore 2019 Past Year Papers with Solutions filter tool

Q1:

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
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Option: 1
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Q2:

The maximum value of the natural number nn for which 21n21^n divides 50!50! is
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Option: 3
Correct Answer
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Q3:

The remainder when (2929)29(29^{29){29}} is divided by 99 is
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Option: 2
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Q4:

Placing which of the following two digits at the right end of 45304530 makes the resultant six digit number divisible by 6,76, 7 and 99:
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Option: 1
Correct Answer
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Q5:

In a school 70%70\% of the boys like cricket and 50%50\% like football. If x%x\% like both Cricket and Football, then
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Option: 1
Correct Answer
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Q6:

In a 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 one sport, then the number of students who like both cricket and hockey is
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Option: 1
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Q7:

If x∈(a,b)x ∈ (a, b) satisfies the inequality x−3x2+3x+2≥1\dfrac{x - 3}{x^2 + 3x + 2} \geq 1, then the largest possible value of b−ab - a is
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Option: 2
Correct Answer
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Q8:

If a,b,ca, b, c are real numbers and a2+b2+c2=1a^2 + b^2 + c^2 = 1, then the set of values ab+bc+caab + bc + ca can take is:
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Option: 4
Correct Answer
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Q9:

The inequality log⁡23x−12−x<1\log_{2} \frac{3x - 1}{2 - x} < 1 holds true for
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Option: 1
Correct Answer
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Q10:

The set of values of xx which satisfy the inequality 0.7(2x2−3x+4)<0.3430.7^{(2x^2 - 3x + 4)} < 0.343 is
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Option: 4
Correct Answer
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Q11:

A chord is drawn inside a circle, such that the length of the chord is equal to the radius of the circle. Now, two circles 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
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Option: 4
Correct Answer
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Q12:

Points PP, QQ, RR, and SS are taken on sides ABAB, BCBC, CDCD, and DADA of square ABCDABCD respectively, so that APPB=BQQC=CRRD=DSSA=1n\frac{AP}{PB} = \frac{BQ}{QC} = \frac{CR}{RD} = \frac{DS}{SA} = \frac{1}{n}. Then the ratio of the area of PQRSPQRS to the area of ABCDABCD is
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Option: 3
Correct Answer
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Q13:

On a circular path of radius 6 m a boy starts from a point AA on the circumference and walks along a chord ABAB of length 3 m. He then walks along another chord BCBC of length 2 m to reach point CC. The point BB lies on the minor arc ACAC. The distance between point CC from point AA is
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Option: 1
Correct Answer
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Q14:

The area enclosed by the curve 2∣x∣+3∣y∣=62|x| + 3|y| = 6 is
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Option: 1
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Q15:

Two points on a ground are 1 m apart. If a cow moves in the field in such a way that its distance from the two points is always in ratio 3:23: 2 then
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Option: 2
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Q16:

Given that cos⁡x+cos⁡y=1\cos x + \cos y = 1, the range of sin⁡x−sin⁡y\sin x - \sin y is
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Option: 4
Correct Answer
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Q17:

If sinθ+cosθ=msin \theta + cos \theta = m, then sin6θ+cos6θsin^6 \theta + cos^6 \theta equals
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Option: 4
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Q18:

If inverse of the matrix [2−0.5−1x]\left[\begin{array}{cc}2 & -0.5 \\ -1 & x\end{array}\right] is [1124]\left[\begin{array}{ll}1 & 1 \\ 2 & 4 \end{array}\right], then the value of xx is
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Option: 1
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Q19:

The function f(x)=x3−5x2−8x3f(x) = \dfrac{x^3 - 5x^2 - 8x}{3} is
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Option: 3
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Q20:

For a>b>c>0a > b > c > 0, the minimum value of the function f(x)=∣x−a∣+∣x−b∣+∣x−c∣f(x) = |x - a| + |x - b| + |x - c| is
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Option: 4
Correct Answer
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Q21:

Let α,β\alpha, \beta be the roots of x2−x+p=0x^2 - x + p = 0 and γ,δ\gamma, \delta be the roots of x2−4x+q=0x^2 - 4x + q = 0 where p and q are integers. If α,β,γ,δ\alpha, \beta, \gamma, \delta are in geometric progression then p+qp + q is
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Option: 1
Correct Answer
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Q22:

