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IPMAT Indore 2023 Past Year Papers with Solutions filter tool

Q1:

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
312
Correct Answer
Explanation →

Q2:

The remainder when 1!+2!+3!+...+95!1! + 2! + 3! + ... + 95! is divided by 1515 is
3
Correct Answer
Explanation →

Q3:

Let a,b,c,da, b, c, d be positive integers such that a+b+c+d=2023a + b + c + d = 2023. If a:b=2:5a: b = 2:5 and c:d=5:2c:d=5:2, then the maximum possible value of a+ca + c is
1442
Correct Answer
Explanation →

Q4:

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
5000
Correct Answer
Explanation →

Q5:

If f(1)=1f(1) = 1 and f(n)=3n−f(n−1)f(n) = 3n - f(n - 1) for all integers n>1n > 1 , then the value of f(2023)f(2023) is
3034
Correct Answer
Explanation →

Q6:

In the xy-plane let A=(−2,0),B=(2,0)A = (- 2, 0), B = (2, 0) . Define the set S as the collection of all points C on the circle x2+y2=4x ^ 2 + y ^ 2 = 4 such that the area of the triangle ABC is an integer. The number of points in the set S is
14
Correct Answer
Explanation →

Q7:

If three consecutive coefficients in the expansion of (x+y)n(x+y)^n are in the ratio 1:9:631:9:63, then the value of nn is
39
Correct Answer
Explanation →

Q8:

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; \newline 2. against each player belonging to one of the remaining three groups exactly twice; \newline 3. against each player belonging to one of the remaining two groups exactly three times; and \newline 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
8
Correct Answer
Explanation →

Q9:

The product of the roots of the equation log⁡22(log⁡2x)2−5log⁡2x+6=0\log_{2} 2^{(\log_{2}x)^{2}} -5 \log_{2}x+6=0 is
32
Correct Answer
Explanation →

Q10:

The total number of positive integer solutions of 21≤a+b+c≤2521 ≤ a + b + c ≤ 25 is
1160
Correct Answer
Explanation →

Q11:

The length of the line segment joining the two intersection points of the curves y=4970−∣x∣y = 4970 - |x| and y=x2y = x ^ 2 is
140
Correct Answer
Explanation →

Q12:

If f(n)=1+2+3+⋯+(n+1)f(n)= 1 + 2 + 3 +\cdots+(n+1) and g(n)=∑k=1k=n1f(k)g(n)= \sum_{k=1}^{k=n} \dfrac{1}{f(k)}, then the least value of nn for which g(n)g(n) exceeds the value 99100\dfrac{99}{100} is:
199
Correct Answer
Explanation →

Q13:

The polynomial 4x10−x9+3x11−5x7+cx6+2x5−x4+x3−4x2+6x−24x ^ {10} - x ^ 9 + 3x ^ {11} - 5x ^ 7 + c x ^ 6 + 2x ^ 5 - x ^ 4 + x ^ 3 - 4x ^ 2 + 6x - 2 when divided by x−1x - 1 leaves a remainder 22. Then the value of c+6c + 6 is
5
Correct Answer
Explanation →

Q14:

Assume it is the beginning of the year today. Ankita will earn INR 10,000 at the end of the year, which she plans to invest in a bank deposit immediately at a fixed simple interest of 0.5% per annum. Her yearly income will increase by INR 10,000 every year, and the fixed simple interest offered by the bank on new deposits will also increase by 0.5% per annum every year. If Ankita continues to invest all her yearly income in new bank deposits at the end of each year, the total interest earned by her, in INR, in five years from today will be
2500
Correct Answer
Explanation →

Q15:

Amisha can complete a particular task in twenty days. After working for four days she fell sick for four days and resumed the work on the ninth day but with half of her original work rate. She completed the task in another twelve days with the help of a co-worker who joined her from the ninth day. The number of days required for the co-worker to complete the task alone would be
24
Correct Answer
Explanation →

IPMAT Indore 2023 SA Past Year Questions (Free PDF Download)

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