IPMAT Rohtak (QA) PYQs

A container contains X litres of milk. A thief stole 50 litres of milk and replaced it with the same quantity of water. He repeated the same process further two times. And thus, milk in the container is only X-122 litres. What is the quantity of water in the final mixture?

Veena has to pay Rs. 2460 to Sita, 5 months later at 6% simple interest per annum, and Gita has to pay Sita the same amount at 7.5% simple interest per annum after certain months. If both took the same amount of loan from Sita then Gita paid the loan after how many months?

<img src="https://balti.afterboards.in/Y6y1nS3bwbKovTU" width="300px"/> What is the area of the shaded figure? Use the figure below to answer questions.

<img src="https://balti.afterboards.in/Y6y1nS3bwbKovTU" width="300px"/> What is the ratio of the area of Circle M to the area of Circle K?

If $x\%$ of $y$ is equal to $z$ then what percentage of $z$ is $x$?

Train A takes 45 minutes more than train B to travel 450 km. Due to engine trouble, the speed of train B falls by a quarter. So it takes 30 minutes more than Train A to complete the same journey. Find the speed of Train A.

One Trader calculates the percentage of profit on the buying price and another calculates on the selling price. When their selling prices are the same, then the difference of their actual profit is Rs 85 and both claim to have made 20% profit. What is the selling price for each?

Due to increase of 20% in the price of eggs, 2 eggs less are available for Rs 24. The present rate of eggs per dozen is

$\sin(\frac{13\pi}{6})$

Fruits were purchased for Rs 350. 9 boys ate $\frac{3}{5}$ of them in 2 hours. 6 boys feel their stomach as full so do not eat further. In how many hours the remaining fruits will get finished by remaining boys?

If the minimum value of $f(x) = x^2 + 2bx + 2c^2$ is greater than the maximum value of $g(x) = -x^2 - 2cx + b^2$, then for real value of x.

The set of all real numbers x for which $x^2 - |x + 2| + x > 0$, is

What should come at the place of question mark? $\newline 46080, 3840, 384, 48, 8, 2, ?$

A room has floor size of $15 \times 6$ sq.cm. What is the height of the room, if the sum of the areas of the base and roof is equal to the sum of the areas of the four walls?

The sum of third and ninth term of an A.P is 8. Find the sum of the first 11 terms of the progression.

Given $(A = 2^{65})$ and $(B = 2^{64} + 2^{63} + 2^{62} + ... + 2^0)$, which of the following is true?

A line from center to circumference of a circle is known as

A bag contains 4 blue, 5 white and 6 green balls. Two balls are drawn at random. What is the probability that one ball is white?

Two pipes P and Q can fill a tank in $20$ hrs and $25$ hrs respectively while a third pipe R can empty the tank in $30$ hrs. If all the pipes are opened together for $10$ hrs and then pipe R is closed, then in what time the tank can be filled?

Given ratios are $a : b = 2 : 3, b : c = 5 : 2, c : d = 1 : 4$. Find $a : b : c$.

If there are Rs 495 in a bag in denominations of one-rupee, 50 paisa and 25 paisa coins, which are in the ratio 1 : 8 : 16. How many 50 paisa coins are there in the bag?

What decimal of an hour is a second?

What will be the vulgar fraction of 0.0056?

One-fifth of a number is equal to $(\frac{5}{8})^{th}$ of another number. If 35 is added to the first number, it becomes four times the second number. Find the second number.

If * = +, / = -, + = *, - = / then 43 * 561 + 500 - 100 / 10 = ?

A circle is inscribed in an equilateral triangle of side 24 cm, touching its sides. What is the area of the remaining portion of the triangle?

A clock strikes 4 taking 9 seconds. In order to strike 12 at the same rate, the time taken is

John's present age is one fourth of his father's age two years ago. John's father's age will be twice Raman's age after 10 years. If Raman's 12th birthday was celebrated 2 years ago, then what is John's present age?

Raj invested Rs 76000 in a business. After few months Monty joined him and invests Rs 57000. At the end of the year, both of them share the profits at the ratio of 2:1. After how many months Monty joined Raj?

Work done by P in one day is double the work done by Q in one day and work done by Q in one day is thrice the work done by R in one day. If P, Q, and R together can complete the work in 30 days, then in how many days P alone can do the work?

A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes. How long will it take to go 5 km in stationary water?

Simplification: $25^{2.7} \times 5^{4.2} \div 5^{5.4} = ?$

$18800 / 470 / 20 =$

Find the HCF of $\frac{2}{3}, \frac{4}{6}, \frac{8}{27}$

If $\log 2, \log (2x - 1), \log (2x + 3)$ are in A.P, then $x$ is equal to ____