GATE Questions

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Given equation is  

  192.5 ×19p = 197   

Here it is in the form of am × an = am+n  

 Here m = 2.5 , n = p, m+n = 7

 => 2.5 + p = 7 

 => p = 7 - 2.5

 => p = 4.5

175760 =2³ x 2 x 5 x 13³
= 2³ x 2 x 5 x 13³

To make perfect cube, it must be divided by 2 x 5 = 10

Stack:

 - Stack is a ordered collection of items

 - Stack is a dynamic object whose size is constantly changing as items are pushed and popped .

 - Stack may contain different data types

Array:

- Array is an ordered collection of items

- Array is a static object i.e. no of item is fixed and is assigned by the declaration of the array

- It contains same data types.

Given ratio of pens and pencils = 3 :2

Number of Pens = 3x

Number of Pencils = 2x

Average number of pencils & Pens = 3x + 2x2 = 180

5x = 360

=> x = 72

Hence, the number of pencils = 2x = 72 x 2 = 144.

The relation is father and daughter. As we go with male gender, will be son of A. But it is given in the question that B is not the son of A. Hence, te only possile is B is female and B is daughter of A.

When water freezes its density decreases.

Water at ordinary temperatures contracts and increases in density as it is cooled, like most substances. But at about 4°C it reaches a maximum density and then decreases in density as it approaches the freezing point.

Given word is THERAPY.

Number of letters in the given word = 7

These 7 letters can be arranged in 7! ways.

Number of vowels in the given word = 2 (E, A)

The number of ways of arrangement in which vowels come together is 6! x 2! ways

Hence, the required number of ways can the letters of the word 'THERAPY' be arranged so that the vowels never come together = 7! - (6! x 2!) ways = 5040 - 1440 = 3600 ways.

Let 1kg of Rs. 100 then 840gm is of Rs. 84.
Now (label on can 1kg but contains 840kg ) so for customer it is of Rs. 100 and further gives 4% discount [he sells his article on 4% loss on cost price.]
So now S.P = Rs. 96
But actually it contains 840 gm so C.P for shopkeeper = Rs. 84
S.P = Rs. 96
C.P = Rs. 84
Profit% = {(S.P-C.P)/C.P}x100
{(96-84)/84} x 100 = 14.28571429% PROFIT.