IPMAT Indore 2022 - QA (MCQ)

IPMAT Indore 2022 - QA (MCQ)

Questions: 15 (+4/-1)                                                          Sectional Time:  40 Minutes

16. The sum of the squares of all the roots of the equation x2 + |x + 4| + |x - 4| - 35 = 0 is

• (a) 50
• (b) 74
• (c) 175
• (d) 148

17. Let A – {1, 2, 3} and B - {a, b}. Assuming all relations front set A to set B are equally likely, what is the probability that a relation from A to B is also a function?

• (a) 1/2
• (b) 32/26
• (c) 1/8
• (d) 1

18. If the five-digit number abcde is divisible by 6, then which of the following numbers is not necessarily divisible by 6?

• (a) edcba
• (b) eee
• (c) bbadcacede
• (d) cdbae

19. The set of real values of x for which the inequality log27 8 ≤ log3x < 9^1/log23 hold

• (a) [2,81)
• (b) [2,27]
• (c) [2,81]
• (d) (2,27]

20. Suppose a, b and c are integers such that a > b > c > 0, and A = [ a b c b c a c a b ] Then the value of the determinant of A

• (a) can be positive or negative
• (b) is positive
• (c) is negative
• (d) is zero

21. The lengths of the sides of a triangle are x, 21 and 40, where x is the shortest side. A possible value of x is

• (a) 16
• (b) 18
• (c) 20
• (d) 19

22. If A = [ 1 0 1/2 0 ] , then A^2022 is

• (a) [ 1 0 2022 0 ]
• (b) [ 1 0 2011 0 ]
• (c) [ 1 0 1/22022 0 ]
• (d) None of these

23. The sum of the first 15 terms in an arithmetic progression is 200, while the sum of the next 15 terms is 350. Then the common difference is

• (a) 7/9
• (b) 1/3
• (c) 4/9
• (d) 2/3

24. The cost of a piece of jewellery is proportional to the square of its weight. A piece of jewellery weighing 10 grams is INR 3600. The cost of a piece of jewellery of the same kind weighing 4 grams is

• (a) INR 576
• (b) INR 1220
• (c) INR 1440
• (d) INR 600

25. When the square of the difference of two natural numbers is subtracted from the square of the sum of the same two numbers and the result is divided by four, we get

• (a) the HCF of the two numbers
• (b) the LCM of the two numbers
• (c) the square of the product of the two numbers
• (d) the product of the LCM and HCF of the two numbers

26. In a 400-metre race, Ashok beats Bipin and Chandan respectively by 15 seconds and 25 seconds. If Ashok beats Bipin by 150 metres, by how many metres does Bipin beat Chandan in the race?

• (a) 150
• (b) 50
• (c) 80
• (d) 100

27. The set of all possible values of f(x) for which (81)x + (81)f(x) = 3 is

• (a) (-∞, 0.25)
• (b) (3,4)
• (c) (0.25,3)
• (d) (-∞, 4)

28. Let A and B be two sets such that the Cartesian product A × B consists of four elements. If two elements of A × B are (1, 4) and (4, 1), then

• (a) ∅ ∈A×B
• (b) A×B=B×A
• (c) None of these
• (d) A×B≠B×A

29. In a right-angled triangle ABC, the hypotenuse AC is of length 13 cm. A line drawn connecting the midpoints D and E of sides AB and AC is found to be 6 cm in length. The length of BC is

• (a) 8 cm
• (b) 5 cm
• (c) 2√3 cm
• (d) 12 cm

30. In a bowl containing 60 ml orange juice, 40 ml of water is poured. Thereafter, 100 ml of apple juice is poured to make a fruit punch. Madhu drinks 50 ml of this fruit punch and comments that the proportion of orange juice needs to be higher for better taste. How much orange juice should be poured into the fruit punch that remained, in order to bring up the level of orange juice to 50 percentage?

