IPM Question Paper 2022 | IPM Indore Quants

IPMAT Question Paper | IPMAT Sample Paper

IPMAT 2022 Question Paper Indore Quants. Solve questions from IPMAT 2022 Question Paper from IPM Indore and check the solutions to get adequate practice.

  1. IPMAT 2022 Question Paper - IPM Indore Quants

    If \(\log _{\left(x^{2}\right)} y+\log _{\left(y^{2}\right)} x=1\) and \(y=x^{2}-30\), then the value of \(x^{2}+y^{2}\) is ___________.

    72

  2. IPMAT 2022 Question Paper - IPM Indore Quants

    The area enclosed by \(2|x|+3|y| \leq 6\) is ____________ sq. units.

    12

  3. IPMAT 2022 Question Paper - IPM Indore Quants

    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 ___________ \(km .\)

    30

  4. IPMAT 2022 Question Paper - IPM Indore Quants

    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

  5. IPMAT 2022 Question Paper - IPM Indore Quants

    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 _________.

    50

  6. IPMAT 2022 Question Paper - IPM Indore Quants

    Given that \( f(x)=|x|+2|x-1|+|x-2|+|x-4|+|x-6|+2|x-10|, x \in(-\infty, \infty) \) the minimum value of \(f(x)\) is _________.

    26

  7. IPMAT 2022 Question Paper - IPM Indore Quants

    If \(A=\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0\end{array}\right]\), then the absolute value of the determinant of \(\left(A^{9}+A^{6}+A^{3}+A\right)\) is __________.

    32

  8. IPMAT 2022 Question Paper - IPM Indore Quants

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

    256

  9. IPMAT 2022 Question Paper - IPM Indore Quants

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

    2067

  10. IPMAT 2022 Question Paper - IPM Indore Quants

    If \(\sin \alpha+\sin \beta=\frac{\sqrt{2}}{\sqrt{3}}\) and \(\cos \alpha+\cos \beta=\frac{1}{\sqrt{3}}\), then the value of \(\left(20 \cos \left(\frac{\alpha-\beta}{2}\right)\right)^{2}\) is _________.

    100

  11. IPMAT 2022 Question Paper - IPM Indore Quants

    The \(3^{\text {rd }}, 14^{\text {th }}\) and \(69^{\text {th }}\) 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 \(n^{\text {th }}\) term of the arithmetic progression, then \(n\) equals ________.

    344

  12. IPMAT 2022 Question Paper - IPM Indore Quants

    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 _________.

    16

  13. IPMAT 2022 Question Paper - IPM Indore Quants

    The numbers \(-16,2^{x+3}-2^{2 x-1}-16,2^{2 x-1}+16\) are in an arithmetic progression. Then \(x\) equals ________.

    3

  14. IPMAT 2022 Question Paper - IPM Indore Quants

    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

  15. IPMAT 2022 Question Paper - IPM Indore Quants

    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

  16. IPMAT 2022 Question Paper - IPM Indore Quants

    The set of real values of \(x\) for which the inequality \(\log _{27} 8 \leq \log _{3} x \lt 9^{\frac{1}{\log _{2} 3}}\) holds is

    1. [2,81)
    2. (2,27)
    3. [2,81]
    4. (2,27]
    Choice A
    [2,81)

  17. IPMAT 2022 Question Paper - IPM Indore Quants

    The set of all possible values of \(f(x)\) for which \((81)^{x}+(81)^{f(x)}=3\) is

    1. (0.25,3)
    2. \((-\infty, 4)\)
    3. \((-\infty, 0.25)\)
    4. (3,4)
    Choice C
    \((-\infty, 0.25)\)

  18. IPMAT 2022 Question Paper - IPM Indore Quants

    The value of \(k\) for which the following lines \[ \begin{array}{l} x-y-1=0 \\ 2 x+3 y-12=0 \\ 2 x-3 y+k=0 \end{array} \] are concurrent is

