GATE Questions

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Suppose that the original price of the car = Rs. x 

Then new price of the car

=> (x) + (x ×25/100) = Rs. 5x/4 

To restore the original price, the new price must be decreased by

5x/4 − x = x/4

So required percentage =(x/4)/(5x/4) × 100%

= 20%

Carbon dioxide is present under pressure in soft drinks.

Lithium is the lightest of all the metals due to its low atomic number among metals. It is the lightest solid element.

Properties ::

* It is a soft silvery-white alkali metal.

* Lithium is highly reactive and flammable and is stored in mineral oil.

These two events cannot be disjoint because P(K) + P(L) > 1.

P(AꓴB) = P(A) + P(B) - P(AꓵB).

An event is disjoint if P(A ꓵ B) = 0. If K and L are disjoint P(K ꓴ L) = 0.8 + 0.6 = 1.4

And Since probability cannot be greater than 1, these two mentioned events cannot be disjoint.

The first indicator of an approaching thunderstorm is a buildup of dark clouds.

A thunderstorm is a storm with lightning and thunder; it is usually produced by heavy rain, gusty wind, and the cumulonimbus cloud. The thunderstorm is made up of moisture, unstable air and lift.

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.

Given, Manideep purchases 30kg of barley at the rate of 11.50/kg nad 20kg at the rate of 14.25/kg.

Total cost of the mixture of barley = (30 x 11.50) + (20 x 14.25)

=> Total cost of the mixture = Rs. 630

Total kgs of the mixture = 30 + 20 = 50kg

Cost of mixture/kg = 630/50 = 12.6/kg

To make 30% of profit

=> Selling price for manideep = 12.6 + 30% x 12.6

=> Selling price for manideep = 12.6 + 3.78 = 16.38/kg.

Total number of possible ways = 9C3 = 84 ways

Required atleast one girl in the group of three = total possible ways - ways in which none is girl

None of the members in the group is girl = 6C3 = 20

Therefore, number of ways that at least one member is a girl in the group of three

= 84 - 20

= 64 ways.