If (1+x−2x2)6=A0+∑r=112Arxr(1 + x - 2x^2)^6 = A_0 + \sum_{r=1}^{12} A_r x^r, then the value of A2+A4+A6+⋯+A12A_2 + A_4 + A_6 + \cdots + A_{12} is
Answer options
Option: 1
Correct Answer
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Q23:

The number of terms common to both the arithmetic progressions 2,5,8,11,...,1792, 5, 8, 11, ..., 179 and 3,5,7,9,...,1013, 5, 7, 9, ..., 101 is
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Option: 1
Correct Answer
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Q24:

From a pack of 52 cards, we draw one by one, without replacement. If f(n)f(n) is the probability that an Ace will appear at the nthn^{\text{th}} turn, then
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Option: 2
Correct Answer
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Q25:

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
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Option: 3
Correct Answer
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Q26:

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
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Option: 2
Correct Answer
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Q27:

The value of (log⁡330)−1+(log⁡4900)−1+(log⁡530)−1(\log_{3} 30)^{-1} + (\log_{4} 900)^{-1} + (\log_{5} 30)^{-1} is
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Option: 4
Correct Answer
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Q28:

The inequality log⁡af(x)<log⁡ag(x)\log_{a}{f(x)} < \log_{a}{g(x)} implies that
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Option: 1
Correct Answer
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Q29:

Three cubes with integer edge lengths are given. It is known that the sum of their surface areas is 564 cm2564 \ \text{cm}^2. Then the possible values of the sum of their volumes are
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Option: 1
Correct Answer
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Q30:

Determine the greatest number among the following four numbers:
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Option: 2
Correct Answer
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Q31:

The number of points, having both coordinates as integers, that lie in the interior of the triangle with vertices (0,0),(0,31),(0, 0), (0, 31), and (31,0)(31, 0) is
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Option: 1
Correct Answer
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Q32:

Two small insects, which are xx metres apart, take uu minutes to pass each other when they are flying towards each other, and vv 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
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Option: 3
Correct Answer
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Q33:

An alloy PP has copper and zinc in the proportion of 5:25:2 (by weight), while another alloy QQ has the same metals in the proportion of 3:43:4 (by weight). If these two alloys are mixed in the proportion of a:ba:b (by weight), a new alloy RR is formed, which has equal contents of copper and zinc. Then, the proportion of copper and zinc in the alloy SS, formed by mixing the two alloys PP and QQ in the proportion of b:ab:a (by weight) is
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Option: 3
Correct Answer
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Q34:

How many different numbers can be formed by using only the digits 1 and 3 which are smaller than 3000000?
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Option: 3
Correct Answer
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Q35:

There are numbers a1,a2,a3,…,ana_1, a_2, a_3, \ldots, a_n each of them being +1+1 or −1-1. If it is known that a1a2+a2a3+a3a4+…an−1an+ana1=0a_1 a_2 + a_2 a_3 + a_3 a_4 + \ldots a_{n-1} a_n + a_n a_1 = 0 then
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Option: 3
Correct Answer
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Q36:

Analyze 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 period 2006-2017 was approximately
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Option: 2
Correct Answer
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Q37:

Analyze 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
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Option: 1
Correct Answer
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Q38:

Analyze 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
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Option: 3
Correct Answer
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Q39:

Analyze 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 ( = exports - imports). Which of the following blocks of three years has witnessed the largest average negative balance of trade?
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Option: 4
Correct Answer
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Q40:

Analyze 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
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Option: 1
Correct Answer
Explanation →

IPMAT Indore 2019 MCQ Past Year Questions (Free PDF Download)

Practice with our comprehensive collection of IPMAT Indore 2019 MCQ Past Year Questions (PYQs) with detailed solutions. These questions are carefully curated from previous year papers to help you understand the exam pattern and improve your preparation.

Our free resources include handwritten solutions for all questions, making it easier to understand the concepts and approach. Use these PYQs to assess your preparation level and identify areas that need more focus. No login required. We have created handwritten solutions for all IPMAT Indore questions for free!