    1. 1
    2. -1
    3. 0
    4. 12
    Choice C
    0

  19. IPMAT 2022 Question Paper - IPM Indore Quants

    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

    1. 18
    2. 20
    3. 19
    4. 16
    Choice B
    20

  20. IPMAT 2022 Question Paper - IPM Indore Quants

    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

    1. 12 cm
    2. 5 cm
    3. \(2 \sqrt{3} cm\)
    4. 8 cm
    Choice A
    12 cm

  21. IPMAT 2022 Question Paper - IPM Indore Quants

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

    1. edcba
    2. eee
    3. bbadcacede
    4. cdbae
    Choice A
    edcba

  22. IPMAT 2022 Question Paper - IPM Indore Quants

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

    1. 75600
    2. 25200
    3. 37800
    4. 21600
    Choice C
    37800

  23. IPMAT 2022 Question Paper - IPM Indore Quants

    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

    1. 1 : 2
    2. 1 : 3
    3. 3 : 1
    4. 2 : 1
    Choice A
    1 : 2

  24. IPMAT 2022 Question Paper - IPM Indore Quants

    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

    1. \(\frac{7}{9}\)
    2. \(\frac{2}{3}\)
    3. \(\frac{4}{9}\)
    4. \(\frac{1}{3}\)
    Choice B
    \(\frac{2}{3}\)

  25. IPMAT 2022 Question Paper - IPM Indore Quants

    Suppose \(a, b\) and \(c\) are integers such that \(a>b>c>0\), and \(A=\left[\begin{array}{lll}a & b & c \\ b & c & a \\ c & a & b\end{array}\right]\). Then the value of the determinant of \(A\)

    1. can be positive or negative
    2. is positive
    3. is negative
    4. is zero
    Choice C
    is negative

  26. IPMAT 2022 Question Paper - IPM Indore Quants

    If \(A=\left[\begin{array}{ll}1 & 0 \\ \frac{1}{2} & 0\end{array}\right]\) then \(A^{2022}\) is

    1. None of these
    2. \(\left[\begin{array}{cc}1 & 0 \\ 1011 & 0\end{array}\right]\)
    3. \(\left[\begin{array}{cc}1 & 0 \\ 2022 & 0\end{array}\right]\)
    4. \(\left[\begin{array}{cc}1 & 0 \\ \frac{1}{2^{2022}} & 0\end{array}\right]\)
    Choice B
    \(\left[\begin{array}{cc}1 & 0 \\ 1011 & 0\end{array}\right]\)

  27. IPMAT 2022 Question Paper - IPM Indore Quants

    For \(0\lt\theta\lt\frac{\pi}{4}\), let \(a=\left((\sin \theta)^{\sin \theta}\right)\left(\log _{2} \cos \theta\right), b=\left((\cos \theta)^{\sin \theta}\right)\left(\log _{2} \sin \theta\right)\), \(c=\left((\sin \theta)^{\cos \theta}\right)\left(\log _{2} \cos \theta\right)\) and \(d=\left((\sin \theta)^{\sin \theta}\right)\left(\log _{2} \sin \theta\right)\). Then, the median value in the sequence \(a, b, c, d\) is

    1. \(\frac{a+b}{2}\)
    2. \(\frac{a+d}{2}\)
    3. \(\frac{b+c}{2}\)
    4. \(\frac{c+d}{2}\)
    Choice B
    \(\frac{a+d}{2}\)

  28. IPMAT 2022 Question Paper - IPM Indore Quants

    Let \(A=\{1,2,3\}\) and \(B=\{a, b\}\). Assuming all relations from set \(A\) to set \(B\) are equally likely, what is the probability that a relation from \(A\) to \(B\) is also a function?

    1. \(\frac{1}{8}\)
    2. \(\frac{1}{2}\)
    3. 1
    4. \(\frac{3^{2}}{2^{6}}\)
    Choice A
    \(\frac{1}{8}\)

  29. IPMAT 2022 Question Paper - IPM Indore Quants

    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?

    1. 80
    2. 100
    3. 150
    4. 50
    Choice A
    80

  30. IPMAT 2022 Question Paper - IPM Indore Quants

    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?

