Practice IPMAT Indore 2023 Question Paper with Solutions

Vinita drives a car which has four gears. The speed of the car in the fourth gear is five times its speed in the first gear. The car takes twice the time to travel a certain distance in the second gear as compared to the third gear. In a 100 km journey, if Vinita travels equal distances in each of the gears, she takes 585 minutes to complete the journey. Instead, if the distances covered in the first, second, third, and fourth gears are 4 km, 4 km, 32 km, and 60 km, respectively, then the total time taken, in minutes, to complete the journey, will be

The remainder when \(1! + 2! + 3! + ... + 95!\) is divided by \(15\) is

Let \(a, b, c, d\) 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 of \(a + c\) is

In an election with only two contesting candidates, 15% of the voters did not turn up to vote and 50 voters cast invalid votes. It is known that 44% of all the voters in the voting list voted for the winner. If the winner got 200 votes more than the other candidate, then the number of voters in the voting list is

If \(f(1) = 1\) and \(f(n) = 3n - f(n - 1)\) for all integers \(n > 1\) , then the value of \(f(2023)\) is

If three consecutive coefficients in the expansion of \((x+y)^n\) are in the ratio \(1:9:63\), then the value of \(n\) is

In a chess tournament, there are four groups, each containing an equal number of players. Each player plays

1. against every other player belonging to one's own group exactly once;

2. against each player belonging to one of the remaining three groups exactly twice;

3. against each player belonging to one of the remaining two groups exactly three times; and

4. against each player belonging to the remaining group exactly four times.

If there are more than 1000 matches being played in the tournament, the minimum possible number of players in each group is

The product of the roots of the equation \(\log_{2} 2^{(\log_{2}x)^{2}} -5 \log_{2}x\) \({}+6 = 0\) is

The total number of positive integer solutions of \(21 ≤ a + b + c ≤ 25\) is

The length of the line segment joining the two intersection points of the curves \(y = 4970 - |x|\) and \(y = x ^ 2\) is