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IPMAT Indore 2022 (SA) PYQs

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IPMAT Indore 2022 Past Year Papers with Solutions filter tool

Q1:

If log⁡(x2)y+log⁡(y2)x=1\log _{\left(x^{2}\right)} y+\log _{\left(y^{2}\right)} x=1 and y=x2−30y=x^{2}-30, then the value of x2+y2x^{2}+y^{2} is ___________.
72
Correct Answer
Explanation →

Q2:

The area enclosed by 2∣x∣+3∣y∣≤62|x|+3|y| \leq 6 is ____________ sq. units.
12
Correct Answer
Explanation →

Q3:

When Geeta increases her speed from 1212 km/hr to 2020 km/hr, she takes one hour less than the usual time to cover the distance between her home and office. The distance between her home and office is ___________ km.
30
Correct Answer
Explanation →

Q4:

The number of triangles that can be formed by choosing points from 7 points on a line and 5 points on another parallel line is _________.
175
Correct Answer
Explanation →

Q5:

Aruna purchases a certain number of apples for INR 20 each and a certain number of mangoes for INR 25 each. If she sells all the apples at 10%10 \% profit and all the mangoes at 20%20 \% loss, overall she makes neither profit nor loss. Instead, if she sells all the apples at 20%20 \% loss and all the mangoes at 10%10 \% profit, overall she makes a loss of INR 150. Then the number of apples purchased by Aruna is _________.
50
Correct Answer
Explanation →

Q6:

Given that f(x)=∣x∣+2∣x−1∣+∣x−2∣+∣x−4∣+∣x−6∣+2∣x−10∣,x∈(−∞,∞) f(x)=|x|+2|x-1|+|x-2|+|x-4|+|x-6|+2|x-10|, x \in(-\infty, \infty) the minimum value of f(x)f(x) is _________.
26
Correct Answer
Explanation →

Q7:

If A=[100001010]A=\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0\end{array}\right], then the absolute value of the determinant of (A9+A6+A3+A)\left(A^{9}+A^{6}+A^{3}+A\right) is __________.
32
Correct Answer
Explanation →

Q8:

The sum of the coefficients of all the terms in the expansion of (5x−9)4(5 x-9)^{4} is __________.
256
Correct Answer
Explanation →

Q9:

A new sequence is obtained from the sequence of positive integers (1,2,3,…)(1,2,3, \ldots) by deleting all the perfect squares. Then the 2022nd 2022^{\text {nd }} term of the new sequence is ________.
2067
Correct Answer
Explanation →

Q10:

If sin⁡α+sin⁡β=23\sin \alpha+\sin \beta=\frac{\sqrt{2}}{\sqrt{3}} and cos⁡α+cos⁡β=13\cos \alpha+\cos \beta=\frac{1}{\sqrt{3}}, then the value of (20cos⁡(α−β2))2\left(20 \cos \left(\frac{\alpha-\beta}{2}\right)\right)^{2} is _________.
100
Correct Answer
Explanation →

Q11:

The 3rd ,14th 3^{\text {rd }}, 14^{\text {th }} and 69th 69^{\text {th }} terms of an arithmetic progression form three distinct and consecutive terms of a geometric progression. If the next term of the geometric progression is the nth n^{\text {th }} term of the arithmetic progression, then nn equals ________.
344
Correct Answer
Explanation →

Q12:

Let P(X)P(X) denote power set of a set XX. If AA is the null set, then the number of elements in P(P(P(P(A))))P(P(P(P(A)))) is _________.
16
Correct Answer
Explanation →

Q13:

The numbers −16,2x+3−22x−1−16,22x−1+16-16,2^{x+3}-2^{2 x-1}-16,2^{2 x-1}+16 are in an arithmetic progression. Then xx equals ________.
3
Correct Answer
Explanation →

Q14:

Mrs and Mr Sharma, and Mrs and Mr Ahuja along with four other persons are to be seated at a round table for dinner. If Mrs and Mr Sharma are to be seated next to each other, and Mrs and Mr Ahuja are not to be seated next to each other, then the total number of seating arrangements is _________.
960
Correct Answer
Explanation →

Q15:

Let 50 distinct positive integers be chosen such that the highest among them is 100, and the average of the largest 25 integers among them exceeds the average of the remaining integers by 50. Then the maximum possible value of the sum of all the 50 integers is _________.
3150
Correct Answer
Explanation →

IPMAT Indore 2022 SA Past Year Questions (Free PDF Download)

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