• (a) 60 ml
• (b) 80 ml
• (c) 40 ml
• (d) 100 ml

31. In a room, there are n persons whose average height is 160 cm. If m more persons, whose average height is 172 cm, enter the room, then the average height of all persons in the room becomes 164 cm. Then m : n is

• (a) 1 : 3
• (b) 2 : 1
• (c) 1 : 2
• (d) 3 : 1

32. For 0 < θ <π/4 , let a = ((sinθ)^sinθ)(log2 cosθ), b = ((cosθ)^sinθ)(log2 sinθ), c = ((sinθ)^cosθ)(log2 cosθ) and d = ((sinθ)^sinθ)(log2 sinθ). Then, the median value in the sequence a, b, c, d is

• (a) c+d/2
• (b) a+d/2
• (c) a+c/2
• (d) b+c/2

33. If f(x^2 + f(y)) = xf(x) + y for all non-negative integers x and y, then the value of [f(0)]2+f (0) equals________.

• (a) 0
• (b) 6
• (c) 2
• (d) 1

34. The curve represented by the equation x^2/sin√2−sin√3 + y^2/cos√2−cos√3 =1

• (a) a hyperbola with the foci on the x-axis
• (b) an ellipse with the foci on the x-axis
• (c) an ellipse with the foci on the y-axis
• (d) a hyperbola with the foci on the y-axis

35. The number of four-digit integers which are greater than 1000 and divisible by both 2 and 3, but not by 5, is

• (a) 1334
• (b) 1500
• (c) 1666
• (d) 1200

36. Ayesha is standing atop a vertical tower 200m high and observes a car moving away from the tower on a straight horizontal road from the foot of the tower. At 11:00 AM, she observes the angle of depression of the car to be 45°. At 11:02 AM, she observes the angle of depression of the car to be 30°. The speed at which the car is moving is approximately

• (a) 6.3 km per hour
• (b) 4.39 km per hour
• (c) 8.45 km per hour
• (d) 10.6 km per hour

37. If one of the factors of the number 37 28 173 is randomly chosen, then the probability that the chosen factor will be a perfect square is.

• (a) 5/32
• (b) 5/36
• (c) 3/40
• (d) 1/12

38. The value of k for which the following lines x-y-1 = 0 2x+3y-12 = 0 2x-3y+k = 0 are concurrent is

• (a) -1
• (b) 12
• (c) 0
• (d) 1

39. A set of all possible values the function f(x)= x/|x| , where x ≠ 0, takes is

• (a) {1,−1}
• (b) {1,0}
• (c) {1,0,−1}
• (d) {1}

40. In how many ways can the letters of the word MANAGEMENT be arranged such that no two vowels appear together?

• (a) 21600
• (b) 25200
• (c) 37800
• (d) 75600

Directions (Q.41-Q.45): A showroom is open on all seven days of the week throughout the year. There are five employees Alex, Bhabha, Cathy, Dilip and Ethan who work in the showroom. Every day except Sunday, two employees are required while on Sunday three employees need to work. Every employee works for three days in a week. Some additional information is also provided: • Every employee works on two consecutive days while the third day is not consecutive. • Alex and Dilip work together on Tuesday and Wednesday while the other working day differs for them. • Neither Bhabha nor Cathy works with Alex on any day. • Cathy does not work either on Saturday or on Monday.

41. Number of days Bhabha and Cathy work together in a week is

• (a) 0
• (b) 1
• (c) 3
• (d) 2

42. The consecutive days on which Ethan works are

• (a) Thursday and Friday
• (b) Sunday and Monday
• (c) Saturday and Sunday
• (d) Friday and Saturday

43. Which among the following employees do not work together on any of the days?

• (a) Cathy and Dilip
• (b) Bhabha and Dilip
• (c) Dilip and Ethan
• (d) Bhabha and Ethan

44. Employees who work on Sunday are

• (a) Alex, Dilip and Ethan
• (b) Bhabha, Cathy and Dilip
• (c) Bhabha, Cathy and Ethan
• (d) Cathy, Dilip and Ethan

45. One of the days Alex works on is

• (a) Saturday
• (b) Friday
• (c) Monday
• (d) Sunday