GATE Questions

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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

Diamond is the hardest substance available on Earth.

Diamond is the hardest substance available on Earth due to the giant molecular structure of diamond in which each carbon atom is covalently bonded to four other carbon atoms. A covalent bond is very strong and requires a large amount of energy to break itself, and diamond has many covalent bonds.

Qualm means feeling confused, uneasiness, very doubtful and being in worry.

Hence, among the given options, Qualm is the opposite of Confidence.

In each row, 

Sum of 1st two digit number + last two digit number = Middle two digit number

i.e., 1st row 15 + 40 = 55

2nd row 46 + 47 = 93

Similarly, 7x + 16 = 87 => x = 1.

What has Hands But cannot Clap is a Clock or a Watch.

A Clock technically has 3 hands.

1 Hour Hand Which tells Hours

1 Minute Hand Which tells Minutes

1 Second Hand Which tells Seconds.

But cannot clap with these hands.

Given A,B,C can complete a work in 15,20 and 30 respectively.

The total work is given by the LCM of 15, 20, 30 i.e, 60.

A's 1 day work = 60/15 = 4 units

B's 1 day work = 60/20 = 3 units

C's 1 day work = 60/30 = 2 units

(A + B + C) worked for 2 days = (4 + 3 + 2) 2 = 18 units

 Let B + C worked for x days = (3 + 2) x = 5x units

C worked for 2 days = 2 x 2 = 4 units

Then, 18 + 5x + 4 = 60

22 + 5x = 60

5x = 38

x = 7.6

Therefore, total number of days taken to complete the work = 2 + 7.6 + 2 = 11.6 = 11 3/5 days.

Let the speed of the train be 'S' kmph

From the given data,

Distance = Length of train = D = 200 mts = 200 x 18/5 kms

Time = 10 sec

given speed of the motorcycler = 12 kmph

Relative speed as they are moving in the same direction = (S - 12) kmph

$$\begin{gathered} (S- 12) = 200 x 18515 \\ S - 12 = 48 \\ S = 60 kmph \\ \end{gathered}$$

Hence, the speed of the train = S = 60 kmph

Now,

Let the speed of the jeep be 'x' kmph

$$\begin{gathered} 60 - x = 200 x 18520 \\ 60 - x = 36 \\ x = 60 - 36 \\ x = 24 kmph \end{gathered}$$

Therefore, the speed of the jeep = x = 24 kmph.