Quantitative Aptitude - Arithmetic Ability Questions

In the following question, four groups of three numbers are given. In each group the second and third number are related to the first number by a Logic/Rule/Relation. Three are similar on basis of same Logic/Rule/Relation. Select the odd one out from the given alternatives.

If the ∠ABC and ∠ACB of triangle ABC is 80 deg and 60 deg respectively. If the Incenter of the triangle is at point ‘I’ then calculate angle BIC.

The value of sec2θ + 2tanθcotθ - tan2θ is

If (x + y)/z = 2, then what is the value of [y/(y – z)] + [x/(x – z)]?

The lengths of two diagonals of a rhombus are 24 cm and 32 cm. What is the side (in cm) of the rhombus?

If the number x4562 is divisible by 9, what is the face value of x?

A boat is moving away from an observation tower. It makes an angle of depression of 60° with an observer's eye when at a distance of 50m from the tower. After 8 sec., the angle of depression becomes 30°. By assuming that it is running in still water, the approximate speed of the boat is

If 2x - 6 ≤ x - 3 and 1+3x < 4x + 4, then x can take which of the following values?