IPMAT Indore 2022 question paper with solutions

All 90 questions of IPMAT Indore 2022, section by section, each with its answer and a step-by-step solution. Sections: Quantitative Ability (45), Verbal Ability (45).

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Quantitative Ability · 45 questions

Set 1Showroom staffing – five employees across seven days Q41–Q45

Q1If log_x²y+log_y²x=1 and y=x²-30 , then the value of x²+y² is _________IPMAT Indore 2022 · Quantitative Ability · Logarithms
Q2The area enclosed by 2 | x |+3 | y |≤ 6 is ____________ sq. units.IPMAT Indore 2022 · Quantitative Ability · Coordinate Geometry Basics
Q3When Geeta increases her speed from 12 km/hr to 20 km/hr, she takes one hour less than the usual time to cover the…IPMAT Indore 2022 · Quantitative Ability · Time Speed and Distance
Q4The number of triangles that can be formed by choosing points from 7 points on a line and 5 points on another parallel…IPMAT Indore 2022 · Quantitative Ability · Permutation and Combination
Q5Aruna purchases a certain number of apples for INR 20 each and a certain number of mangoes for INR 25 each. If she…IPMAT Indore 2022 · Quantitative Ability · Profit Loss and Discount
Q6Given that f ( x )= | x |+2 | x-1 |+ | x-2 |+ | x-4 |+ | x-6 |+2 | x-10 | , xin ( -∞ ,∞ ) , the minimum value of f ( x…IPMAT Indore 2022 · Quantitative Ability · Inequalities and Modulus
Q7If A= [ beginmatrix1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0endmatrix ] , then the absolute value of the determinant of…IPMAT Indore 2022 · Quantitative Ability · Matrices and Determinants
Q8The sum of the coefficients of all the terms in the expansion of ( 5x-9 )⁴ is __________IPMAT Indore 2022 · Quantitative Ability · Binomial Theorem
Q9A new sequence is obtained from the sequence of positive integers ( 1,2,3,ldots ) by deleting all the perfect squares.…IPMAT Indore 2022 · Quantitative Ability · Sequences and Counting
Q10If sin α +sin β =(√2)/(√3) and cos α +cos β =(1)/(√3) , then the value of ( 20cos (α -β)/(2) )² is _______IPMAT Indore 2022 · Quantitative Ability · Trigonometry
Q11The 3^textrd , 14^textth and 69^textth terms of an arithmetic progression form three distinct and consecutive terms of…IPMAT Indore 2022 · Quantitative Ability · Progressions
Q12Let P ( X ) denote the power set of a set X . If A is the null set, then the number of elements in P ( P ( P ( P ( A )…IPMAT Indore 2022 · Quantitative Ability · Set Theory
Q13The numbers -16 , 2^(x+3)-2^(2x-1)-16 , 2^(2x-1)+16 are in an arithmetic progression. Then x equals ________IPMAT Indore 2022 · Quantitative Ability · Exponents and Indices
Q14Mrs and Mr Sharma, and Mrs and Mr Ahuja along with four other persons are to be seated at a round table for dinner. If…IPMAT Indore 2022 · Quantitative Ability · Permutation and Combination
Q15Let 50 distinct positive integers be chosen such that the highest among them is 100, and the average of the largest 25…IPMAT Indore 2022 · Quantitative Ability · Averages
Q16The set of real values of x for which the inequality log_278≤log_3x<9^((1)/(log_23)) holds isIPMAT Indore 2022 · Quantitative Ability · Logarithms
Q17The set of all possible values of f ( x ) for which ( 81 )^(x)+ ( 81 )^(f ( x ))=3 isIPMAT Indore 2022 · Quantitative Ability · Functions
Q18The value of k for which the following lines x-y-1=0 2x+3y-12=0 2x-3y+k=0 are concurrent isIPMAT Indore 2022 · Quantitative Ability · Linear Equations
Q19The lengths of the sides of a triangle are x , 21 and 40, where x is the shortest side. A possible value of x isIPMAT Indore 2022 · Quantitative Ability · Triangles
Q20In a right-angled triangle ABC, the hypotenuse AC is of length 13 cm. A line drawn connecting the midpoints D and E of…IPMAT Indore 2022 · Quantitative Ability · Triangles
Q21If the five-digit number overlineabcde is divisible by 6, then which of the following numbers is not necessarily…IPMAT Indore 2022 · Quantitative Ability · Divisibility