    1. 100 ml
    2. 40 ml
    3. 80 ml
    4. 60 ml
    Choice D
    60 ml

  31. IPMAT 2022 Question Paper - IPM Indore Quants

    The curve represented by the equation \( \frac{x^{2}}{\sin \sqrt{2}-\sin \sqrt{3}}+\frac{y^{2}}{\cos \sqrt{2}-\cos \sqrt{3}}=1 \) is

    1. an ellipse with the foci on the y-axis
    2. an ellipse with the foci on the x-axis
    3. a hyperbola with the foci on the x-axis
    4. a hyperbola with the foci on the y-axis
    Choice A
    an ellipse with the foci on the y-axis

  32. IPMAT 2022 Question Paper - IPM Indore Quants

    A set of all possible values the function \(f(x)=\frac{x}{|x|}\), where \(x \neq 0\), takes is

    1. \(\{1\}\)
    2. \(\{1,-1\}\)
    3. \(\{1,0\}\)
    4. \(\{1,0,-1\}\)
    Choice B
    \(\{1,-1\}\)

  33. IPMAT 2022 Question Paper - IPM Indore Quants

    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

    1. the product of the LCM and HCF of the two numbers
    2. the HCF of the two numbers
    3. the LCM of the two numbers
    4. the square of the product of the two numbers
    Choice A
    the product of the LCM and HCF of the two numbers

  34. IPMAT 2022 Question Paper - IPM Indore Quants

    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

    1. INR 1220
    2. INR 600
    3. INR 576
    4. INR 1440
    Choice C
    INR 576

  35. IPMAT 2022 Question Paper - IPM Indore Quants

    The sum of the squares of all the roots of the equation \(x^{2}+|x+4|+|x-4|-35=0\) is

    1. 74
    2. 175
    3. 50
    4. 148
    Choice C
    50

  36. IPMAT 2022 Question Paper - IPM Indore Quants

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

    1. None of these
    2. \(A \times B \neq B \times A\)
    3. \(\emptyset \in A \times B\)
    4. \(A \times B=B \times A\)
    Choice D
    \(A \times B=B \times A\)

  37. IPMAT 2022 Question Paper - IPM Indore Quants

    If \(f\left(x^{2}+f(y)\right)=x f(x)+y\) for all non-negative integers \(x\) and \(y\), then the value of \([f(0)]^{2}+f(0)\) equals _________.

    1. 2
    2. 0
    3. 6
    4. 1
    Choice B
    0

  38. IPMAT 2022 Question Paper - IPM Indore Quants

    If one of the factors of the number \(3^{7} 2^{8} 17^{3}\) is randomly chosen, then the probability that the chosen factor will be a perfect square is

    1. \(\frac{5}{36}\)
    2. \(\frac{1}{12}\)
    3. \(\frac{3}{40}\)
    4. \(\frac{5}{32}\)
    Choice A
    \(\frac{5}{36}\)

  39. IPMAT 2022 Question Paper - IPM Indore Quants

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

    1. 1333
    2. 1666
    3. 1200
    4. 1500
    Choice C
    1200

  40. IPMAT 2022 Question Paper - IPM Indore Quants

    Ayesha is standing atop a vertical tower \(200 m\) 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 \(45^{\circ}\). At 11:02 AM, she observes the angle of depression of the car to be \(30^{\circ}\). The speed at which the car is moving is approximately

    1. 6.3 km per hour
    2. 8.45 km per hour
    3. 10.6 km per hour
    4. 4.39 km per hour
    Choice D
    4.39 km per hour

  41. 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.

  42. IPMAT 2022 Question Paper - IPM Indore Quants

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

    1. 0
    2. 1
    3. 3
    4. 2
    Choice D
    2

  43. IPMAT 2022 Question Paper - IPM Indore Quants

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

    1. Bhabha and Dilip
    2. Bhabha and Ethan
    3. Cathy and Dilip
    4. Dilip and Ethan
    Choice D
    Dilip and Ethan

  44. IPMAT 2022 Question Paper - IPM Indore Quants

    One of the days Alex works on is

    1. Monday
    2. Friday
    3. Sunday
    4. Saturday
    Choice D
    Saturday

  45. IPMAT 2022 Question Paper - IPM Indore Quants

    The consecutive days on which Ethan works are

    1. Thursday and Friday
    2. Saturday and Sunday
    3. Friday and Saturday
    4. Sunday and Monday
    Choice C
    Friday and Saturday

  46. IPMAT 2022 Question Paper - IPM Indore Quants

    Employees who work on Sunday are

    1. Bhabha, Cathy and Dilip
    2. Bhabha, Cathy and Ethan
    3. Alex, Dilip and Ethan
    4. Cathy, Dilip and Ethan
    Choice A
    Bhabha, Cathy and Dilip

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