GATE Questions

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Given Prabhas is twice as good a workman as Rana.

Prabhas finishes the work in 3 hrs

=> Rana finishes the work in 6 hrs.

Number of hours required together they could finish the work

= 3 x 6 / 3 + 6

= 18/9

= 2 hrs.

Money invested by Rajan before 1 year was = Rs. 100000

Money in UK pounds @ 75 is = 100000/75 = 1333.33 Pounds

Now, after 1 year invested amount was appreciated by 20%

=> 20% of 1333.33 = 266.66

Total investment becomes = 1333.33 + 266.66 = 1600 Pounds

This 1600 Pounds @ Indian currency at 80 = 1600 x 80 = Rs. 1,28,000

Hence, Rajan's investment of Rs. 1,00,000 becomes Rs. 1,28,000 in 1 year

Therefore, his profit % = [(128000 - 100000)/100000] x 100 = 28%.

Nutrients are necessary for break down the food and supply energy to the organisms and to carry out essential life functions.

• Important nutrients are Hydrogen, Carbon and Oxygen.

• Some more important nutrients for plants are : Potassium, Sulphur, Nitrogen, Phosphorous, Calcium and Magnesium. 

Time taken to cover 600 km = 600/100 = 6 hrs.

Number of stoppages = 600/75 - 1 = 7

Total time of stoppages = 4 x 7 = 28 min

Hence, total time taken = 6 hrs 28 min.

As you were asleep, none of the things could have happened without doing "open your eyes" first.

Draw the two chords as shown in the figure. Let O be the center of the circle. Draw OC
perpendicular to both chords. That divides the two chords in half.
So CD = 10 and AB = 14. Draw radii OA and OD, both equal to radius r.
We are given that BC = 5, the distance between the two chords. Let
OB = x.

We use the Pythagorean theorem on right triangle ABO

AO² = AB² + OB²
r² = 14² + x²

We use the Pythagorean theorem on right triangle DCO

DO² = CD² + OC²

We see that OC = OB+BC = x+5, so

r² = 10² + (x+5)²

So we have a system of two equations:

r² = 14² + x²
r² = 10² + (x+5)²

Since both left sides equal r², set the right sides
equal to each other.

14² + x² = 10² + (x+5)²
196 + x² = 100 + x² + 10x + 25
196 = 125 + 10x
71 = 10x
7.1 = x

r² = 14² + x²
r² = 196 + (7.1)²
r² = 196 + 50.41
r² = 246.41
r = √246.41
r = 15.69745202 cm

Given

6 = 3 => Number of letters in SIX = 3

12 = 6 => Number of letters in TWELVE = 6

14 = 8 => Number of letters in FOURTEEN = 8

Similarly,

22 = 9 => Number of letters in TWENTY TWO = 9

Therefore, 22 = 9.