IPMAT Indore 2022 - QA (SA)

IPMAT Indore 2022 - QA (SA)

Questions: 15 (+4/-0)                                                          Sectional Time:  40 Minutes

1. The 3rd, 14th and 69th terms of an arithmetic progression form three distinct and consecutive terms of a geometric progression. If the next terms of the geometric progression is the nth term of the arithmetic progression, then n equals____________.

2. The area enclosed by 2|x| + 3|y| ≤ 6 is____________ sq. units

3. 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_________.

4. If sin α + sin β= √2/√3 and cos α + cos β = 1/√3 , then the value of (20 cos( α − β/2 ))^2 is.

5. The sum of the coefficients of all the terms in the expansion of (5x - 9)^4 is __________.

6. 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% profit and all the mangoes at 20% loss, overall she makes neither profit nor loss. Instead, if she sells all the apples at 20% loss and all the mangoes at 10% profit, overall she makes a loss of INR 150. Then the number of apples purchased by Aruna is_________.

7. If 𝑙𝑜𝑔𝑥2𝑦+𝑙𝑜𝑔𝑦2𝑥=1 and y = x2 - 30. Then the value of x2 + y2 is___________.

8. Let P(X) denote power set of a set X. If A is the null set, then the number of elements in P(P(P(P(A)))) is_____________.

9. A new sequence is obtained from the sequence of positive integers (1, 2, 3,...) by deleting all the perfect squares. Then the 2022nd term of the new sequence is___________.

10. If A=[ 1 0 0 0 0 1 0 1 0 ] ,Then the absolute value of the determinant of (A^0+A^6+A^3+A) is __________________.

11. The numbers -16, 2^x+3 - 2^2x -1 -16, 2^2x-1 + 16 are in an arithmetic progression. Then x equals _________.

12. Given that f(x) = |x| + 2|x - 1| + |x - 2| + |x - 4| + |x - 6| + 2|x - 10|, x ∈ (-∞, ∞), the minimum value of f(x) is_________.

13. When Geeta increases her speed from 12 km/hr to 20 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.

14. 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 _________.

15. 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 _____