2013(Gate ) Questions and Answers
After several defeats in wars, Robert Bruce went in exile and wanted to commit suicide. Just
before committing suicide, he came across a spider attempting tirelessly to have its net. Time
and again, the spider failed but that did not deter it to refrain from making attempts. Such
attempts by the spider made Bruce curious. Thus, Bruce started observing the nearimpossible
goal of the spider to have the net. Ultimately, the spider succeeded in having its
net despite several
failures. Such act of the spider encouraged Bruce not to commit suicide. And then, Bruce went
back again and won many a battle, and the rest is history.
Which one of the following assertions
is best supported by the above information?
Explanation:-
Answer: Option D. -> No adversity justifies giving up hopeExplanation:-
Answer: Option B. -> 15,180Let 'W' be the labour wages, and 'T' be the working hours.
Now, total cost is a function of `W` x `T`
Increase in wages = 20%
`:.` Revised wages = 1.2 `W`
Decrease in labour time = (`100/24`)%
`:.` Re vised time = (1 - `1/24`) `T` = `23/24` `T`
`:.` Revised Total cost = 1.2 x `23/24` `WT` = 1.15 `WT`
= 1.15 x 13200 = 15180
Explanation:-
Answer: Option B. -> 8`1/(sqrt(1) + sqrt(2))` + `1/(sqrt(2) + sqrt(3))` + `1/(sqrt(3) + sqrt(4))` +..... +`1/(sqrt(80) + sqrt(81))`
= `(sqrt(2) - sqrt(1))/((sqrt(2))^2 - (sqrt(1))^2)` + `(sqrt(3) - sqrt(2))/((sqrt(3))^2 - (sqrt(2))^2)` + `(sqrt(4) - sqrt(3))/((sqrt(4))^2 - (sqrt(3))^2)` +..... + `(sqrt(81) - sqrt(80))/((sqrt(81))^2 - (sqrt(80))^2)`
= `sqrt(81)` - `sqrt(1)` = 8
Explanation:-
Answer: Option C. -> 24Let the total distance covered be 'D'
Now, average speed = `D/(Total time taken)`
= `D/(D/2/60 + D/4/30 + D/4/10)` = `1/(1/120 + 1/120 + 1/40)` =`(120)/5` = 24 km /hr
Explanation:-
Answer: Option D. -> 77/90The number of 2 digit multiples of 7 = 13
`:.` Probability of choosing a number
Not divisible by 7= `(90 - 13)/90` = `77/90`