GATE Questions

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Let S be the sample space.
Here n(S)= 23 = 8
Let E be the event of getting atmost two heads. Then,
n(E) = {(H,T,T), (T,H,T), (T,T,H), (H,H,T), (T,H,H), (H,T,H)}
Required probability = n(E)/n(S) = 6/8 = 3/4.

At least one black can be chosen in two ways from each box:
Now, probability of choosing at least one black ball from first box 

= 1/2 × [ (2C1× 2C1)/4C2 + 2C2/ 4C2 ]= 5/12

Probability of choosing at least one black ball from 2nd box
= 1/2 × [(4C1×12C1)/16C2 + 4C2/ 16C2] = 9/40

Final probability

= 5/12 + 9/40 = (50 + 27)/120 = 77/120

In the given series 1 4 9 16 22 36

1 = 1 x 1 

4 = 2 x 2

9 = 3 x 3

16 = 4 x 4

25 = 5 x 5 (Not 22)

36 = 6 x 6

Hence, the odd man in the series is 22.

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)

The ratio of money she lended is

24000 : 16000 = 3 : 2

Let the rate of interest be R%

8%                   R%
     

           10

3          :           2

R = 13%.

Africa is the second largest continent both by popolation and area wise. Asia being first by both popolation and area wise.

Yes, all the above given sentences have an interjection.

1. Hey ! is an interjection in the sentence , Hey!, where did I park my car? 

2. Well is an interjection in the sentence, Well!, that's a relief.

3. Oh! is an interjection in the sentence , Oh!, now I remember where i put my wallet.

In the figure, there are 21 columns containing 2 cubes each and 4 columns containing 1 cube each. 

∴Total number of cubes = (21 x 2) + (4 x 1) = 42 + 4 = 46.