IPMAT Indore 2023 question paper with solutions

All 90 questions of IPMAT Indore 2023, 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 1Five drugs and three organisms Q41–Q45

Q1In a chess tournament, there are four groups, each containing an equal number of players. Each player plays against…IPMAT Indore 2023 · Quantitative Ability · Permutation and Combination
Q2The remainder when 1!+2!+3!+cdots +95! is divided by 15 is _____IPMAT Indore 2023 · Quantitative Ability · Remainder Theorem
Q3Amisha can complete a particular task in twenty days. After working for four days she fell sick for four days and…IPMAT Indore 2023 · Quantitative Ability · Time and Work
Q4The length of the line segment joining the two intersection points of the curves y=4970- | x | and y=x² is _____IPMAT Indore 2023 · Quantitative Ability · Graphs and Transformations
Q5If f ( 1 )=1 and f ( n )=3n-f ( n-1 ) for all integer n>1 , then the value of f ( 2023 ) is _____IPMAT Indore 2023 · Quantitative Ability · Functions
Q6The product of the roots of the equation log_2 (2^( (log_2x )²) )-5log_2x+6=0 is _____IPMAT Indore 2023 · Quantitative Ability · Logarithms
Q7Assume it is the beginning of the year today. Ankita will earn ₹10,000 at the end of the year which she plans to…IPMAT Indore 2023 · Quantitative Ability · Simple Interest
Q8The polynomial 4x¹⁰-x⁹+3x⁸-5x⁷+cx⁶+2x⁵-x⁴+x³-4x²+6x-2 when divided by x-1 leaves a remainder 2. Then the value of c+6…IPMAT Indore 2023 · Quantitative Ability · Polynomials
Q9In an election with only two contesting candidates, 15% of the voters did not turn up to vote, and 50 voters cast…IPMAT Indore 2023 · Quantitative Ability · Percentage
Q10If f ( n )=1+2+3+cdots + ( n+1 ) and g ( n )=sum_k=1ⁿ(1)/(f ( k )) , then the least value of n for which g ( n )…IPMAT Indore 2023 · Quantitative Ability · Sequences and Series
Q11Vinita drives a car which has four gears. The speed of the car in the fourth gear is five times its speed in the first…IPMAT Indore 2023 · Quantitative Ability · Time Speed and Distance
Q12The total number of positive integer solutions of 21≤ a+b+c≤ 25 is _____IPMAT Indore 2023 · Quantitative Ability · Permutation and Combination
Q13Let a, b, c, d be positive integers such that a+b+c+d=2023 . If a:b=2:5 and c:d=5:2 , then the maximum possible value…IPMAT Indore 2023 · Quantitative Ability · Ratio and Proportion
Q14In the xy-plane let A = (-2, 0), B = (2, 0). Define the set S as the collection of all points C on the circle x²+y²=4…IPMAT Indore 2023 · Quantitative Ability · Coordinate Geometry (Basics)
Q15If three consecutive coefficients in the expansion of ( x+y )ⁿ are in the ratio 1 : 9 : 63, then the value of n is _____IPMAT Indore 2023 · Quantitative Ability · Binomial Theorem
Q16In a triangle ABC, let D be the mid-point of BC, and AM be the altitude on BC. If the lengths of AB, BC and CA are in…IPMAT Indore 2023 · Quantitative Ability · Triangles
Q17Let a, b, c be real numbers greater than 1, and n be a positive real number not equal to 1. If log_n (log_2a )=1 ,…IPMAT Indore 2023 · Quantitative Ability · Logarithms
Q18Let a_1,a_2,a_3 be three distinct real numbers in geometric progression. If the equations a_1x²+2a_2x+a_3=0 and…IPMAT Indore 2023 · Quantitative Ability · Quadratic Equations
Q19In a chess tournament there are 5 contestants. Each player plays against all the others exactly once. No game results…IPMAT Indore 2023 · Quantitative Ability · Deductive Reasoning
Q20If cos α +cos β =1 , then the maximum value of sin α -sin β isIPMAT Indore 2023 · Quantitative Ability · Trigonometry
Q21In a group of 120 students, 80 students are from the Science stream and the rest are from the Commerce stream. It is…IPMAT Indore 2023 · Quantitative Ability · Set Theory
