GATE Questions

---

Given speed of jogger = 9 kmph
Speed of train = 45 kmph
As they are in same direction,
Relative speed = 45 - 9 = 36 kmph = 36x5/18 = 10 m/s
Distance = 240 + 120 = 360 mts
Time = distance/speed = 360/10 = 36 sec.

Let the price of 1 litre of diesel be Rs.x and let Karthik initially buy 'y' litres of diesel.
Therefore, he would have spent Rs. xy on diesel.

When the price of diesel increases by 25%, the new price per litre of diesel is 1.25x.

Karthik intends to increase the amount he spends on diesel by 15%.
i.e., he is willing to spend xy + 15% of xy = 1.15xy

Let the new quantity of diesel that he can get be 'q'.
Then, 1.25x x q = 1.15xy
Or q = (1.15/1.25)y = 0.92y.

As the new quantity that he can buy is 0.92y, he gets 0.08y lesser than what he used to get earlier.

Or a reduction of 8%.

Let a, b and c be the amounts invested in schemes X, Y and Z respectively. Then,

As we know:

Simple interest (S.I.) = PTR/100

(a × 10 × 1/100) + (b × 12 × 1/100) + (c × 15 × 1/100) = 3200

= 10a + 12b + 15c = 320000 .........(1)

Now, c = 240% of b = 12b/5 .........(2)

And, c = 150% of a = 3a/2 => a = 2/3 c = (2 × 12)b/(3 × 5) = 8b/5 .......(3)

From (1), (2) and (3), we have

16b + 12b + 36b = 320000 => 64b = 320000 => b = 5000

∴ Sum invested in Scheme Y = Rs.5000.

Let the Efficiency of pavan be E(P)

Let the Efficiency of sravan be E(S)

Here Work W = LCM(25,20) = 100

Now, E(P+2S) = 100/25 = 4 ....(1)

E(2P+S) = 100/20 = 5 ....(2)

Hence, from (1) & (2) we get

E(S) = 1

=> Number of days Savan alone work to complete the work  = 100/1 = 100 days.

A+7B=112

it is clear that A = 14, then it becomes A>=B, but A is smallest angle) given
so, range of A is 0.0001 to 13.9999 ( I am taking upto 4 decimal places)
so, range of B becomes 14 to 16 ( after rounding off to 4 decimal places)
so, range of C becomes 152 to 164 ( after rounding off to 4 decimal places)

P( only one of them will be selected) = p[(E and not F) or (F and not E)] 

 = PE∩F∪F∩E 

= PEPF+PFPE

 =17×45+15×67=27

We know that each successive IE is greater than the previous one, because each ionization process removes one electron and hence increases the total attractive force on the remaining electrons from the nucleus. Hence, C3+ (g) → C4+ (g) + e- needs more energy.

Speed = 108 km/hr
enter a tunnel,, means that the train covers a distance equal to its own length
so (108 x 5/18) = x/4 where x= length of train
hence x = 120 mtrs
to pass completely train has to travel a distance = (x + tunnel length) that is 1120 mtrs.
so (1120/t) = (108x5/18)
t = 37.33 sec