GATE Questions

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Given Word is PROMISE.

Number of letters in the word PROMISE = 7

Number of ways 7 letters can be arranged = 7! ways

Number of Vowels in word PROMISE = 3 (O, I, E)

Number of ways the vowels can be arranged that 3 Vowels come together = 5! x 3! ways

Now, the number of ways of arrangements so that three vowels should not come together

= 7! - (5! x 3!) ways = 5040 - 720 = 4320.

From the given data,

let the initial quantity of the mixture = 5x

Then,

$$\begin{gathered} 2x - 163x - 24 + 40 = 14 \\ 8x - 64 = 3x + 16 \\ 5x = 80 \\ x = 16 lit \end{gathered}$$

Then the initial quantity of the mixture = 5x = 5 x 16 = 80 lit.

Let the speed of the faster train be 'S' kmph

Then speed of the slower train will be '(S-5)' kmph

Time taken by faster train = 350/S hrs

Time taken by slower train = 350/(S-5) hrs

 350s-5 - 350s = 2 hrs 20 min = 213 = 73

=> S = 30 km/hr.

1/3 ---- 8

1 -------?
Hari can do total work in = 24 days

As satya is 60% efficient as Hari, then

Satya = 1/24 x 60/100 = 1/40

=> Satya can do total work in 40 days

1 ----- 40

2/3 ---- ? => 26 2/3 days.

Given sum of present ages of A, B, C & D

A + B + C + D = 176

and also given that,

(A-4) : (B-4) : (C-4) : (D-4) = 11 : 9 : 6 : 14

Let the ratio = x

=> A-4 + B-4 + C-4 + D-4 = 11x + 9x + 6x + 14x

=> (A + B + C + D ) - 16 = 40x

=> 176 - 16 = 40x

=> x = 4

=> A = 44 + 4 = 48

=> B = 40

=> C = 28

=> D = 60

Therefore, from the above conclusions

D is eldest with 60 years and C is youngest with 28 years of ages.

Alloy of copper and zinc is called as Brass.

Total money decided to contribute = 750 x 12 = 9000

Let 'b' boys dropped

The rest paid 150/- more

=> (12 - b) x 900 = 9000

=> b = 2

Hence, the number of boys who dropped out is 2.

Jatindra Nath Das, also known as Jatin Das, was a revolutionary and Independence activist. He embraced death in Lahore jail after fasting for 64 days in 1929 at the age of 24 yrs.