GATE Questions

---

let speed of boat= X, speed of stream= Y
Upstream speed= X-Y
Downstream speed= X+Y
Sum of upstream & downstream= (X-Y) +(X+Y)= 2X
So, 2X= 40
X= 20 km/hr
Speed of boat : speed of stream= 600+100 :100= 7:1
So speed of Stream= 20/7 km/hr
ATQ, D/( X-Y) + D/( X+Y) = 5
D/(120/7) + D/(160/7)= 5
D= 480×5/49= 48.97 km= 50 Km(approx)

Let the present ages of the mother and daughter be 2x and x years respectively.
Then, (2x - 18) = 3(x - 18) => x = 36
Required sum = (2x + x) = 108 years.

Class can have a public method for specific data type conversions.
for example:
class B
{
double value;
public  B(int i )
operator double()
{
return value;
}
};
B BObject;
double i = BObject; // assigning object to variable i of type double.
now conversion operator gets called to assign the value.

Time taken to cover 600 km = 600/100 = 6 hrs.

Number of stoppages = 600/75 - 1 = 7

Total time of stoppages = 4 x 7 = 28 min

Hence, total time taken = 6 hrs 28 min.

Udaipur, a city in the state of Rajasthan which was named after the Maharana Udai Singh - II, is known for its beautiful artificial lakes around the city and lavish royal residences.

Thus, Udaipur nickname is City of Lakes in India.

Total number of possible ways = 

9C5 = 9 x 8 x 7 x 6 x 55 x 4 x 3 x 2 x 1 = 126

Number of favorable cases = 

$$\begin{gathered} 4C2 x 5C3 + 4C3 x 5C2 + 4C4 x 5C1 \\ 4 x 32 x 1 x 5 x 4 x 33 x 2 x 1 + 4 x 3 x 23 x 2 x 1 x 5 x 4 2 x 1 + 1 x 5 \\ = 6 x 10 + 4 x 10 + 5 \\ = 60 + 40 + 5 \\ = 105 \end{gathered}$$

Therefore, required probability = 105/126 = 5/6

The number of letters in the given word CREATIVITY = 10

Here T & I letters are repeated

=> Number of Words that can be formed from CREATIVITY = 10!/2!x2! = 3628800/4 = 907200

From the given series of numbers, if half of the second highest number is subtracted from the third highest number, what will be the value ?

Now arranging the given numbers in descending order.
837 746 519 495 328

519 - 746/2 = 519 - 373 = 146.