Choose the odd word/letters/number/number pair from the given alternatives.

During   the   mid   19th century   Industrial Revolution,   the   average   life   span   of workers in Manchester was

Which phenomena shows the particle nature of light?

If x+1/x = 2, then the value of x7+2/x6 is equal to?

Look at the underlined part of each sentence. Below each sentence are given three possible substitutions for the underlined part. If one of them (a), (b) or (c) is better than the underlined part, indicate your response on the Answer Sheet against the corresponding letter. If none of the substitutions imporves the sentence, indicate (d) as your response on the Answer Sheet.

Your services are dispensed for.

Each item consists of six sentences of a passage. The first and sixth sentences are given in the beginning as S1 and S6. The middle four sentences in each have been jumbled up and labelled as P, Q, R and S. You are required to find the proper sequence of the four sentences and mark your response accordingly on the Answer Sheet.

S1 :The Nobel Prize for Economics in 2018 was awarded to Paul Romer and William Nordhaus for their work in two separate areas : economic growth and environmental economics respectively.
S6 :Among recent winners of Nobel Prize in Economics, it’s hard to think of one issue which is more topical and relevant to India.
P :But there is a common thread in their work.
Q : In economic jargon it’s termed as externality.
R : Productive activity often has spillovers, meaning that it can impact an unrelated party.
S :Romer and Nordhaus both studied the impact of externalities and came up with profound insights and economic models.
The correct sequence should be

If x2+ y2+ z2= xy + yz + zx, then what is the value of (7x + 3y – 5z)/5x?

A cube is inscribed in a sphere. A right circular cylinder is within the cube touching all the vertical faces. A right circular once is inside the cylinder. Their heights are same and the diameter of the cone is equal to that of the cylinder.

What is the ratio of the volume of the sphere to that of cone?