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Q1:

The terms of a geometric progression are real and positive. If the pp-th term of the progression is qq and the qq-th term is pp, then the logarithm of the first term is
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Option: 2
Correct Answer
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Q2:

If the shortest distance of a given point to a given circle is 4 cm4 \, \text{cm} and the longest distance is 9 cm9 \, \text{cm}, then the radius of the circle is
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Option: 4
Correct Answer
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Q3:

If ∣x+1∣+(y+2)2=0|x+1| + (y+2)^2 = 0 and ax−3ay=1ax - 3ay = 1, then the value of aa is
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Option: 1
Correct Answer
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Q4:

The number of real solutions of the equation x2−10∣x∣−56=0x^2 - 10|x| - 56 = 0 is
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Option: 4
Correct Answer
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Q5:

The greatest number among 23002^{300}, 32003^{200}, 41004^{100}, 2100+31002^{100} + 3^{100} is
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Option: 2
Correct Answer
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Q6:

The sum of a given infinite geometric progression is 80 and the sum of its first two terms is 35. Then the value of nn for which the sum of its first nn terms is closest to 100, is
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Option: 2
Correct Answer
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Q7:

Let nn be the number of ways in which 20 identical balloons can be distributed among 5 girls and 3 boys such that everyone gets at least one balloon and no girl gets fewer balloons than a boy does. Then
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Option: 0
Correct Answer
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Q8:

Let a=(log⁡74)(log⁡75−log⁡72)log⁡725(log⁡78−log⁡74)a = \dfrac{(\log_7 4)(\log_7 5 - \log_7 2)}{\log_{7} 25 (\log_7 8 - \log_7 4)}. Then the value of 5a5^a is
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Option: 2
Correct Answer
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Q9:

The smallest possible number of students in a class if the girls in the class are less than 50% but more than 48% is
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Option: 1
Correct Answer
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Q10:

The side AB of a triangle ABC is c. The median BD is of length k. If ∠BDA=θ\angle BDA = \theta and θ<90∘\theta < 90^\circ, then the area of triangle ABC is
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Option: 2
Correct Answer
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Q11:

Let △ABC\triangle ABC be a triangle with AB=ACAB = AC and DD be a point on BCBC such that ∠BAD=30∘\angle BAD = 30^\circ. If EE is a point on ACAC such that AD=AEAD = AE, then ∠CDE\angle CDE equals
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Option: 4
Correct Answer
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Q12:

If log⁡4x=a\log_4 x = a and log⁡25x=b\log_{25} x = b, then log⁡x10\log_x 10 is
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Option: 3
Correct Answer
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Q13:

If 5 boys and 3 girls sit randomly around a circular table, the probability that there will be at least one boy sitting between any two girls is
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Option: 2
Correct Answer
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Q14:

A fruit seller had a certain number of apples, bananas, and oranges at the start of the day. The number of bananas was 10 more than the number of apples, and the total number of bananas and apples was a multiple of 11. She was able to sell 70% of the apples, 60% of bananas, and 50% of oranges during the day. If she was able to sell 55% of the fruits she had at the start of the day, then the minimum number of oranges she had at the start of the day was
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Option: 2
Correct Answer
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Q15:

A boat goes 96 km upstream in 8 hours and covers the same distance moving downstream in 6 hours. On the next day it starts from point A, goes downstream for 1 hour, then upstream for 1 hour, and repeats this for four more times, that is, 5 upstream and 5 downstream journeys. Then the boat would be
Answer options
Option: 2
Correct Answer
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Q16:

The number of solutions of the equation x1+x2+x3+x4=50x_1 + x_2 + x_3 + x_4 = 50, where x1,x2,x3,x4x_1, x_2, x_3, x_4 are integers with x1≥1,x2≥2,x3≥0,x4≥0x_1 \geq 1, x_2 \geq 2, x_3 \geq 0, x_4 \geq 0 is
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Option: 3
Correct Answer
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Q17:

The numbers 220242^{2024} and 520245^{2024} are expanded and their digits are written out consecutively on one page. The total number of digits written on the page is
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Option: 2
Correct Answer
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Q18:

If θ \theta is the angle between the pair of tangents drawn from the point (0,72)(0,\frac{7}{2}) to the circle x2+y2−14x+16y+88=0x^2 + y^2 - 14x + 16y + 88 = 0, then tan⁡θ\tan \theta equals
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Option: 4
Correct Answer
Explanation →

Q19:

The difference between the maximum real root and the minimum real root of the equation (x2−5)4+(x2−7)4=16(x^2 - 5)^4 + (x^2 - 7)^4 = 16 is
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Option: 4
Correct Answer
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Q20:

The angle of elevation of the top of a pole from a point A on the ground is 30°. The angle of elevation changes to 45°, after moving 20 meters towards the base of the pole. Then the height of the pole, in meters, is
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Option: 4
Correct Answer
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Q21:

The number of values of xx for which C(17−x3x+1)C \binom {17-x}{3x+1} is defined as an integer is
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Option: 4
Correct Answer
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Q22:

Let ABC be an equilateral triangle, with each side of length kk. If a circle is drawn with diameter AB, then the area of the portion of the triangle lying inside the circle is
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Option: 1
Correct Answer
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Q23:

Sagarika divides her savings of 1000010000 rupees to invest across two schemes A and B. Scheme A offers an interest rate of 10%10\% per annum, compounded half-yearly, while scheme B offers a simple interest rate of 12%12\% per annum. If at the end of first year, the value of her investment in scheme B exceeds the value of her investment in scheme A by 23102310 rupees, then the total interest, in rupees, earned by Sagarika during the first year of investment is
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Option: 4
Correct Answer
Explanation →

Q24:

In a survey of 500 people, it was found that 250 owned a 4-wheeler but not a 2-wheeler, 100 owned a 2-wheeler but not a 4-wheeler, and 100 owned neither a 4-wheeler nor a 2-wheeler. Then the number of people who owned both is
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Option: 4
Correct Answer
Explanation →

Q25:

For some non-zero real values of a,ba, b and cc, it is given that ∣ca∣=4,∣ab∣=13\left|\frac{c}{a}\right|=4,\left|\frac{a}{b}\right|=\frac{1}{3} and bc=−34\frac{b}{c}=-\frac{3}{4}. If ac>0a c>0, then (b+ca)\left(\frac{b+c}{a}\right) equals
Answer options
Option: 1
Correct Answer
Explanation →

Q26:

In an election there were five constituencies S1, S2, S3, S4, and S5 with 20 voters each all of whom voted. Three parties A, B, and C contested the elections. The party that gets the maximum number of votes in a constituency wins that seat. In every constituency there was a clear winner. The following additional information is available:
- Total number of votes obtained by A, B, and C across all constituencies are 49, 35 and 16 respectively.\newline - S2 and S3 were won by C while A won only S1. \newline - Number of votes obtained by B in S1, S2, S3, S4, and S5 are distinct natural numbers in increasing order.
The constituency in which B got lower number of votes compared to A and C is
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Option: 3
Correct Answer
Explanation →

Q27:

In an election there were five constituencies S1, S2, S3, S4, and S5 with 20 voters each all of whom voted. Three parties A, B, and C contested the elections. The party that gets the maximum number of votes in a constituency wins that seat. In every constituency there was a clear winner. The following additional information is available:
- Total number of votes obtained by A, B, and C across all constituencies are 49, 35 and 16 respectively.\newline - S2 and S3 were won by C while A won only S1. \newline - Number of votes obtained by B in S1, S2, S3, S4, and S5 are distinct natural numbers in increasing order.
The number of votes obtained by B in S2 is
Answer options
Option: 3
Correct Answer
Explanation →

Q28:

In an election there were five constituencies S1, S2, S3, S4, and S5 with 20 voters each all of whom voted. Three parties A, B, and C contested the elections. The party that gets the maximum number of votes in a constituency wins that seat. In every constituency there was a clear winner. The following additional information is available:
- Total number of votes obtained by A, B, and C across all constituencies are 49, 35 and 16 respectively.\newline - S2 and S3 were won by C while A won only S1. \newline - Number of votes obtained by B in S1, S2, S3, S4, and S5 are distinct natural numbers in increasing order.
The number of votes obtained by A in S5 is
Answer options
Option: 3
Correct Answer
Explanation →

Q29:

In an election there were five constituencies S1, S2, S3, S4, and S5 with 20 voters each all of whom voted. Three parties A, B, and C contested the elections. The party that gets the maximum number of votes in a constituency wins that seat. In every constituency there was a clear winner. The following additional information is available:
- Total number of votes obtained by A, B, and C across all constituencies are 49, 35 and 16 respectively.\newline - S2 and S3 were won by C while A won only S1. \newline - Number of votes obtained by B in S1, S2, S3, S4, and S5 are distinct natural numbers in increasing order.
Comparing the number votes obtained by A across different constituencies, the lowest number of votes were in constituency
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Option: 4
Correct Answer
Explanation →

Q30:

In an election there were five constituencies S1, S2, S3, S4, and S5 with 20 voters each all of whom voted. Three parties A, B, and C contested the elections. The party that gets the maximum number of votes in a constituency wins that seat. In every constituency there was a clear winner. The following additional information is available:
- Total number of votes obtained by A, B, and C across all constituencies are 49, 35 and 16 respectively.\newline - S2 and S3 were won by C while A won only S1. \newline - Number of votes obtained by B in S1, S2, S3, S4, and S5 are distinct natural numbers in increasing order.
Assume that A and C had formed an alliance and any voter who voted for either A or C would have voted for this alliance. Then the number of seats this alliance would have won is
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Option: 3
Correct Answer
Explanation →

IPMAT Indore 2024 MCQ Past Year Questions (Free PDF Download)

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