Q22In how many ways can the letters of the word MANAGEMENT be arranged such that no two vowels appear together?IPMAT Indore 2022 · Quantitative Ability · Permutation and Combination
Q23In a room, there are n persons whose average height is 160 cm. If m more persons, whose average height is 172 cm,…IPMAT Indore 2022 · Quantitative Ability · Averages
Q24The sum of the first 15 terms in an arithmetic progression is 200, while the sum of the next 15 terms is 350. Then the…IPMAT Indore 2022 · Quantitative Ability · Progressions
Q25Suppose a , b and c are integers such that a>b>c>0 , and A= [ beginmatrixa & b & c \\ b & c & a \\ c & a & bendmatrix…IPMAT Indore 2022 · Quantitative Ability · Matrices and Determinants
Q26If A= [ beginmatrix1 & 0 \\ (1)/(2)& 0endmatrix ] then A²⁰²² isIPMAT Indore 2022 · Quantitative Ability · Matrices and Determinants
Q27For 0<θ <(π)/(4) , let a= ( sin θ )^(sin θ) (log_2cos θ ) , b= ( cos θ )^(sin θ) (log_2sin θ ) , c= ( sin θ )^(cos θ)…IPMAT Indore 2022 · Quantitative Ability · Trigonometry
Q28Let A=\1,2,3\ and B=a,b\ . Assuming all relations from set A to set B are equally likely, what is the probability that…IPMAT Indore 2022 · Quantitative Ability · Probability
Q29In a 400-metre race, Ashok beats Bipin and Chandan respectively by 15 seconds and 25 seconds. If Ashok beats Bipin by…IPMAT Indore 2022 · Quantitative Ability · Time Speed and Distance
Q30In a bowl containing 60 ml orange juice, 40 ml of water is poured. Thereafter, 100 ml of apple juice is poured to make…IPMAT Indore 2022 · Quantitative Ability · Mixtures and Alligation
Q31The curve represented by the equation (x²)/(sin √2-sin √3)+(y²)/(cos √2-cos √3)=1 isIPMAT Indore 2022 · Quantitative Ability · Conic Sections
Q32A set of all possible values the function f ( x )=(x)/( | x |) , where x≠ 0 , takes isIPMAT Indore 2022 · Quantitative Ability · Functions
Q33When the square of the difference of two natural numbers is subtracted from the square of the sum of the same two…IPMAT Indore 2022 · Quantitative Ability · HCF and LCM
Q34The cost of a piece of jewellery is proportional to the square of its weight. A piece of jewellery weighing 10 grams…IPMAT Indore 2022 · Quantitative Ability · Ratio and Proportion
Q35The sum of the squares of all the roots of the equation x²+ | x+4 |+ | x-4 |-35=0 isIPMAT Indore 2022 · Quantitative Ability · Inequalities & Modulus
Q36Let A and B be two sets such that the Cartesian product A× B consists of four elements. If two elements of A× B are (…IPMAT Indore 2022 · Quantitative Ability · Set Theory
Q37If f (x²+f ( y ) )=xf ( x )+y for all non-negative integers x and y , then the value of [ f ( 0 ) ]²+f ( 0 ) equalsIPMAT Indore 2022 · Quantitative Ability · Functions
Q38If one of the factors of the number 3⁷2⁸17³ is randomly chosen, then the probability that the chosen factor will be a…IPMAT Indore 2022 · Quantitative Ability · Probability
Q39The number of four-digit integers which are greater than 1000 and divisible by both 2 and 3, but not by 5, isIPMAT Indore 2022 · Quantitative Ability · Divisibility
Q40Ayesha is standing atop a vertical tower 200 m high and observes a car moving away from the tower on a straight,…IPMAT Indore 2022 · Quantitative Ability · Heights and Distances
Q41Number of days Bhabha and Cathy work together in a week isIPMAT Indore 2022 · Quantitative Ability · Arrangement and Distribution
Q42Which among the following employees do not work together on any of the days?IPMAT Indore 2022 · Quantitative Ability · Arrangement and Distribution
Q43One of the days Alex works on isIPMAT Indore 2022 · Quantitative Ability · Arrangement and Distribution
Q44The consecutive days on which Ethan works areIPMAT Indore 2022 · Quantitative Ability · Arrangement and Distribution
Q45Employees who work on Sunday areIPMAT Indore 2022 · Quantitative Ability · Arrangement and Distribution

Verbal Ability · 45 questions

RC passage 1Passage 1 – Why some fruits keep ripening after picking Q34–Q39 RC passage 2Passage 2 – Edward Jenner and the first vaccinations Q40–Q45