IPM Indore 2022

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?

Suppose a, b and c are integers such that a > b > c > 0, and $$A =\begin{bmatrix}a & b & c \\ b & c & a \\c & a & b \end{bmatrix}$$. Then the value of the determinant of A

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

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

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

If $$A = \begin{bmatrix}1 & 0 \\ \frac{1}{2} & 0 \end{bmatrix}$$. Then $$A^{2022}$$ is

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.

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

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

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 $$45^{\circ}$$. 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