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Q1:

For 0<θ<π40\lt\theta\lt\frac{\pi}{4}, let a=((sin⁡θ)sin⁡θ)(log⁡2cos⁡θ),b=((cos⁡θ)sin⁡θ)(log⁡2sin⁡θ),c=((sin⁡θ)cos⁡θ)(log⁡2cos⁡θ)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=((sin⁡θ)sin⁡θ)(log⁡2sin⁡θ)d=\left((\sin \theta)^{\sin \theta}\right)\left(\log _{2} \sin \theta\right). Then, the median value in the sequence a,b,c,da, b, c, d is
Answer options
Option: 2
Correct Answer
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Q2:

The set of real values of xx for which the inequality log⁡278≤log⁡3x<91log⁡23\log _{27} 8 \leq \log _{3} x \lt 9^{\frac{1}{\log _{2} 3}} holds is
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Option: 1
Correct Answer
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Q3:

The set of all possible values of f(x)f(x) for which (81)x+(81)f(x)=3(81)^{x}+(81)^{f(x)}=3 is
Answer options
Option: 3
Correct Answer
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Q4:

Ayesha is standing atop a vertical tower 200m200 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∘45^{\circ}. At 11:02 AM, she observes the angle of depression of the car to be 30∘30^{\circ}. The speed at which the car is moving is approximately
Answer options
Option: 4
Correct Answer
Explanation →

Q5:

The value of kk for which the following lines are concurrent is
x−y−1=02x+3y−12=02x−3y+k=0x-y-1=0 \newline 2x+3y-12=0 \newline 2x-3y+k=0
Answer options
Option: 3
Correct Answer
Explanation →

Q6:

The sum of the squares of all the roots of the equation x2+∣x+4∣+∣x−4∣−35=0x^{2}+|x+4|+|x-4|-35=0 is
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Option: 3
Correct Answer
Explanation →

Q7:

The lengths of the sides of a triangle are x,21x, 21 and 4040, where xx is the shortest side. A possible value of xx is:
Answer options
Option: 2
Correct Answer
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Q8:

If the five-digit number abcde is divisible by 6, then which of the following numbers is not necessarily divisible by 6?
Answer options
Option: 1
Correct Answer
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Q9:

In how many ways can the letters of the word MANAGEMENT be arranged such that no two vowels appear together?
Answer options
Option: 3
Correct Answer
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Q10:

In a room, there are nn persons whose average height is 160 cm160 \ \text{cm}. If mm more persons, whose average height is 172 cm172 \ \text{cm}, enter the room, then the average height of all persons in the room becomes 164 cm164 \ \text{cm}. Then m:nm: n is
Answer options
Option: 1
Correct Answer
Explanation →

Q11:

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
Answer options
Option: 2
Correct Answer
Explanation →

Q12:

Suppose a,ba, b and cc are integers such that a>b>c>0a>b>c>0, and A=[abcbcacab]A=\left[\begin{array}{lll}a & b & c \\ b & c & a \\ c & a & b\end{array}\right]. Then the value of the determinant of AA is
Answer options
Option: 3
Correct Answer
Explanation →

Q13:

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
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Option: 1
Correct Answer
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Q14:

If A=[10120]A=\left[\begin{array}{ll}1 & 0 \\ \frac{1}{2} & 0\end{array}\right] then A2022A^{2022} is
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Option: 4
Correct Answer
Explanation →

Q15:

Let A={1,2,3}A=\{1,2,3\} and B={a,b}B=\{a, b\}. Assuming all relations from set AA to set BB are equally likely, what is the probability that a relation from AA to BB is also a function?
Answer options
Option: 1
Correct Answer
Explanation →

Q16:

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?
Answer options
Option: 1
Correct Answer
Explanation →

Q17:

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?
Answer options
Option: 4
Correct Answer
Explanation →

Q18:

The curve represented by the equation x2sin⁡2−sin⁡3+y2cos⁡2−cos⁡3=1 \dfrac{x^{2}}{\sin \sqrt{2}-\sin \sqrt{3}}+\dfrac{y^{2}}{\cos \sqrt{2}-\cos \sqrt{3}}=1 is
Answer options
Option: 1
Correct Answer
Explanation →

Q19:

A set of all possible values the function f(x)=x∣x∣f(x)=\dfrac{x}{|x|}, where x≠0x \neq 0, takes is
Answer options
Option: 2
Correct Answer
Explanation →

Q20:

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
Answer options
Option: 1
Correct Answer
Explanation →

Q21:

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
Answer options
Option: 3
Correct Answer
Explanation →

Q22:

Let AA and BB be two sets such that the Cartesian product A×BA \times B consists of four elements. If two elements of A×BA \times B are (1,4)(1,4) and (4,1)(4,1), then
Answer options
Option: 4
Correct Answer
Explanation →

Q23:

If f(x2+f(y))=xf(x)+yf\left(x^{2}+f(y)\right)=x f(x)+y for all non-negative integers xx and yy, then the value of [f(0)]2+f(0)[f(0)]^{2}+f(0) equals _________.
Answer options
Option: 2
Correct Answer
Explanation →

Q24:

If one of the factors of the number 37281733^{7} 2^{8} 17^{3} is randomly chosen, then the probability that the chosen factor will be a perfect square is
Answer options
Option: 1
Correct Answer
Explanation →

Q25:

The number of four-digit integers which are greater than 1000 and divisible by both 2 and 3, but not by 5, is
Answer options
Option: 3
Correct Answer
Explanation →

Q26:

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.

Number of days Bhabha and Cathy work together in a week is
Answer options
Option: 4
Correct Answer
Explanation →

Q27:

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.

Which among the following employees do not work together on any of the days?
Answer options
Option: 4
Correct Answer
Explanation →

Q28:

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.

One of the days Alex works on is
Answer options
Option: 4
Correct Answer
Explanation →

Q29:

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.

The consecutive days on which Ethan works are
Answer options
Option: 3
Correct Answer
Explanation →

Q30:

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.

Employees who work on Sunday are
Answer options
Option: 1
Correct Answer
Explanation →

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

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