GATE Questions

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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.

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.

A filament is a metal wire that glows when electricity is channeled into it. The filament of an electric bulb is made of Tunsten. 

Because of its high melting point and its greatest tensile strength, it makes for a good filament in light bulbs.

Ans. 
540 = 3240/6
108 = 540/5
27 = 108/4
? = 27/3, i.e. ? = 9

There are 26 English Alphabets. They are:

A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z.

Therefore, from the left end the 13th letter is M and is Consonent. And from the right end the 13th letter is N and is Consonent.

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

|-----------20--------------------|
50                           40

Difference = 20kms

Relative Speed = 50 – 40 = 10 kmph

Time = 20/10 = 2 hours.

(5m + 9w)10 = (6m + 12w)8 

=> 50m + 90w = 48w + 96 w    => 1m = 3w

5m + 9w = 5m + 3m = 8m

8 men can do the work in 10 days.

3m +3w = 3m + 1w = 4m

So, 4 men can do the work in (10 x 8)/4 = 20 days.