GATE Questions

---

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.

Q = mc∆T refers to Specific Heat formula.

When heat energy is added to a substance, the temperature will change by a certain amount.

The relationship between heat energy and temperature is different for every material, and the specific heat is a value that describes how they relate.

Q = mc∆T

Q = heat energy (Joules, J)

m = mass of a substance (kg)

c = specific heat (units J/kg∙K)

∆T = change in temperature (Kelvins, K)

Given Prabhas is twice as good a workman as Rana.

Prabhas finishes the work in 3 hrs

=> Rana finishes the work in 6 hrs.

Number of hours required together they could finish the work

= 3 x 6 / 3 + 6

= 18/9

= 2 hrs.

Abhinav Bindra is an Indian professional shooter who is the world and Olympic champion in the 10 m air rifle event.

Given in the question that, there are 7 boys and 6 girls. 

Team members = 5

Now, required number of ways in which a team of 5 having atleast 3 girls in the team = 

$$\begin{gathered} 6C3 x 7C2 + 6C4 x 7C1 + 6C5 \\ = 6x5x43x2x1 x 7x62x1 + 6x5x4x34x3x2x1 x 7 + 6x5x4x3x25x4x3x2x1 \\ = 420 + 105 + 6 \\ = 531. \end{gathered}$$

The given number series is 2, 16, 3, 81, 4, ?

2

2^4 = 16

3

3^4 = 81

4

4^4 = 256

Hence, the next number is 256.

From the given data,

11+ 11 = 4 => 1 + 1  +  1 + 1 = 4

12 + 12 = 6 => 1 + 2  + 1 + 2 = 6

13 + 1 3 = 8 => 1 + 3  + 1 + 3 = 8

Similarly,

14 + 14 = 10 => 1 + 4  +  1 + 4  = 5 + 5 = 10

Number = 271 x 96 + 0 = 26016

=> 95) 26016 (273
           25935
           --------
              81

Required number = 81.