IPMAT Rohtak 2019

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

Simplification: 18800 / 470 / 20

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

If $$\log 2, \log(2^{x}-1)$$ and $$\log(2^{x}+3)$$ are in A.P, then x is equal to ______________