SOLVE_IN_SECONDS_III_YRS

If a, b, c and d are positive integers such that 1/a, 1/b, 1/c and 1/d form an arithmetic progression, which of the following is true?

• ab > cd

• ab < cd

• ab = cd

• can't be determined

In the festival of Diwali, Vishnu lights some diyas. At 6:30 p.m, he lights one ‘diya’. At 7:30 p.m, he lights two ‘diyas’. At 8:30 p.m, he lights 3 diyas and so on. But due to wind the ‘diyas’ extinguish exactly after burning for half an hour, i.e. at 7:00 p.m. , 8:00 p.m. and so on. The oil in the diyas lasts for exactly one hour. Knowing this, Vishnu reuses the ‘diya’ without changing the oil. Find the minimum number of ‘diyas’ if Vishnu lights the last set of diyas at 12:30 am.

• 10

• 7

• 14

• 28

In a school fete, a participant arranged a total of 1000 balls, of four types, in a long straight line. If he first placed one green ball, then two red balls, three blue balls, four yellow balls, five green balls, six red balls, seven blue balls, eight yellow balls and so on (with green balls followed by red balls followed by blue balls followed by yellow balls) up to 1000 balls, what was the position of the 100^th red ball? (in numerical value)

• 439

• 437

• 412

• 413

Two trains T₁ and T₂ are travelling on parallel tracks and in opposite directions. P₁ and P₂ are two persons who are travelling in T₁ and T₂ respectively. When the two trains just start to cross each other, P₁, who is at the tail end of T₁, starts running towards the front end of T₁, at a speed of 6 m/s, and P₂, who is at the front end of T₂ starts running towards the tail end of T₂ at a speed of 4 m/s. If the lengths of T₁ and T₂ are 216m and 432 m respectively, and the speeds of T₁and T₂ are 108km/hr and 144 km/hr respectively, in how much time (from the time T₁ and T₂ start to cross each other) will the two persons cross each other? (in seconds)

Enter the numerical value alone, without unit.

It is given that log₆ a + log₆ b + log₆ c = 6, where a, b, and c are positive integers that form an increasing geometric sequence and (b – a) is the square of an integer. Find a + b + c. (Type in the answer)

What is the value of f(2), if f(x) = |5 – 3x|?

• f(1)

• f(2/3)

• f(4/3)

• f(-4/3)

A function is defined as f(x + y) = f(x).f(y), for all natural numbers x and y. If f(1) = 2 and a and n are natural numbers such that f(a + 1) + f(a + 2) + f(a + 3) + ................. + f(a + n) = 16(2ⁿ - 1), what is the value of a? (in numerical value)

• 1

• 2

• 3

• 4

Fresh grapes 90% water by weight while dry grapes contain 10% of water. What is the weight (kg) of dry grapes available from 270 kg of fresh grapes.

• 24

• 27

• 30

• 33

Raghu and Raj have got 70% of the marbles accumulated by four of the friends. Kala and Dev 30%; and Dev and Raghu together have 50%. If Raj has 25 more marbles than Kala and Kala in turn has 25 more marbles than what Dev has, then what is the total number of marbles?

• 100

• 250

• 225

• can't be determined

A rabbit is feeding on some carrots at the corner of a square field. It has its burrow at an adjacent corner. During its carrot-chewing, the rabbit spots a fox at the other adjacent corner and starts running towards its burrow. The fox keeps on running towards the rabbit during the chase (of course it does not know about the burrow). If the rabbit’s speed is 10 m/s and given that the fox follows the shortest route then what should be the range of fox’s speed, so that he is just able to catch the rabbit as it enters the burrow?

• Between 10 m/s and 13.9 m/s

• Between 14.14 m/s and 20 m/s

• Between 5.2 m/s and 9.1 m/s

• Between 20.1 m/s and 24.2 m/s