Aptitude and Reasoning Questions

PQ and RS are common tangents to two circles intersecting at A and B. AB, when produced both sides, meet the tangents PQ and RS at X and Y, respectively. If AB = 3 cm, XY = 5 cm, then PQ (in cm) will be

Of the 3 numbers whose average is 40, the first is 1/3 rd the sum of other 2. What is the first number?

If X + Y + Z = 9 then the value of (X -­ 4)3 + (Y -­ 2)3 + (Z -­ 3)3 - 3 (X -­ 4) (Y -­ Z) (Z ­- 3) is

Select the related number from the given alternatives.
-3/7 : 7/3 :: 9/2 : ?

In the question two statements are given, followed by two conclusions, I and II. You have to consider the statements to be true even if it seems to be at variance from commonly known facts. You have to decide which of the given conclusions, if any, follows from the given statements
 
Statement I:
All cells are chargers
Statement II:
All batteries are cells

Conclusion I:
Some chargers are batteries
Conclusion II:
All batteries are chargers

If in a two digit number, the digit at unit place is y and the digit at tens place is 5, then the number is

Find equation of the perpendicular to segment joining the points A(0,4) and B(-5,9) and passing through the point P. Point P divides segment AB in the ratio 2:3.

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., 'B' can be represented by 00, 13 etc., and 'A' can be represented by 55, 69 etc.

Similarly you have to identify the set for the word 'GIRL'