GATE Questions

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Let the two numbers be x and y

Given x : y = 3 : 7 .....(1)

Now, x+6 : y+6 = 5 : 9 .....(2)

From (1), x = 3y/7

From (2), 5y - 9x = 24

=> 5y - 9(3y/7) = 24

=> y = 21

=> From(1), x = 9

Hence, the two numbers be 9 and 21

It is Blackboard or Chalkboard which is Black when clean, and as you write on it with white chalk it becomes dirty in White color.

Given that Rs. 1860 will become Rs. 2641.20 at 12%

=> Simple Interest = 2641.20 - 1860 = Rs. 781.20

We know I = PTR/100

=> 781.20 x 100 = 1860 x T x 12

=> T = 78120/1860x12

=> T = 78120/22320

=> T = 3.5 years.

Let the speed of the boat upstream be p kmph and that of downstream be q kmph

Time for upstream = 8 hrs 48 min = 845hrs

Time for downstream = 4 hrs

Distance in both the cases is same.

=> p x  845= q x 4

=> 44p/5 = 4q

=> q = 11p/5

 Now, the required ratio of Speed of boat : Speed of water current

= q+p2:q-p2

=> (11p/5 + p)/2  : (11p/5 - p)/2

=> 8 : 3

Helium has the highest First Ionization Energy in the Noble Gases group.

Ionization Energy ::

Ionisation energy is the energy required to remove one mole of electrons from one mole of gaseous atoms. Atoms are more stable when they have full valence shells.

Noble Gases have a very stable electron configuration, therefore, they have the highest amount of ionization energy within their periods. It decreases down a family because electrons farther from the nucleus are easier to remove.

Ionization Energy levels of Noble Gases group in Descending Order :: He, Ne, Ar, Kr, Xe, Rn

The light from the sun takes about 8 minutes to reach the Earth after it has been emitted from the sun's surface.

The time it takes for light to reach planets in our Solar System varies from about 3 minutes for Mercury to about 5.3 hours for Pluto.

Let Karan’s present age be x years and Shiva’s present age be y years.
Then, according to the first condition,
x - 10 = 3(y - 10) or x - 3y = - 20 ..(1)
Now, Karan’s age after 10 years = (x + 10) years
Shiva’s age after 10 years = (y + 10)
(x + 10) = 2 (y + 10) or x - 2y = 10 ..(2)
Solving (1) and (2), we get x = 70 and y = 30
Karan’s age = 70 years and Shiva’s age = 30 years.

O should be immediately followed by M ie, the order OM should be followed. N should be immediately followed by L ie, the order NL should be followed. One play is staged between k and L and N or O should not be the first or last play. So, the order is

Monday             K

Tuesday            N

Wednesday        L

Thursday           O

Friday               M