Q22The probability that a randomly chosen positive divisor of 10²⁰²³ is an integer multiple of 10²⁰⁰¹ isIPMAT Indore 2023 · Quantitative Ability · Probability
Q23Consider an 8 × 8 chessboard. The number of ways 8 rooks can be placed on the board such that no two rooks are in the…IPMAT Indore 2023 · Quantitative Ability · Permutation and Combination
Q24A polynomial p(x) leaves a remainder 2 when divided by ( x-1 ) and a remainder 1 when divided by ( x-2 ) . The…IPMAT Indore 2023 · Quantitative Ability · Polynomials
Q25A rabbit is sitting at the base of a staircase which has 10 steps. It proceeds to the top of the staircase by climbing…IPMAT Indore 2023 · Quantitative Ability · Permutation and Combination
Q26If A= [ beginmatrix1 & 2 \\ 3 & aendmatrix ] , where a is a real number and det (A³-3A²-5A )=0 , then one of the…IPMAT Indore 2023 · Quantitative Ability · Matrices and Determinants
Q27If (a+b)/(b+c)=(c+d)/(d+a) , which of the following is always true?IPMAT Indore 2023 · Quantitative Ability · Algebraic Identities
Q28If the difference between compound interest and simple interest for a certain amount of money invested for 3 years at…IPMAT Indore 2023 · Quantitative Ability · Compound Interest
Q29A person standing at the center of an open ground first walks 32 meters towards the east, takes a right turn and walks…IPMAT Indore 2023 · Quantitative Ability · Sequences and Series
Q30Let p be a positive integer such that the unit digit of p³ is 4. What are the possible unit digits of ( p+3 )³ ?IPMAT Indore 2023 · Quantitative Ability · Unit Digit and Cyclicity
Q31The set of all real values of x satisfying the inequality (x² ( x+1 ))/( ( x-1 ) ( 2x+1 )³)>0 isIPMAT Indore 2023 · Quantitative Ability · Inequalities & Modulus
Q32A goldsmith bought a large solid golden ball at ₹1000000 and melted it to make a certain number of solid spherical…IPMAT Indore 2023 · Quantitative Ability · Profit Loss and Discount
Q33Which of the following straight lines are both tangent to the circle x²+y²-6x+4y-12=0 ?IPMAT Indore 2023 · Quantitative Ability · Circles
Q34The equation x²+y²-2x-4y+5=0 representsIPMAT Indore 2023 · Quantitative Ability · Circles
Q35Let [x] denote the greatest integer not exceeding x and x\=x- [ x ] . If n is a natural number, then the sum of all…IPMAT Indore 2023 · Quantitative Ability · Functions
Q36If log_cos x ( sin x )+log_sin x ( cos x )=2 , then the value of x isIPMAT Indore 2023 · Quantitative Ability · Trigonometry
Q37The minimum number of times a fair coin must be tossed so that the probability of getting at least one head exceeds…IPMAT Indore 2023 · Quantitative Ability · Probability
Q38If a three-digit number is chosen at random, what is the probability that it is divisible neither by 3 nor by 4?IPMAT Indore 2023 · Quantitative Ability · Probability
Q39If the harmonic mean of the roots of the quadratic ( 5+√2 )x²-bx+8+2√5=0 is 4, then the value of b isIPMAT Indore 2023 · Quantitative Ability · Quadratic Equations
Q40A helicopter flies along the sides of a square field of side length 100 kms. The first side is covered at a speed of…IPMAT Indore 2023 · Quantitative Ability · Time Speed and Distance
Q41Organism R can be treated withIPMAT Indore 2023 · Quantitative Ability · Reasoning Based DI
Q42Drug E works onIPMAT Indore 2023 · Quantitative Ability · Reasoning Based DI
Q43The organism(s) that can be treated with three of these five drugs is(are)IPMAT Indore 2023 · Quantitative Ability · Reasoning Based DI
Q44Drug D works onIPMAT Indore 2023 · Quantitative Ability · Reasoning Based DI
Q45Organism P can be treated withIPMAT Indore 2023 · Quantitative Ability · Reasoning Based DI

Verbal Ability · 45 questions

RC passage 1Passage 1 – Sleep, fitness and the cost of insomnia Q34–Q39 RC passage 2Passage 2 – Apple’s retail stores and the Indian market Q40–Q45