If x and y are two digits and the number 4x5y790 is divisible by 11, then what is the remainder, if x + y is divided by 11?

A cut on a solid object divides the object into two parts where the new surfaces thus produced are plane. On the other hand, one single cut can be used to cut more than one object at a time. In an experiment, the total number of pieces produced by applying n cuts is denoted by xn. The experiment is performed on a solid cube where pieces remain unmoved after each cut. In this experiment, if after the third cut, the pieces are identical, then which of the following is not a possible value for x4?

There are three types of rectangular tiles: 3′ × 3′, 3′ × 7′ and 3′ × 11′. An area of rectangular shape of dimensions 3′ × 100′ is to be covered using these tiles without breaking them. If x and y are the maximum and minimum numbers of tiles of various sizes, respectively, that can be used to cover the area exactly, then x − y is

If the product of the HCF and LCM of two distinct numbers is the cube of one of the numbers, then which of the following statements is/are correct?
I. The difference of the numbers is an even number.
II. One of the numbers is a perfect square.

Alloy P contains 20% copper and 80% zinc by weight. Alloy Q contains 60% copper and 40% zinc.

A third alloy R is prepared by mixing P and Q so that R contains equal quantities of copper and zinc.

In what ratio should P and Q be mixed?

A train travels at 100 km/h and a person at 4 km/h. When the person travels in the same direction as the train, the train takes 15 seconds to cross him. If the person travels in the opposite direction, approximately how long will the train take to cross him?

X travels 6 km by bicycle. He travels the first 1 km at 5 km/h, the next 2 km at 10 km/h and the final 3 km at 4 km/h.

Y covers the same distances at 4 km/h, 10 km/h and 5 km/h respectively. If both start together, how many minutes earlier does Y finish?

A train has to cover 800 km. After a minor accident its speed becomes half of its existing speed; after a mechanical defect it becomes one-fourth of its existing speed.

In the actual journey, the accident occurs after 200 km and the mechanical defect occurs 400 km later. In the alternative order, the mechanical defect occurs after 200 km and the accident 400 km later. The alternative journey takes 4 hours more. Find the original speed.

X and Y run on the same circular track in the same direction. When X completes 7 rounds, Y completes 5 rounds. After completing 5 rounds, Y reverses direction and runs at twice his original speed. X continues at the same speed. They stop when X completes 21 rounds. How many times do they meet after starting and before stopping?

An explosion occurs at some distance from an army camp. When the sound reaches the camp, a drone starts flying to the explosion site at 30 m/s. The first picture is received at 5:02 PM. Another drone immediately starts and reaches the explosion site 3 minutes later, with the second picture received at 5:05 PM. If sound travels at 300 m/s, when did the explosion occur?

P, Q, R, S and T are ranked 1 to 5 (not necessarily in that order).

The rank of P is 4.

The rank of Q is not 5.

The rank of R is 1.

The rank of S is not 2.

The rank of T is not 3.

Then which of the following is/are correct?

I. If the rank of S is 3, then that of T is 2.

II. If the rank of Q is 3, then that of T is 5.

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