Aptitude and Reasoning Questions

Two circles touch each other at point X. Two common tangents of the circles meet at point P and none of the tangents passes through X. These tangents touch the larger circle at points B and C. If the radius of the larger circle is 15 cm and CP = 20 cm, then what is the radius (in cm) of the smaller circle?

Select the odd letters from the given alternatives.

A boy and a girl are facing each other. If the boy is standing at the north-west direction of the girl, in which direction is the girl to the boy?

Facing North, Aishwarya turns 45 deg clockwise, then 135 deg anticlockwise and then 180 deg clockwise. Which direction is she is facing now?

In the following question, select the odd letter/letters from the given alternatives.

In the following question, two statements are given each followed by two conclusions I and II. You have to consider the statements to be true even if they seem to be at variance from commonly known facts. You have to decide which of the given conclusions, if any, follows from the given statements.

Statements:
(I) Library is a place where one may find any answer to his/her question.
(II) Books in any form whether physical or electronic are advantageous for resolving any kind of query.

Conclusion:
(I) Every question has an answer and one can find it in a book.
(II) Books give all related information pertaining to the title they have.

The table given below shows the information about bats manufactured by 6 different companies. Each company manufactures only plastic and wooden bats. Each company labels these bats as Brand A and Brand B. The table shows the number of plastic bats as a percentage of total bats manufactured by each company. It also shows the ratio of wooden bats labeled A and B. Each company manufactured a total of 550000 bats.

P = Sum of wooden bats of Brand B manufactured by S and wooden bats of Brand A manufactured by W.
Q = Difference of Brand B wooden bats and Brand A wooden bats manufactured by U.
What is the value P – Q?

In the question, a word is represented by only one set of numbers as given in any one of the alternatives. The sets of numbers given in the alternatives are represented by two classes of alphabets as in two matrices given below. The columns and rows of Matrix I are numbered from 0 to 4 and that of Matrix II are numbered from 5 to 9. A letter from these matrices can be represented first by its row and next by its column, e.g., 'K' can be represented by 42, 34, etc. and 'Z' can be represented by 96, 79 etc. You have to identify the set for the word 'ROAD'.